180:
4853:: the buoyancy force produced by a float in a homogeneous liquid is equal to the weight of the liquid that is displaced by the float. Since buoyancy force is linear with respect to the density of the liquid within which the float is submerged, the measure of the buoyancy force yields a measure of the density of the liquid. One commercially available unit claims the instrument is capable of measuring relative density with an accuracy of ± 0.005 RD units. The submersible probe head contains a mathematically characterized spring-float system. When the head is immersed vertically in the liquid, the float moves vertically and the position of the float controls the position of a permanent magnet whose displacement is sensed by a concentric array of Hall-effect linear displacement sensors. The output signals of the sensors are mixed in a dedicated electronics module that provides a single output voltage whose magnitude is a direct linear measure of the quantity to be measured.
2637:
3721:, the gas-based manifestation of a pycnometer, compares the change in pressure caused by a measured change in a closed volume containing a reference (usually a steel sphere of known volume) with the change in pressure caused by the sample under the same conditions. The difference in change of pressure represents the volume of the sample as compared to the reference sphere, and is usually used for solid particulates that may dissolve in the liquid medium of the pycnometer design described above, or for porous materials into which the liquid would not fully penetrate.
2310:
1562:
4643:
2632:{\displaystyle RD={\frac {\rho _{\mathrm {object} }}{\rho _{\mathrm {ref} }}}={\frac {\frac {{\text{Deflection}}_{\mathrm {Obj.} }}{{\text{Displacement}}_{\mathrm {Obj.} }}}{\frac {{\text{Deflection}}_{\mathrm {Ref.} }}{{\text{Displacement}}_{\mathrm {Ref.} }}}}={\frac {\frac {3\ \mathrm {in} }{20\ \mathrm {mm} }}{\frac {5\ \mathrm {in} }{34\ \mathrm {mm} }}}={\frac {3\ \mathrm {in} \times 34\ \mathrm {mm} }{5\ \mathrm {in} \times 20\ \mathrm {mm} }}=1.02.}
7445:
1278:
4418:
252:). Where it is not, it is more usual to specify the density directly. Temperatures for both sample and reference vary from industry to industry. In British brewing practice, the specific gravity, as specified above, is multiplied by 1000. Specific gravity is commonly used in industry as a simple means of obtaining information about the concentration of solutions of various materials such as
3623:
3615:
4820:: This technology relies upon Pascal's Principle which states that the pressure difference between two points within a vertical column of fluid is dependent upon the vertical distance between the two points, the density of the fluid and the gravitational force. This technology is often used for tank gauging applications as a convenient means of liquid level and density measure.
4364:
2303:
2787:
readings gives the weight of the displaced water. The relative density result is the dry sample weight divided by that of the displaced water. This method allows the use of scales which cannot handle a suspended sample. A sample less dense than water can also be handled, but it has to be held down, and the error introduced by the fixing material must be considered.
4826:: This type of instrument requires a vibrating element to be placed in contact with the fluid of interest. The resonant frequency of the element is measured and is related to the density of the fluid by a characterization that is dependent upon the design of the element. In modern laboratories precise measurements of relative density are made using
2117:, which lists sucrose concentration by mass against true RD, were originally (20 °C/4 °C) that is based on measurements of the density of sucrose solutions made at laboratory temperature (20 °C) but referenced to the density of water at 4 °C which is very close to the temperature at which water has its maximum density of
5751:
1975:
variations caused by changing weather patterns) but as relative density usually refers to highly incompressible aqueous solutions or other incompressible substances (such as petroleum products) variations in density caused by pressure are usually neglected at least where apparent relative density is being measured. For true (
1557:{\displaystyle SG_{\mathrm {true} }={\frac {\rho _{\mathrm {sample} }}{\rho _{\mathrm {H_{2}O} }}}={\frac {\frac {m_{\mathrm {sample} }}{V}}{\frac {m_{\mathrm {H_{2}O} }}{V}}}={\frac {m_{\mathrm {sample} }}{m_{\mathrm {H_{2}O} }}}{\frac {g}{g}}={\frac {W_{\mathrm {V} ,{\text{sample}}}}{W_{\mathrm {V} ,\mathrm {H_{2}O} }}},}
4638:{\displaystyle RD_{\mathrm {A} }={{\rho _{\mathrm {s} } \over \rho _{\mathrm {w} }}-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }} \over 1-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }}}={RD_{\mathrm {V} }-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }} \over 1-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }}}.}
4002:
4180:
2167:
4830:
meters. These are capable of measurement to 5 to 6 places beyond the decimal point and are used in the brewing, distilling, pharmaceutical, petroleum and other industries. The instruments measure the actual mass of fluid contained in a fixed volume at temperatures between 0 and 80 °C but as they
1693:
The density of water and of the sample varies with temperature and pressure, so it is necessary to specify the temperatures and pressures at which the densities or weights were determined. Measurements are nearly always made at 1 nominal atmosphere (101.325 kPa ± variations from changing weather
885:
effects, sink in it. Those with an SG less than 1 are less dense than water and will float on it. In scientific work, the relationship of mass to volume is usually expressed directly in terms of the density (mass per unit volume) of the substance under study. It is in industry where specific gravity
3713:
of a powder, to which the usual method of weighing cannot be applied, can also be determined with a pycnometer. The powder is added to the pycnometer, which is then weighed, giving the weight of the powder sample. The pycnometer is then filled with a liquid of known density, in which the powder is
2147:
Relative density can be calculated directly by measuring the density of a sample and dividing it by the (known) density of the reference substance. The density of the sample is simply its mass divided by its volume. Although mass is easy to measure, the volume of an irregularly shaped sample can be
2138:
table in use today in North
America, while it is derived from the original Plato table is for apparent relative density measurements at (20 °C/20 °C) on the IPTS-68 scale where the density of water is 0.9982071 g/cm. In the sugar, soft drink, honey, fruit juice and related industries
1726:
the temperature at which the reference (water) density is specified. For example, SG (20 °C/4 °C) would be understood to mean that the density of the sample was determined at 20 °C and of the water at 4 °C. Taking into account different sample and reference temperatures, we note
4760:
Since the density of dry air at 101.325 kPa at 20 °C is 0.001205 g/cm and that of water is 0.998203 g/cm we see that the difference between true and apparent relative densities for a substance with relative density (20 °C/20 °C) of about 1.100 would be 0.000120. Where
2112:
As the principal use of relative density measurements in industry is determination of the concentrations of substances in aqueous solutions and these are found in tables of RD vs concentration it is extremely important that the analyst enter the table with the correct form of relative density. For
2007:
the temperature at which the reference (water) density is specified. For example, SG (20 °C/4 °C) would be understood to mean that the density of the sample was determined at 20 °C and of the water at 4 °C. Taking into account different sample and reference temperatures we note
5087:
Specific gravity (SG) is a useful concept but has several limitations. One major issue is its sensitivity to temperature since the density of both the substance being measured and the reference changes with temperature, affecting accuracy. It also assumes materials are incompressible, which isn't
2786:
Another practical method uses three measurements. The sample is weighed dry. Then a container filled to the brim with water is weighed, and weighed again with the sample immersed, after the displaced water has overflowed and been removed. Subtracting the last reading from the sum of the first two
1816:
lists sucrose concentration by weight against true SG, and was originally (20 °C/4 °C) i.e. based on measurements of the density of sucrose solutions made at laboratory temperature (20 °C) but referenced to the density of water at 4 °C which is very close to the temperature at
240:
If a substance's relative density is less than 1 then it is less dense than the reference; if greater than 1 then it is denser than the reference. If the relative density is exactly 1 then the densities are equal; that is, equal volumes of the two substances have the same mass. If the reference
1811:
As the principal use of specific gravity measurements in industry is determination of the concentrations of substances in aqueous solutions and as these are found in tables of SG versus concentration, it is extremely important that the analyst enter the table with the correct form of specific
1974:
The density of substances varies with temperature and pressure so that it is necessary to specify the temperatures and pressures at which the densities or masses were determined. It is nearly always the case that measurements are made at nominally 1 atmosphere (101.325 kPa ignoring the
1694:
patterns), but as specific gravity usually refers to highly incompressible aqueous solutions or other incompressible substances (such as petroleum products), variations in density caused by pressure are usually neglected at least where apparent specific gravity is being measured. For true (
3864:
must be subtracted. The bottle is filled with air but as that air displaces an equal amount of air the weight of that air is canceled by the weight of the air displaced. Now we fill the bottle with the reference fluid e.g. pure water. The force exerted on the pan of the balance becomes:
840:
2044:
scale and the densities used here and in the rest of this article are based on that scale. On the previous IPTS-68 scale the densities at 20 °C and 4 °C are, respectively, 0.9982041 and 0.9999720 resulting in an RD (20 °C/4 °C) value for water of 0.99823205.
3829:
4756:
3305:
2646:
Relative density is more easily and perhaps more accurately measured without measuring volume. Using a spring scale, the sample is weighed first in air and then in water. Relative density (with respect to water) can then be calculated using the following formula:
3868:
1186:
5001:
241:
material is water, then a substance with a relative density (or specific gravity) less than 1 will float in water. For example, an ice cube, with a relative density of about 0.91, will float. A substance with a relative density greater than 1 will sink.
2825:
The application of simple physical principles allows the relative density of the unknown liquid to be calculated from the change in displacement. (In practice the stalk of the hydrometer is pre-marked with graduations to facilitate this measurement.)
5407:
3464:
2139:
sucrose concentration by mass is taken from this work which uses SG (17.5 °C/17.5 °C). As a final example, the
British RD units are based on reference and sample temperatures of 60 °F and are thus (15.56 °C/15.56 °C).
987:
437:
4843:: Radiation is passed from a source, through the fluid of interest, and into a scintillation detector, or counter. As the fluid density increases, the detected radiation "counts" will decrease. The source is typically the radioactive isotope
172:
179:
3598:
4837:: Ultrasonic waves are passed from a source, through the fluid of interest, and into a detector which measures the acoustic spectroscopy of the waves. Fluid properties such as density and viscosity can be inferred from the spectrum.
4359:{\displaystyle SG_{\mathrm {A} }={\frac {gV(\rho _{\mathrm {s} }-\rho _{\mathrm {a} })}{gV(\rho _{\mathrm {w} }-\rho _{\mathrm {a} })}}={\frac {\rho _{\mathrm {s} }-\rho _{\mathrm {a} }}{\rho _{\mathrm {w} }-\rho _{\mathrm {a} }}}.}
2743:
2298:{\displaystyle \rho ={\frac {\text{Mass}}{\text{Volume}}}={\frac {{\text{Deflection}}\times {\frac {\text{Spring Constant}}{\text{Gravity}}}}{{\text{Displacement}}_{\mathrm {WaterLine} }\times {\text{Area}}_{\mathrm {Cylinder} }}}.}
729:
4847:, with a half-life of about 30 years. A key advantage for this technology is that the instrument is not required to be in contact with the fluid—typically the source and detector are mounted on the outside of tanks or piping.
5088:
true for gasses or some liquids under varying pressures. It doesn't provide detailed information about a material’s composition or properties beyond density. Errors can also occur due to impurities, incomplete mixing, or air
4168:
4084:
1951:
3731:
5425:
normally has a specific gravity between 1.003 and 1.030. The Urine
Specific Gravity diagnostic test is used to evaluate renal concentration ability for assessment of the urinary system. Low concentration may indicate
2822:, is noted. In the example depicted, the hydrometer has dropped slightly in the green liquid; hence its density is lower than that of the reference liquid. It is necessary that the hydrometer floats in both liquids.
2156:
of the water may keep a significant amount of water from overflowing, which is especially problematic for small samples. For this reason it is desirable to use a water container with as small a mouth as possible.
4650:
3185:
2802:
1078:
1848:
table in use today in North
America for apparent specific gravity measurements at (20 °C/20 °C) is derived from the original Plato table using Plato et al.‘s value for SG(20 °C/4 °C) =
4890:
a measure of the current void ratio in relation to the maximum and minimum void rations, and applied effective stress control the mechanical behavior of cohesionless soil. Relative density is defined by
4894:
5627:"Density, Thermal Expansivity, and Compressibility of Liquid Water from 0 to 150°C: Correlations and Tables for Atmospheric Pressure and Saturation Reviewed and Expressed on 1968 Temperature Scale"
3147:
5057:
1270:
2073:
where the superscript indicates the temperature at which the density of the material is measured, and the subscript indicates the temperature of the reference substance to which it is compared.
681:
5296:
1688:
1645:
1860:, which uses SG (17.5 °C/17.5 °C). As a final example, the British SG units are based on reference and sample temperatures of 60 °F and are thus (15.56 °C/15.56 °C).
566:
513:
3360:
2989:
892:
333:
4090:
indicated that this force is net of the force of the empty bottle. The bottle is now emptied, thoroughly dried and refilled with the sample. The force, net of the empty bottle, is now:
3043:
1070:
1031:
3694:
through it, so that air bubbles may escape from the apparatus. This device enables a liquid's density to be measured accurately by reference to an appropriate working fluid, such as
3482:
This equation allows the relative density to be calculated from the change in displacement, the known density of the reference liquid, and the known properties of the hydrometer. If Δ
2808:
The relative density of a liquid can be measured using a hydrometer. This consists of a bulb attached to a stalk of constant cross-sectional area, as shown in the adjacent diagram.
3503:
1221:
3997:{\displaystyle F_{\mathrm {w} }=g\left(m_{\mathrm {b} }-\rho _{\mathrm {a} }{\frac {m_{\mathrm {b} }}{\rho _{\mathrm {b} }}}+V\rho _{\mathrm {w} }-V\rho _{\mathrm {a} }\right).}
4888:
2650:
3860:
is the density of the material of which the bottle is made (usually glass) so that the second term is the mass of air displaced by the glass of the bottle whose weight, by
4376:(the stem displaces air). Note that the result does not depend on the calibration of the balance. The only requirement on it is that it read linearly with force. Nor does
2916:, the downward gravitational force acting upon it must exactly balance the upward buoyancy force. The gravitational force acting on the hydrometer is simply its weight,
1787:
scale and the densities used here and in the rest of this article are based on that scale. On the previous IPTS-68 scale, the densities at 20 °C and 4 °C are
80:
7375:
4093:
4009:
3709:
If the flask is weighed empty, full of water, and full of a liquid whose relative density is desired, the relative density of the liquid can easily be calculated. The
726:
at a temperature of 20 °C and a pressure of 101.325 kPa absolute, which has a density of 1.205 kg/m. Relative density with respect to air can be obtained by
217:(mass of a unit volume) of a substance to the density of a given reference material. Specific gravity for solids and liquids is nearly always measured with respect to
2927:
principle, the buoyancy force acting on the hydrometer is equal to the weight of liquid displaced. This weight is equal to the mass of liquid displaced multiplied by
1866:
586:
4831:
are microprocessor based can calculate apparent or true relative density and contain tables relating these to the strengths of common acids, sugar solutions, etc.
6026:
5876:
460:
324:
301:
5077:
860:
2152:
and read off how much water it displaces. Alternatively the container can be filled to the brim, the sample immersed, and the volume of overflow measured. The
1955:
Occasionally a reference substance other than water is specified (for example, air), in which case specific gravity means density relative to that reference.
719:, which makes relative density calculations particularly convenient: the density of the object only needs to be divided by 1000 or 1, depending on the units.
7255:
7234:
5805:
874:. Ideal behaviour is usually only seen at very low pressure. For example, one mol of an ideal gas occupies 22.414 L at 0 °C and 1 atmosphere whereas
5581:
Hough, J.S., Briggs, D.E., Stevens, R and Young, T.W. Malting and
Brewing Science, Vol. II Hopped Wort and Beer, Chapman and Hall, London, 1997, p. 881
7344:
5601:
Bettin, H.; Spieweck, F. (1990). "Die Dichte des
Wassers als Funktion der Temperatur nach Einführung des Internationalen Temperaturskala von 1990".
2109:. Water is preferred as the reference because measurements are then easy to carry out in the field (see below for examples of measurement methods).
2898:
is here taken to be negative if the displacement line rises on the stalk of the hydrometer, and positive if it falls. In the example depicted, Δ
835:{\displaystyle {\mathit {RD}}={\frac {\rho _{\mathrm {gas} }}{\rho _{\mathrm {air} }}}\approx {\frac {M_{\mathrm {gas} }}{M_{\mathrm {air} }}},}
6870:
4372:, denoted by subscript A, because it is what we would obtain if we took the ratio of net weighings in air from an analytical balance or used a
5963:
5852:
3087:
2135:
1845:
1856:. In the sugar, soft drink, honey, fruit juice and related industries, sucrose concentration by weight is taken from a table prepared by
6019:
5286:
Substances with a relative density of 1 are neutrally buoyant, those with RD greater than one are denser than water, and so (ignoring
2815:(the level of the liquid on the stalk) is marked (blue line). The reference could be any liquid, but in practice it is usually water.
4006:
If we subtract the force measured on the empty bottle from this (or tare the balance before making the water measurement) we obtain.
3824:{\displaystyle F_{\mathrm {b} }=g\left(m_{\mathrm {b} }-\rho _{\mathrm {a} }{\frac {m_{\mathrm {b} }}{\rho _{\mathrm {b} }}}\right),}
7474:
6931:
5998:
5982:
5586:
5544:
4761:
the relative density of the sample is close to that of water (for example dilute ethanol solutions) the correction is even smaller.
3710:
6908:
2944:
3714:
completely insoluble. The weight of the displaced liquid can then be determined, and hence the relative density of the powder.
3001:
7361:
3061:
Exactly the same equation applies when the hydrometer is floating in the liquid being measured, except that the new volume is
2089:
or gas, or determine the density of an unknown substance from the known density of another. Relative density is often used by
7420:
2307:
When these densities are divided, references to the spring constant, gravity and cross-sectional area simply cancel, leaving
5006:
4751:{\displaystyle RD_{\mathrm {V} }=RD_{\mathrm {A} }-{\rho _{\mathrm {a} } \over \rho _{\mathrm {w} }}(RD_{\mathrm {A} }-1).}
7368:
7199:
7088:
6429:
6012:
5658:
ASBC Methods of
Analysis Preface to Table 1: Extract in Wort and Beer, American Society of Brewing Chemists, St Paul, 2009
3650:
3300:{\displaystyle RD_{\mathrm {new/ref} }={\frac {\rho _{\mathrm {new} }}{\rho _{\mathrm {ref} }}}={\frac {V}{V-A\Delta x}}.}
1841:
1698:) specific gravity calculations, air pressure must be considered (see below). Temperatures are specified by the notation (
1226:
700:
5843:
Lewis, Sharon Mantik; Dirksen, Shannon Ruff; Heitkemper, Margaret M.; Bucher, Linda; Harding, Mariann (5 December 2013).
1979:) relative density calculations air pressure must be considered (see below). Temperatures are specified by the notation (
598:
6903:
1181:{\displaystyle SG_{\mathrm {apparent} }={\frac {W_{\mathrm {A} ,{\text{sample}}}}{W_{\mathrm {A} ,\mathrm {H_{2}O} }}},}
187:
1650:
1602:
2776:
This technique cannot easily be used to measure relative densities less than one, because the sample will then float.
6979:
6948:
6860:
3843:
4996:{\displaystyle D_{\mathrm {R} }={\frac {e_{\mathrm {max} }-e}{e_{\mathrm {max} }-e_{\mathrm {min} }}}\times 100\%}
1863:
Given the specific gravity of a substance, its actual density can be calculated by rearranging the above formula:
518:
465:
7103:
6434:
870:
of the gas and 1 mol of air occupy the same volume at a given temperature and pressure, i.e., they are both
6505:
5822:
4393:, the true relative density (the subscript V is used because this is often referred to as the relative density
1036:
992:
35:
6108:
5290:
effects) will sink in it, and those with an RD of less than one are less dense than water, and so will float.
3861:
1075:
The apparent specific gravity is simply the ratio of the weights of equal volumes of sample and water in air:
244:
Temperature and pressure must be specified for both the sample and the reference. Pressure is nearly always 1
5776:
2818:
The hydrometer is then floated in a liquid of unknown density (shown in green). The change in displacement, Δ
6938:
6855:
6319:
3487:
699:(or, more precisely, 3.98 °C, which is the temperature at which water reaches its maximum density). In
5801:
5402:{\displaystyle RD_{\mathrm {H_{2}O} }={\frac {\rho _{\mathrm {Material} }}{\rho _{\mathrm {H_{2}O} }}}=RD,}
1191:
7384:
6541:
6289:
6258:
3641:
327:
206:
7469:
7410:
6531:
6409:
6121:
4647:
In the usual case we will have measured weights and want the true relative density. This is found from
2894:
is the change in displacement. In accordance with the way in which hydrometers are usually graduated, Δ
4864:
6827:
6487:
6329:
2812:
3459:{\displaystyle RD_{\mathrm {new/ref} }={\frac {1}{1-{\frac {A\Delta x}{m}}\rho _{\mathrm {ref} }}}.}
2048:
The temperatures of the two materials may be explicitly stated in the density symbols; for example:
982:{\displaystyle SG_{\mathrm {true} }={\frac {\rho _{\mathrm {sample} }}{\rho _{\mathrm {H_{2}O} }}},}
432:{\displaystyle {\mathit {RD}}={\frac {\rho _{\mathrm {substance} }}{\rho _{\mathrm {reference} }}},}
7430:
7415:
6515:
6324:
6239:
6176:
3662:
167:{\displaystyle SG_{\mathrm {true} }={\frac {\rho _{\mathrm {sample} }}{\rho _{\mathrm {H_{2}O} }}}}
7395:
7042:
7025:
6964:
6865:
6789:
6725:
6720:
6638:
6459:
5870:
5427:
4827:
4765:
3703:
3684:
2913:
2149:
184:
2884:
5915:
7310:
7300:
7108:
7098:
6875:
6679:
6669:
6664:
6510:
6424:
6419:
6171:
5978:
5959:
5858:
5848:
5704:
5582:
5540:
5539:. Wiley, John & Sons, Incorporated. pp. 111, 142, 144, 147, 109, 155, 157, 160, 175.
5517:
5242:
3699:
3593:{\displaystyle RD_{\mathrm {new/ref} }\approx 1+{\frac {A\Delta x}{m}}\rho _{\mathrm {ref} }.}
245:
5891:
5561:
6648:
6613:
6603:
6595:
6570:
6554:
6464:
6371:
6274:
6166:
5730:
5683:
DIN51 757 (04.1994): Testing of mineral oils and related materials; determination of density
5638:
5603:
5534:
5252:
5089:
3491:
716:
222:
571:
7479:
7449:
7325:
7052:
6918:
6700:
6674:
6449:
6344:
5476:
5287:
4795:
2783:
becomes a negative quantity, representing the force needed to keep the sample underwater.
2153:
2040:= 0.9982288 (20 °C/4 °C). Here temperature is being specified using the current
882:
31:
4780:, pear shaped, with perforated stopper, adjusted, capacity 1, 2, 5, 10, 25, 50 and 100 mL
3606:, changes in displacement are approximately proportional to changes in relative density.
2738:{\displaystyle RD={\frac {W_{\mathrm {air} }}{W_{\mathrm {air} }-W_{\mathrm {water} }}},}
3724:
When a pycnometer is filled to a specific, but not necessarily accurately known volume,
442:
306:
283:
7405:
7320:
7270:
7160:
7134:
7078:
7035:
7030:
6969:
6628:
6618:
6279:
6161:
6126:
6088:
6073:
5692:
5481:
5466:
5062:
3718:
3691:
3687:
3631:
2811:
First the hydrometer is floated in the reference liquid (shown in light blue), and the
875:
845:
1275:
It can be shown that true specific gravity can be computed from different properties:
7463:
7400:
7265:
7144:
6974:
6643:
6580:
6244:
6078:
5491:
5162:
2756:
249:
7305:
7093:
7057:
6984:
6880:
6850:
6845:
6773:
6608:
6394:
6349:
6266:
6234:
6217:
6196:
6186:
6116:
6098:
221:
at its densest (at 4 °C or 39.2 °F); for gases, the reference is air at
4163:{\displaystyle F_{\mathrm {s,n} }=gV(\rho _{\mathrm {s} }-\rho _{\mathrm {a} }),}
4079:{\displaystyle F_{\mathrm {w,n} }=gV(\rho _{\mathrm {w} }-\rho _{\mathrm {a} }),}
7219:
7047:
7007:
6943:
6926:
6799:
6768:
6753:
6748:
6710:
6585:
6549:
6399:
6201:
6156:
5950:
Second
Edition, McGraw-Hill, International Edition, Y.A. Cengel & M.A. Boles
5496:
5461:
5431:
4844:
4784:
2871:
is the volume of reference liquid displaced, i.e. the red volume in the diagram.
2760:
2114:
1946:{\displaystyle \rho _{\mathrm {substance} }=SG\times \rho _{\mathrm {H_{2}O} }.}
1813:
867:
708:
257:
17:
2148:
more difficult to ascertain. One method is to put the sample in a water-filled
1783:(20 °C/4 °C). Here, temperature is being specified using the current
691:". If the reference is not explicitly stated then it is normally assumed to be
7224:
7214:
7165:
7083:
6895:
6740:
6715:
6575:
6454:
6414:
6384:
6339:
6334:
6314:
6284:
6181:
6083:
6035:
5845:
Medical-surgical nursing : assessment and management of clinical problems
5486:
5435:
5182:
5111:
4777:
4373:
3622:
3614:
2921:
2796:
2094:
2000:
representing the temperature at which the sample's density was determined and
1837:
1719:
representing the temperature at which the sample's density was determined and
863:
5862:
866:
and the approximately equal sign is used because equality pertains only if 1
7315:
7113:
6763:
6376:
6191:
6151:
6093:
5192:
5142:
2090:
871:
5735:
5718:
5522:
New York, London(Chapman Hall): John Wiley and Sons. pp. 195–200, 316.
4764:
The pycnometer is used in ISO standard: ISO 1183-1:2004, ISO 1014–1985 and
4177:
is the density of the sample. The ratio of the sample and water forces is:
1801:
respectively, resulting in an SG (20 °C/4 °C) value for water of
5519:
A text-book of mineralogy: with an extended treatise on crystallography...
881:
Those with SG greater than 1 are denser than water and will, disregarding
7353:
7260:
7139:
7129:
6885:
6794:
6758:
6439:
6389:
5471:
5172:
2924:
2106:
2102:
2082:
704:
5642:
2865:
is the relative density of the new liquid with respect to the reference.
7280:
7275:
7073:
6730:
6705:
6695:
6623:
6444:
6404:
6004:
5132:
4791:
3676:
2098:
1969:
for a table of the measured densities of water at various temperatures.
1966:
696:
214:
61:
5626:
4808:
Boot, with vacuum jacket and thermometer, capacity 5, 10, 25 and 50 mL
889:
True specific gravity of a liquid can be expressed mathematically as:
6633:
5566:. U.S. Department of the Interior, Bureau of Reclamation. p. 37.
5411:
5272:
5222:
5202:
2844:
2041:
1784:
225:(20 °C or 68 °F). The term "relative density" (abbreviated
722:
The relative density of gases is often measured with respect to dry
237:, whereas the term "specific gravity" is gradually being abandoned.
5414:
gas has a density of 0.164 g/L; it is 0.139 times as dense as
4413:
gives the relationship between apparent and true relative density:
7250:
7229:
5719:"The newtonian constant of gravitation as affected by temperature"
5447:
5441:
5422:
5152:
3695:
3680:
3621:
3613:
2772:
is the weight of the sample in water (measured in the same units).
2086:
692:
261:
253:
218:
210:
178:
6804:
6103:
5262:
5232:
5212:
4799:
2840:
2801:
1857:
712:
269:
265:
191:
7357:
7186:
7005:
6825:
6485:
6046:
6008:
5944:
Fourth
Edition, Wiley, SI Version, R.W. Fox & A.T. McDonald
5415:
5121:
2016:= 1.000000 (20 °C/20 °C) it is also the case that RD
1574:
is the volume of the sample and of water (the same for both),
723:
589:
2800:
1657:
1609:
878:
has a molar volume of 22.259 L under those same conditions.
738:
735:
342:
339:
3655:
234:
30:"Specific gravity" redirects here. Not to be confused with
3846:
at the location at which the measurements are being made.
595:
The reference material can be indicated using subscripts:
5723:
2134:) equal to 0.999972 g/cm (or 62.43 lb·ft). The
703:
units, the density of water is (approximately) 1000
1272:
the weight of an equal volume of water measured in air.
1223:
represents the weight of the sample measured in air and
5444:
normally has a specific gravity of approximately 1.060.
5283:(Samples may vary, and these figures are approximate.)
3853:
is the density of the air at the ambient pressure and
3142:{\displaystyle m=\rho _{\mathrm {new} }(V-A\Delta x).}
886:
finds wide application, often for historical reasons.
5450:
80° proof (40% v/v) has a specific gravity of 0.9498.
5299:
5065:
5052:{\displaystyle e_{\mathrm {max} },e_{\mathrm {min} }}
5009:
4897:
4867:
4653:
4421:
4183:
4096:
4012:
3871:
3734:
3506:
3363:
3188:
3090:
3004:
2947:
2653:
2313:
2170:
1869:
1653:
1605:
1281:
1229:
1194:
1081:
1039:
995:
895:
848:
732:
601:
574:
521:
468:
445:
336:
309:
286:
83:
34:. For the album by Joe McPhee and Joe Giardullo, see
3728:
and is placed upon a balance, it will exert a force
1265:{\displaystyle {W_{\mathrm {A} ,\mathrm {H_{2}O} }}}
515:
is the density of the substance being measured, and
330:, as it is the ratio of either densities or weights
7293:
7243:
7197:
7153:
7122:
7066:
7018:
6957:
6917:
6894:
6838:
6782:
6739:
6688:
6657:
6594:
6563:
6540:
6524:
6498:
6364:
6298:
6210:
6135:
6057:
4805:
as above, conical type, ASTM D 115 and D 234, 25 mL
1812:gravity. For example, in the brewing industry, the
676:{\displaystyle RD_{\mathrm {substance/reference} }}
70:
60:
48:
43:
5596:
5594:
5401:
5079:are the maximum, minimum and actual void rations.
5071:
5051:
4995:
4882:
4750:
4637:
4358:
4162:
4078:
3996:
3823:
3592:
3458:
3299:
3141:
3037:
2983:
2737:
2631:
2297:
1945:
1745:(20 °C/20 °C), it is also the case that
1682:
1639:
1556:
1264:
1215:
1180:
1064:
1025:
981:
854:
834:
675:
580:
560:
507:
454:
431:
318:
295:
166:
5954:Munson, B. R.; D. F. Young; T. H. Okishi (2001).
4386:Further manipulation and finally substitution of
2856:is the unknown density of the new (green) liquid.
1683:{\displaystyle {\mathit {m}}_{\mathrm {H_{2}O} }}
1640:{\displaystyle {\mathit {m}}_{\mathrm {sample} }}
5938:Wiley, B.R. Munson, D.F. Young & T.H. Okishi
2755:is the weight of the sample in air (measured in
568:is the density of the reference. (By convention
5533:Schetz, Joseph A.; Allen E. Fuhs (1999-02-05).
4383:depend on the actual volume of the pycnometer.
2931:, which in the case of the reference liquid is
2081:Relative density can also help to quantify the
5890:Shmukler, Michael (2004). Elert, Glenn (ed.).
5777:"Specific Gravity: Liquids, Gases, and Solids"
5756:. US Army Materiel Command. 1971. p. 3-38
7369:
6020:
5705:Process Control Digital Electronic Hydrometer
3679:of a liquid. A pycnometer is usually made of
8:
5753:Engineering Design Handbook:Hydraulic Fluids
5666:
5664:
5654:
5652:
5560:United States Bureau of Reclamation (1978).
2847:) of the reference liquid (typically water).
561:{\displaystyle \rho _{\mathrm {reference} }}
508:{\displaystyle \rho _{\mathrm {substance} }}
6980:Nuclear magnetic resonance (NMR) instrument
4394:
2984:{\displaystyle mg=\rho _{\mathrm {ref} }Vg}
7376:
7362:
7354:
7207:
7194:
7183:
7015:
7002:
6835:
6822:
6495:
6482:
6054:
6043:
6027:
6013:
6005:
5875:: CS1 maint: location missing publisher (
5695:. Ohmartvega.com. Retrieved on 2011-09-30.
5099:
3038:{\displaystyle m=\rho _{\mathrm {ref} }V.}
2105:use it as an aid in the identification of
1570:is the local acceleration due to gravity,
5734:
5373:
5368:
5367:
5335:
5334:
5328:
5313:
5308:
5307:
5298:
5064:
5036:
5035:
5015:
5014:
5008:
4968:
4967:
4947:
4946:
4921:
4920:
4913:
4903:
4902:
4896:
4873:
4872:
4866:
4729:
4728:
4709:
4708:
4697:
4696:
4690:
4680:
4679:
4662:
4661:
4652:
4620:
4619:
4608:
4607:
4601:
4584:
4583:
4572:
4571:
4565:
4555:
4554:
4544:
4529:
4528:
4517:
4516:
4510:
4493:
4492:
4481:
4480:
4474:
4462:
4461:
4450:
4449:
4443:
4440:
4430:
4429:
4420:
4343:
4342:
4328:
4327:
4314:
4313:
4299:
4298:
4291:
4275:
4274:
4260:
4259:
4234:
4233:
4219:
4218:
4202:
4192:
4191:
4182:
4147:
4146:
4132:
4131:
4102:
4101:
4095:
4063:
4062:
4048:
4047:
4018:
4017:
4011:
3979:
3978:
3961:
3960:
3941:
3940:
3929:
3928:
3922:
3915:
3914:
3900:
3899:
3877:
3876:
3870:
3804:
3803:
3792:
3791:
3785:
3778:
3777:
3763:
3762:
3740:
3739:
3733:
3574:
3573:
3551:
3525:
3515:
3514:
3505:
3437:
3436:
3414:
3402:
3382:
3372:
3371:
3362:
3270:
3252:
3251:
3234:
3233:
3227:
3207:
3197:
3196:
3187:
3102:
3101:
3089:
3016:
3015:
3003:
2962:
2961:
2946:
2908:is the cross sectional area of the shaft.
2710:
2709:
2689:
2688:
2670:
2669:
2663:
2652:
2612:
2595:
2579:
2562:
2553:
2538:
2522:
2504:
2488:
2478:
2456:
2455:
2450:
2433:
2432:
2427:
2408:
2407:
2402:
2385:
2384:
2379:
2375:
2357:
2356:
2330:
2329:
2323:
2312:
2261:
2260:
2255:
2220:
2219:
2214:
2201:
2193:
2190:
2177:
2169:
1928:
1923:
1922:
1875:
1874:
1868:
1690:is the mass of an equal volume of water.
1668:
1663:
1662:
1656:
1655:
1652:
1615:
1614:
1608:
1607:
1604:
1537:
1532:
1524:
1523:
1512:
1504:
1503:
1497:
1484:
1470:
1465:
1464:
1438:
1437:
1431:
1410:
1405:
1404:
1373:
1372:
1365:
1348:
1343:
1342:
1316:
1315:
1309:
1290:
1289:
1280:
1249:
1244:
1236:
1235:
1230:
1228:
1206:
1199:
1193:
1161:
1156:
1148:
1147:
1136:
1128:
1127:
1121:
1090:
1089:
1080:
1065:{\displaystyle \rho _{\mathrm {H_{2}O} }}
1050:
1045:
1044:
1038:
1026:{\displaystyle \rho _{\mathrm {sample} }}
1001:
1000:
994:
962:
957:
956:
930:
929:
923:
904:
903:
894:
847:
814:
813:
796:
795:
789:
771:
770:
753:
752:
746:
734:
733:
731:
638:
610:
609:
600:
573:
527:
526:
520:
474:
473:
467:
444:
393:
392:
357:
356:
350:
338:
337:
335:
308:
285:
150:
145:
144:
118:
117:
111:
92:
91:
82:
7345:Instruments used in medical laboratories
5631:Journal of Chemical and Engineering Data
5577:
5575:
5573:
5430:, while high concentration may indicate
5418:, which has a density of 1.18 g/L.
1828:equal to 999.972 kg/m in SI units (
1599:represents a weight obtained in vacuum,
6861:Inductively coupled plasma (ICP) device
5948:Thermodynamics: An Engineering Approach
5817:
5815:
5620:
5618:
5508:
6909:Transmission electron microscope (TEM)
5868:
4857:The relative density in soil mechanics
4818:Hydrostatic Pressure-based Instruments
2113:example, in the brewing industry, the
40:
5999:Specific Gravity Weights Of Materials
5847:(9th ed.). St. Louis, Missouri.
5838:
5836:
3618:An empty glass pycnometer and stopper
2877:is the mass of the entire hydrometer.
1817:which water has its maximum density,
1216:{\displaystyle W_{A,{\text{sample}}}}
683:which means "the relative density of
7:
5973:Fox, R. W.; McDonald, A. T. (2003).
5092:in liquids, which can skew results.
3675:, is a device used to determine the
3354:
3179:
3081:
2995:
2912:Since the floating hydrometer is in
3075:(see note above about the sign of Δ
2101:content of a rock or other sample.
6904:Scanning electron microscope (SEM)
5707:. Gardco. Retrieved on 2011-09-30.
5379:
5370:
5357:
5354:
5351:
5348:
5345:
5342:
5339:
5336:
5319:
5310:
5043:
5040:
5037:
5022:
5019:
5016:
4990:
4975:
4972:
4969:
4954:
4951:
4948:
4928:
4925:
4922:
4904:
4874:
4730:
4710:
4698:
4681:
4663:
4621:
4609:
4585:
4573:
4556:
4530:
4518:
4494:
4482:
4463:
4451:
4431:
4344:
4329:
4315:
4300:
4276:
4261:
4235:
4220:
4193:
4148:
4133:
4109:
4103:
4064:
4049:
4025:
4019:
3980:
3962:
3942:
3930:
3916:
3901:
3878:
3805:
3793:
3779:
3764:
3741:
3581:
3578:
3575:
3557:
3536:
3533:
3530:
3522:
3519:
3516:
3444:
3441:
3438:
3420:
3393:
3390:
3387:
3379:
3376:
3373:
3285:
3259:
3256:
3253:
3241:
3238:
3235:
3218:
3215:
3212:
3204:
3201:
3198:
3127:
3109:
3106:
3103:
3023:
3020:
3017:
2969:
2966:
2963:
2723:
2720:
2717:
2714:
2711:
2696:
2693:
2690:
2677:
2674:
2671:
2616:
2613:
2599:
2596:
2583:
2580:
2566:
2563:
2542:
2539:
2526:
2523:
2508:
2505:
2492:
2489:
2463:
2460:
2457:
2440:
2437:
2434:
2415:
2412:
2409:
2392:
2389:
2386:
2364:
2361:
2358:
2346:
2343:
2340:
2337:
2334:
2331:
2283:
2280:
2277:
2274:
2271:
2268:
2265:
2262:
2245:
2242:
2239:
2236:
2233:
2230:
2227:
2224:
2221:
1934:
1925:
1900:
1897:
1894:
1891:
1888:
1885:
1882:
1879:
1876:
1674:
1665:
1631:
1628:
1625:
1622:
1619:
1616:
1543:
1534:
1525:
1505:
1476:
1467:
1454:
1451:
1448:
1445:
1442:
1439:
1416:
1407:
1389:
1386:
1383:
1380:
1377:
1374:
1354:
1345:
1332:
1329:
1326:
1323:
1320:
1317:
1300:
1297:
1294:
1291:
1255:
1246:
1237:
1167:
1158:
1149:
1129:
1112:
1109:
1106:
1103:
1100:
1097:
1094:
1091:
1056:
1047:
1017:
1014:
1011:
1008:
1005:
1002:
968:
959:
946:
943:
940:
937:
934:
931:
914:
911:
908:
905:
821:
818:
815:
803:
800:
797:
778:
775:
772:
760:
757:
754:
667:
664:
661:
658:
655:
652:
649:
646:
643:
635:
632:
629:
626:
623:
620:
617:
614:
611:
552:
549:
546:
543:
540:
537:
534:
531:
528:
499:
496:
493:
490:
487:
484:
481:
478:
475:
418:
415:
412:
409:
406:
403:
400:
397:
394:
382:
379:
376:
373:
370:
367:
364:
361:
358:
156:
147:
134:
131:
128:
125:
122:
119:
102:
99:
96:
93:
25:
5674:Table 1: Extract in Wort and Beer
2829:In the explanation that follows,
2160:For each substance, the density,
1033:is the density of the sample and
7443:
6949:Thermogravimetric analyzer (TGA)
6759:Nuclear magnetic resonance (NMR)
4883:{\displaystyle D_{\mathrm {R} }}
5975:Introduction to Fluid Mechanics
5956:Fundamentals of Fluid Mechanics
5942:Introduction to Fluid Mechanics
5936:Fundamentals of Fluid Mechanics
5536:Fundamentals of fluid mechanics
5516:Dana, Edward Salisbury (1922).
2941:. Setting these equal, we have
1840:or 62.43 lb/cu ft in
5916:"Specific Gravity of Liqueurs"
5750:"Chapter 3-Specific Gravity".
4787:, adjusted, side tube with cap
4742:
4718:
4282:
4252:
4241:
4211:
4154:
4124:
4070:
4040:
3838:is the mass of the bottle and
3667:'dense'), also called
3133:
3115:
1647:is the mass of the sample and
1581:is the density of the sample,
190:tests the specific gravity of
1:
4824:Vibrating Element Transducers
1842:United States customary units
5775:Trento, Chin (Jan 5, 2024).
5693:Density – VEGA Americas, Inc
3656:
3602:This shows that, for small Δ
2885:local gravitational constant
2763:or some other unit of force)
2061:; or specific gravity: 2.432
5781:Stanford Advanced Materials
3496:
3348:
3325:
3173:
3167:
7496:
5802:WO patent 1992005422A1
3844:gravitational acceleration
3645:
3629:
2794:
264:, juices, honeys, brewers
29:
7439:
7391:
7342:
7210:
7193:
7182:
7104:Time-domain reflectometer
7014:
7001:
6871:Liquid chromatograph (LC)
6834:
6821:
6494:
6481:
6053:
6042:
5670:ASBC Methods of Analysis
4783:as above, with ground-in
4370:apparent relative density
3488:first-order approximation
1592:is the density of water,
1072:is the density of water.
188:Aviation boatswain's mate
7475:Dimensionless quantities
5823:"Lecture Demonstrations"
4851:Buoyant Force Transducer
36:Specific Gravity (album)
6939:Melting-point apparatus
6320:Cryogenic storage dewar
5977:(4th ed.). Wiley.
5958:(4th ed.). Wiley.
3683:, with a close-fitting
3673:specific gravity bottle
303:) or specific gravity (
7385:Mineral identification
6876:Mass spectrometer (MS)
6866:Gas chromatograph (GC)
6001:(archived 22 May 2006)
5736:10.1098/rsta.1916.0007
5403:
5073:
5053:
4997:
4884:
4813:Digital density meters
4752:
4639:
4395:
4360:
4164:
4080:
3998:
3825:
3627:
3619:
3594:
3460:
3301:
3143:
3039:
2985:
2839:is the known density (
2805:
2739:
2633:
2299:
2097:to help determine the
2052:relative density: 8.15
1959:Temperature dependence
1947:
1684:
1641:
1558:
1266:
1217:
1182:
1066:
1027:
983:
856:
836:
677:
582:
562:
509:
456:
433:
328:dimensionless quantity
320:
297:
207:dimensionless quantity
195:
168:
27:Ratio of two densities
7251:Acid-resistant gloves
6932:differential scanning
5404:
5074:
5054:
4998:
4885:
4861:The relative density
4841:Radiation-based Gauge
4835:Ultrasonic Transducer
4768:standard: ASTM D854.
4753:
4640:
4361:
4165:
4081:
3999:
3826:
3625:
3617:
3595:
3500:) can be written as:
3461:
3346:. Substituting into (
3302:
3144:
3040:
2986:
2804:
2740:
2634:
2300:
1948:
1685:
1642:
1559:
1267:
1218:
1183:
1067:
1028:
984:
857:
837:
678:
583:
581:{\displaystyle \rho }
563:
510:
462:is relative density,
457:
434:
321:
298:
182:
169:
6828:Analytical chemistry
6330:Laminar flow cabinet
6036:Laboratory equipment
5896:The Physics Factbook
5297:
5063:
5007:
4895:
4865:
4798:, cylindrical type,
4651:
4419:
4181:
4094:
4086:where the subscript
4010:
3869:
3862:Archimedes Principle
3732:
3504:
3486:is small then, as a
3361:
3186:
3088:
3002:
2945:
2651:
2642:Hydrostatic weighing
2311:
2168:
2085:of a substance in a
1867:
1651:
1603:
1279:
1227:
1192:
1079:
1037:
993:
893:
846:
730:
599:
592:, denotes density.)
572:
519:
466:
443:
334:
307:
284:
81:
7450:Minerals portal
7200:Personal protective
6109:Meker–Fisher burner
5717:Shaw, P.E. (1916).
5643:10.1021/je60064a005
4368:This is called the
3626:A filled pycnometer
588:, the Greek letter
272:, etc.) and acids.
7043:Function generator
7026:Bench power supply
6965:Analytical balance
6726:Ostwald viscometer
6721:Graduated cylinder
6460:Inoculation needle
5920:Good Cocktails.com
5892:"Density of blood"
5428:diabetes insipidus
5399:
5069:
5049:
4993:
4880:
4828:oscillating U-tube
4748:
4635:
4356:
4160:
4076:
3994:
3821:
3704:analytical balance
3628:
3620:
3590:
3456:
3297:
3139:
3035:
2981:
2914:static equilibrium
2806:
2735:
2629:
2295:
2150:graduated cylinder
1943:
1680:
1637:
1554:
1262:
1213:
1178:
1062:
1023:
979:
852:
832:
673:
578:
558:
505:
455:{\displaystyle RD}
452:
429:
319:{\displaystyle SG}
316:
296:{\displaystyle RD}
293:
280:Relative density (
233:) is preferred in
196:
185:United States Navy
164:
7457:
7456:
7351:
7350:
7338:
7337:
7334:
7333:
7311:Fire extinguisher
7301:Biosafety cabinet
7289:
7288:
7178:
7177:
7174:
7173:
7109:Transistor tester
7099:Spectrum analyzer
6997:
6996:
6993:
6992:
6817:
6816:
6813:
6812:
6689:Measuring devices
6511:Soxhlet extractor
6477:
6476:
6473:
6472:
6425:Spectrophotometer
6420:Pipeclay triangle
6172:Mortar and pestle
5965:978-0-471-44250-9
5854:978-0-323-10089-2
5385:
5281:
5280:
5106:Specific gravity
5072:{\displaystyle e}
4982:
4716:
4630:
4627:
4591:
4539:
4536:
4500:
4469:
4351:
4286:
3948:
3811:
3666:
3654:
3567:
3480:
3479:
3451:
3430:
3321:
3320:
3292:
3265:
3163:
3162:
3059:
3058:
2730:
2621:
2611:
2594:
2578:
2561:
2548:
2547:
2537:
2521:
2513:
2503:
2487:
2473:
2472:
2453:
2430:
2424:
2405:
2382:
2370:
2290:
2258:
2217:
2209:
2208:
2205:
2196:
2185:
2184:
2181:
1549:
1515:
1492:
1482:
1426:
1425:
1398:
1360:
1209:
1173:
1139:
974:
855:{\displaystyle M}
827:
784:
424:
276:Basic calculation
177:
176:
162:
16:(Redirected from
7487:
7448:
7447:
7446:
7426:Specific gravity
7378:
7371:
7364:
7355:
7208:
7195:
7184:
7089:Network analyzer
7016:
7003:
6836:
6823:
6496:
6483:
6465:Inoculation loop
6335:Microtiter plate
6275:Test tube holder
6167:Magnetic stirrer
6055:
6044:
6029:
6022:
6015:
6006:
5988:
5969:
5924:
5923:
5912:
5906:
5905:
5903:
5902:
5887:
5881:
5880:
5874:
5866:
5840:
5831:
5830:
5827:physics.ucsb.edu
5819:
5810:
5809:
5808:
5804:
5798:
5792:
5791:
5789:
5787:
5772:
5766:
5765:
5763:
5761:
5747:
5741:
5740:
5738:
5714:
5708:
5702:
5696:
5690:
5684:
5681:
5675:
5668:
5659:
5656:
5647:
5646:
5625:Kell, George S.
5622:
5613:
5612:
5604:PTB-Mitteilungen
5598:
5589:
5579:
5568:
5567:
5557:
5551:
5550:
5530:
5524:
5523:
5513:
5408:
5406:
5405:
5400:
5386:
5384:
5383:
5382:
5378:
5377:
5362:
5361:
5360:
5329:
5324:
5323:
5322:
5318:
5317:
5253:Depleted uranium
5100:
5078:
5076:
5075:
5070:
5058:
5056:
5055:
5050:
5048:
5047:
5046:
5027:
5026:
5025:
5002:
5000:
4999:
4994:
4983:
4981:
4980:
4979:
4978:
4959:
4958:
4957:
4940:
4933:
4932:
4931:
4914:
4909:
4908:
4907:
4889:
4887:
4886:
4881:
4879:
4878:
4877:
4796:heavy crude oils
4757:
4755:
4754:
4749:
4735:
4734:
4733:
4717:
4715:
4714:
4713:
4703:
4702:
4701:
4691:
4686:
4685:
4684:
4668:
4667:
4666:
4644:
4642:
4641:
4636:
4631:
4629:
4628:
4626:
4625:
4624:
4614:
4613:
4612:
4602:
4593:
4592:
4590:
4589:
4588:
4578:
4577:
4576:
4566:
4561:
4560:
4559:
4545:
4540:
4538:
4537:
4535:
4534:
4533:
4523:
4522:
4521:
4511:
4502:
4501:
4499:
4498:
4497:
4487:
4486:
4485:
4475:
4470:
4468:
4467:
4466:
4456:
4455:
4454:
4444:
4441:
4436:
4435:
4434:
4398:
4365:
4363:
4362:
4357:
4352:
4350:
4349:
4348:
4347:
4334:
4333:
4332:
4321:
4320:
4319:
4318:
4305:
4304:
4303:
4292:
4287:
4285:
4281:
4280:
4279:
4266:
4265:
4264:
4244:
4240:
4239:
4238:
4225:
4224:
4223:
4203:
4198:
4197:
4196:
4169:
4167:
4166:
4161:
4153:
4152:
4151:
4138:
4137:
4136:
4114:
4113:
4112:
4085:
4083:
4082:
4077:
4069:
4068:
4067:
4054:
4053:
4052:
4030:
4029:
4028:
4003:
4001:
4000:
3995:
3990:
3986:
3985:
3984:
3983:
3967:
3966:
3965:
3949:
3947:
3946:
3945:
3935:
3934:
3933:
3923:
3921:
3920:
3919:
3906:
3905:
3904:
3883:
3882:
3881:
3830:
3828:
3827:
3822:
3817:
3813:
3812:
3810:
3809:
3808:
3798:
3797:
3796:
3786:
3784:
3783:
3782:
3769:
3768:
3767:
3746:
3745:
3744:
3711:particle density
3661:
3659:
3649:
3647:
3599:
3597:
3596:
3591:
3586:
3585:
3584:
3568:
3563:
3552:
3541:
3540:
3539:
3529:
3492:geometric series
3474:
3465:
3463:
3462:
3457:
3452:
3450:
3449:
3448:
3447:
3431:
3426:
3415:
3403:
3398:
3397:
3396:
3386:
3355:
3345:
3315:
3306:
3304:
3303:
3298:
3293:
3291:
3271:
3266:
3264:
3263:
3262:
3246:
3245:
3244:
3228:
3223:
3222:
3221:
3211:
3180:
3157:
3148:
3146:
3145:
3140:
3114:
3113:
3112:
3082:
3074:
3053:
3044:
3042:
3041:
3036:
3028:
3027:
3026:
2996:
2990:
2988:
2987:
2982:
2974:
2973:
2972:
2744:
2742:
2741:
2736:
2731:
2729:
2728:
2727:
2726:
2701:
2700:
2699:
2682:
2681:
2680:
2664:
2638:
2636:
2635:
2630:
2622:
2620:
2619:
2609:
2602:
2592:
2587:
2586:
2576:
2569:
2559:
2554:
2549:
2546:
2545:
2535:
2530:
2529:
2519:
2514:
2512:
2511:
2501:
2496:
2495:
2485:
2480:
2479:
2474:
2471:
2470:
2469:
2454:
2451:
2448:
2447:
2446:
2431:
2428:
2425:
2423:
2422:
2421:
2406:
2403:
2400:
2399:
2398:
2383:
2380:
2377:
2376:
2371:
2369:
2368:
2367:
2351:
2350:
2349:
2324:
2304:
2302:
2301:
2296:
2291:
2289:
2288:
2287:
2286:
2259:
2256:
2250:
2249:
2248:
2218:
2215:
2211:
2210:
2206:
2203:
2202:
2197:
2194:
2191:
2186:
2182:
2179:
2178:
2133:
2131:
2130:
2069:
2068:
2060:
2059:
2039:
2037:
2036:
2033:
2030:
1952:
1950:
1949:
1944:
1939:
1938:
1937:
1933:
1932:
1905:
1904:
1903:
1855:
1854:
1835:
1833:
1807:
1806:
1800:
1799:
1793:
1792:
1782:
1781:
1775:
1774:
1773:
1772:
1765:
1764:
1763:
1744:
1743:
1689:
1687:
1686:
1681:
1679:
1678:
1677:
1673:
1672:
1661:
1660:
1646:
1644:
1643:
1638:
1636:
1635:
1634:
1613:
1612:
1563:
1561:
1560:
1555:
1550:
1548:
1547:
1546:
1542:
1541:
1528:
1518:
1517:
1516:
1513:
1508:
1498:
1493:
1485:
1483:
1481:
1480:
1479:
1475:
1474:
1459:
1458:
1457:
1432:
1427:
1421:
1420:
1419:
1415:
1414:
1399:
1394:
1393:
1392:
1367:
1366:
1361:
1359:
1358:
1357:
1353:
1352:
1337:
1336:
1335:
1310:
1305:
1304:
1303:
1271:
1269:
1268:
1263:
1261:
1260:
1259:
1258:
1254:
1253:
1240:
1222:
1220:
1219:
1214:
1212:
1211:
1210:
1207:
1187:
1185:
1184:
1179:
1174:
1172:
1171:
1170:
1166:
1165:
1152:
1142:
1141:
1140:
1137:
1132:
1122:
1117:
1116:
1115:
1071:
1069:
1068:
1063:
1061:
1060:
1059:
1055:
1054:
1032:
1030:
1029:
1024:
1022:
1021:
1020:
988:
986:
985:
980:
975:
973:
972:
971:
967:
966:
951:
950:
949:
924:
919:
918:
917:
861:
859:
858:
853:
841:
839:
838:
833:
828:
826:
825:
824:
808:
807:
806:
790:
785:
783:
782:
781:
765:
764:
763:
747:
742:
741:
687:with respect to
682:
680:
679:
674:
672:
671:
670:
642:
587:
585:
584:
579:
567:
565:
564:
559:
557:
556:
555:
514:
512:
511:
506:
504:
503:
502:
461:
459:
458:
453:
438:
436:
435:
430:
425:
423:
422:
421:
387:
386:
385:
351:
346:
345:
325:
323:
322:
317:
302:
300:
299:
294:
223:room temperature
203:specific gravity
199:Relative density
173:
171:
170:
165:
163:
161:
160:
159:
155:
154:
139:
138:
137:
112:
107:
106:
105:
74:other quantities
72:Derivations from
44:Specific gravity
41:
21:
18:Specific Gravity
7495:
7494:
7490:
7489:
7488:
7486:
7485:
7484:
7460:
7459:
7458:
7453:
7444:
7442:
7435:
7387:
7382:
7352:
7347:
7330:
7326:Solvent cabinet
7285:
7256:Eyewash station
7239:
7204:
7202:equipment (PPE)
7201:
7189:
7170:
7149:
7118:
7062:
7053:Pulse generator
7019:Control devices
7010:
6989:
6953:
6919:Thermochemistry
6913:
6890:
6830:
6809:
6778:
6735:
6701:Conical measure
6684:
6653:
6590:
6559:
6536:
6520:
6490:
6469:
6450:Test tube brush
6360:
6345:Picotiter plate
6308:
6294:
6290:Lab drying rack
6249:Extension clamp
6225:
6206:
6145:
6131:
6067:
6049:
6038:
6033:
5995:
5985:
5972:
5966:
5953:
5932:
5930:Further reading
5927:
5914:
5913:
5909:
5900:
5898:
5889:
5888:
5884:
5867:
5855:
5842:
5841:
5834:
5821:
5820:
5813:
5806:
5800:
5799:
5795:
5785:
5783:
5774:
5773:
5769:
5759:
5757:
5749:
5748:
5744:
5716:
5715:
5711:
5703:
5699:
5691:
5687:
5682:
5678:
5669:
5662:
5657:
5650:
5624:
5623:
5616:
5600:
5599:
5592:
5580:
5571:
5559:
5558:
5554:
5547:
5532:
5531:
5527:
5515:
5514:
5510:
5506:
5501:
5477:Fluid mechanics
5457:
5369:
5363:
5330:
5309:
5303:
5295:
5294:
5288:surface tension
5098:
5085:
5061:
5060:
5031:
5010:
5005:
5004:
4963:
4942:
4941:
4916:
4915:
4898:
4893:
4892:
4868:
4863:
4862:
4859:
4815:
4724:
4704:
4692:
4675:
4657:
4649:
4648:
4615:
4603:
4594:
4579:
4567:
4550:
4546:
4524:
4512:
4503:
4488:
4476:
4457:
4445:
4442:
4425:
4417:
4416:
4412:
4405:
4392:
4382:
4338:
4323:
4322:
4309:
4294:
4293:
4270:
4255:
4245:
4229:
4214:
4204:
4187:
4179:
4178:
4176:
4142:
4127:
4097:
4092:
4091:
4058:
4043:
4013:
4008:
4007:
3974:
3956:
3936:
3924:
3910:
3895:
3894:
3890:
3872:
3867:
3866:
3859:
3852:
3837:
3799:
3787:
3773:
3758:
3757:
3753:
3735:
3730:
3729:
3634:
3612:
3569:
3553:
3510:
3502:
3501:
3472:
3432:
3416:
3407:
3367:
3359:
3358:
3344:
3330:
3313:
3275:
3247:
3229:
3192:
3184:
3183:
3155:
3097:
3086:
3085:
3062:
3051:
3011:
3000:
2999:
2957:
2943:
2942:
2937:
2864:
2855:
2838:
2799:
2793:
2782:
2771:
2754:
2705:
2684:
2683:
2665:
2649:
2648:
2644:
2588:
2555:
2531:
2515:
2497:
2481:
2449:
2426:
2401:
2378:
2352:
2325:
2309:
2308:
2254:
2213:
2212:
2204:Spring Constant
2192:
2166:
2165:
2154:surface tension
2145:
2129:
2126:
2125:
2124:
2122:
2079:
2067:
2064:
2063:
2062:
2058:
2055:
2054:
2053:
2034:
2031:
2028:
2027:
2025:
2023:
2021:
2015:
2013:
2005:
1998:
1991:
1984:
1961:
1924:
1918:
1870:
1865:
1864:
1852:
1850:
1831:
1829:
1827:
1825:
1804:
1802:
1797:
1795:
1790:
1788:
1779:
1777:
1770:
1768:
1767:
1761:
1759:
1758:
1757:
1755:
1753:
1741:
1739:
1737:
1735:
1725:
1718:
1711:
1704:
1664:
1654:
1649:
1648:
1606:
1601:
1600:
1598:
1591:
1589:
1580:
1533:
1519:
1499:
1466:
1460:
1433:
1406:
1400:
1368:
1344:
1338:
1311:
1285:
1277:
1276:
1245:
1231:
1225:
1224:
1195:
1190:
1189:
1157:
1143:
1123:
1085:
1077:
1076:
1046:
1040:
1035:
1034:
996:
991:
990:
958:
952:
925:
899:
891:
890:
883:surface tension
844:
843:
809:
791:
766:
748:
728:
727:
605:
597:
596:
570:
569:
522:
517:
516:
469:
464:
463:
441:
440:
388:
352:
332:
331:
305:
304:
282:
281:
278:
209:defined as the
146:
140:
113:
87:
79:
78:
75:
73:
51:
39:
32:specific weight
28:
23:
22:
15:
12:
11:
5:
7493:
7491:
7483:
7482:
7477:
7472:
7462:
7461:
7455:
7454:
7440:
7437:
7436:
7434:
7433:
7428:
7423:
7418:
7413:
7408:
7406:Crystal system
7403:
7398:
7392:
7389:
7388:
7383:
7381:
7380:
7373:
7366:
7358:
7349:
7348:
7343:
7340:
7339:
7336:
7335:
7332:
7331:
7329:
7328:
7323:
7321:Safety cabinet
7318:
7313:
7308:
7303:
7297:
7295:
7291:
7290:
7287:
7286:
7284:
7283:
7281:Safety goggles
7278:
7276:Safety glasses
7273:
7271:Nitrile gloves
7268:
7266:Medical gloves
7263:
7258:
7253:
7247:
7245:
7241:
7240:
7238:
7237:
7232:
7227:
7222:
7217:
7211:
7205:
7198:
7191:
7190:
7187:
7180:
7179:
7176:
7175:
7172:
7171:
7169:
7168:
7163:
7161:Alligator clip
7157:
7155:
7151:
7150:
7148:
7147:
7142:
7137:
7135:Soldering iron
7132:
7126:
7124:
7120:
7119:
7117:
7116:
7111:
7106:
7101:
7096:
7091:
7086:
7081:
7079:Logic analyzer
7076:
7070:
7068:
7064:
7063:
7061:
7060:
7055:
7050:
7045:
7040:
7039:
7038:
7036:Voltage source
7033:
7031:Current source
7022:
7020:
7012:
7011:
7006:
6999:
6998:
6995:
6994:
6991:
6990:
6988:
6987:
6982:
6977:
6972:
6970:Colony counter
6967:
6961:
6959:
6955:
6954:
6952:
6951:
6946:
6941:
6936:
6935:
6934:
6923:
6921:
6915:
6914:
6912:
6911:
6906:
6900:
6898:
6892:
6891:
6889:
6888:
6883:
6878:
6873:
6868:
6863:
6858:
6853:
6848:
6842:
6840:
6832:
6831:
6826:
6819:
6818:
6815:
6814:
6811:
6810:
6808:
6807:
6802:
6797:
6792:
6786:
6784:
6780:
6779:
6777:
6776:
6771:
6766:
6761:
6756:
6751:
6745:
6743:
6737:
6736:
6734:
6733:
6728:
6723:
6718:
6713:
6708:
6703:
6698:
6692:
6690:
6686:
6685:
6683:
6682:
6677:
6672:
6667:
6661:
6659:
6655:
6654:
6652:
6651:
6646:
6641:
6636:
6631:
6626:
6621:
6616:
6611:
6609:Vacuum (Dewar)
6606:
6600:
6598:
6592:
6591:
6589:
6588:
6583:
6578:
6573:
6567:
6565:
6561:
6560:
6558:
6557:
6552:
6546:
6544:
6538:
6537:
6535:
6534:
6528:
6526:
6522:
6521:
6519:
6518:
6513:
6508:
6502:
6500:
6492:
6491:
6486:
6479:
6478:
6475:
6474:
6471:
6470:
6468:
6467:
6462:
6457:
6452:
6447:
6442:
6437:
6432:
6427:
6422:
6417:
6412:
6407:
6402:
6397:
6392:
6387:
6382:
6379:
6374:
6368:
6366:
6362:
6361:
6359:
6358:
6355:
6352:
6347:
6342:
6337:
6332:
6327:
6322:
6317:
6311:
6309:
6307:
6306:
6303:
6299:
6296:
6295:
6293:
6292:
6287:
6282:
6280:Test tube rack
6277:
6272:
6269:
6264:
6261:
6256:
6255:Funnel support
6253:
6250:
6247:
6242:
6237:
6232:
6228:
6226:
6224:
6223:
6220:
6215:
6211:
6208:
6207:
6205:
6204:
6199:
6194:
6189:
6184:
6179:
6174:
6169:
6164:
6162:Liquid whistle
6159:
6154:
6148:
6146:
6144:
6143:
6140:
6136:
6133:
6132:
6130:
6129:
6127:Vacuum dry box
6124:
6119:
6114:
6111:
6106:
6101:
6096:
6091:
6089:Heating mantle
6086:
6081:
6076:
6074:Alcohol burner
6070:
6068:
6066:
6065:
6062:
6058:
6051:
6050:
6047:
6040:
6039:
6034:
6032:
6031:
6024:
6017:
6009:
6003:
6002:
5994:
5993:External links
5991:
5990:
5989:
5983:
5970:
5964:
5951:
5945:
5939:
5931:
5928:
5926:
5925:
5907:
5882:
5853:
5832:
5811:
5793:
5767:
5742:
5709:
5697:
5685:
5676:
5660:
5648:
5614:
5590:
5569:
5552:
5545:
5525:
5507:
5505:
5502:
5500:
5499:
5494:
5489:
5484:
5482:Gravity (beer)
5479:
5474:
5469:
5464:
5458:
5456:
5453:
5452:
5451:
5445:
5439:
5398:
5395:
5392:
5389:
5381:
5376:
5372:
5366:
5359:
5356:
5353:
5350:
5347:
5344:
5341:
5338:
5333:
5327:
5321:
5316:
5312:
5306:
5302:
5279:
5278:
5275:
5269:
5268:
5265:
5259:
5258:
5255:
5249:
5248:
5245:
5239:
5238:
5235:
5229:
5228:
5225:
5219:
5218:
5215:
5209:
5208:
5205:
5199:
5198:
5195:
5189:
5188:
5185:
5179:
5178:
5175:
5169:
5168:
5165:
5159:
5158:
5155:
5149:
5148:
5145:
5139:
5138:
5135:
5129:
5128:
5125:
5118:
5117:
5114:
5108:
5107:
5104:
5097:
5094:
5084:
5081:
5068:
5045:
5042:
5039:
5034:
5030:
5024:
5021:
5018:
5013:
4992:
4989:
4986:
4977:
4974:
4971:
4966:
4962:
4956:
4953:
4950:
4945:
4939:
4936:
4930:
4927:
4924:
4919:
4912:
4906:
4901:
4876:
4871:
4858:
4855:
4814:
4811:
4810:
4809:
4806:
4803:
4788:
4781:
4747:
4744:
4741:
4738:
4732:
4727:
4723:
4720:
4712:
4707:
4700:
4695:
4689:
4683:
4678:
4674:
4671:
4665:
4660:
4656:
4634:
4623:
4618:
4611:
4606:
4600:
4597:
4587:
4582:
4575:
4570:
4564:
4558:
4553:
4549:
4543:
4532:
4527:
4520:
4515:
4509:
4506:
4496:
4491:
4484:
4479:
4473:
4465:
4460:
4453:
4448:
4439:
4433:
4428:
4424:
4410:
4403:
4390:
4380:
4355:
4346:
4341:
4337:
4331:
4326:
4317:
4312:
4308:
4302:
4297:
4290:
4284:
4278:
4273:
4269:
4263:
4258:
4254:
4251:
4248:
4243:
4237:
4232:
4228:
4222:
4217:
4213:
4210:
4207:
4201:
4195:
4190:
4186:
4174:
4159:
4156:
4150:
4145:
4141:
4135:
4130:
4126:
4123:
4120:
4117:
4111:
4108:
4105:
4100:
4075:
4072:
4066:
4061:
4057:
4051:
4046:
4042:
4039:
4036:
4033:
4027:
4024:
4021:
4016:
3993:
3989:
3982:
3977:
3973:
3970:
3964:
3959:
3955:
3952:
3944:
3939:
3932:
3927:
3918:
3913:
3909:
3903:
3898:
3893:
3889:
3886:
3880:
3875:
3857:
3850:
3835:
3820:
3816:
3807:
3802:
3795:
3790:
3781:
3776:
3772:
3766:
3761:
3756:
3752:
3749:
3743:
3738:
3719:gas pycnometer
3692:capillary tube
3632:Gas pycnometer
3611:
3608:
3589:
3583:
3580:
3577:
3572:
3566:
3562:
3559:
3556:
3550:
3547:
3544:
3538:
3535:
3532:
3528:
3524:
3521:
3518:
3513:
3509:
3478:
3477:
3468:
3466:
3455:
3446:
3443:
3440:
3435:
3429:
3425:
3422:
3419:
3413:
3410:
3406:
3401:
3395:
3392:
3389:
3385:
3381:
3378:
3375:
3370:
3366:
3342:
3319:
3318:
3309:
3307:
3296:
3290:
3287:
3284:
3281:
3278:
3274:
3269:
3261:
3258:
3255:
3250:
3243:
3240:
3237:
3232:
3226:
3220:
3217:
3214:
3210:
3206:
3203:
3200:
3195:
3191:
3161:
3160:
3151:
3149:
3138:
3135:
3132:
3129:
3126:
3123:
3120:
3117:
3111:
3108:
3105:
3100:
3096:
3093:
3057:
3056:
3047:
3045:
3034:
3031:
3025:
3022:
3019:
3014:
3010:
3007:
2980:
2977:
2971:
2968:
2965:
2960:
2956:
2953:
2950:
2935:
2910:
2909:
2903:
2888:
2878:
2872:
2866:
2862:
2857:
2853:
2848:
2836:
2795:Main article:
2792:
2789:
2780:
2774:
2773:
2769:
2764:
2752:
2734:
2725:
2722:
2719:
2716:
2713:
2708:
2704:
2698:
2695:
2692:
2687:
2679:
2676:
2673:
2668:
2662:
2659:
2656:
2643:
2640:
2628:
2625:
2618:
2615:
2608:
2605:
2601:
2598:
2591:
2585:
2582:
2575:
2572:
2568:
2565:
2558:
2552:
2544:
2541:
2534:
2528:
2525:
2518:
2510:
2507:
2500:
2494:
2491:
2484:
2477:
2468:
2465:
2462:
2459:
2445:
2442:
2439:
2436:
2420:
2417:
2414:
2411:
2397:
2394:
2391:
2388:
2374:
2366:
2363:
2360:
2355:
2348:
2345:
2342:
2339:
2336:
2333:
2328:
2322:
2319:
2316:
2294:
2285:
2282:
2279:
2276:
2273:
2270:
2267:
2264:
2253:
2247:
2244:
2241:
2238:
2235:
2232:
2229:
2226:
2223:
2200:
2189:
2176:
2173:
2164:, is given by
2144:
2141:
2127:
2078:
2075:
2071:
2070:
2065:
2056:
2019:
2017:
2011:
2009:
2003:
1996:
1989:
1982:
1972:
1971:
1960:
1957:
1942:
1936:
1931:
1927:
1921:
1917:
1914:
1911:
1908:
1902:
1899:
1896:
1893:
1890:
1887:
1884:
1881:
1878:
1873:
1823:
1821:
1751:
1749:
1733:
1731:
1723:
1716:
1709:
1702:
1676:
1671:
1667:
1659:
1633:
1630:
1627:
1624:
1621:
1618:
1611:
1596:
1587:
1585:
1578:
1553:
1545:
1540:
1536:
1531:
1527:
1522:
1511:
1507:
1502:
1496:
1491:
1488:
1478:
1473:
1469:
1463:
1456:
1453:
1450:
1447:
1444:
1441:
1436:
1430:
1424:
1418:
1413:
1409:
1403:
1397:
1391:
1388:
1385:
1382:
1379:
1376:
1371:
1364:
1356:
1351:
1347:
1341:
1334:
1331:
1328:
1325:
1322:
1319:
1314:
1308:
1302:
1299:
1296:
1293:
1288:
1284:
1257:
1252:
1248:
1243:
1239:
1234:
1205:
1202:
1198:
1177:
1169:
1164:
1160:
1155:
1151:
1146:
1135:
1131:
1126:
1120:
1114:
1111:
1108:
1105:
1102:
1099:
1096:
1093:
1088:
1084:
1058:
1053:
1049:
1043:
1019:
1016:
1013:
1010:
1007:
1004:
999:
978:
970:
965:
961:
955:
948:
945:
942:
939:
936:
933:
928:
922:
916:
913:
910:
907:
902:
898:
876:carbon dioxide
851:
831:
823:
820:
817:
812:
805:
802:
799:
794:
788:
780:
777:
774:
769:
762:
759:
756:
751:
745:
740:
737:
669:
666:
663:
660:
657:
654:
651:
648:
645:
641:
637:
634:
631:
628:
625:
622:
619:
616:
613:
608:
604:
577:
554:
551:
548:
545:
542:
539:
536:
533:
530:
525:
501:
498:
495:
492:
489:
486:
483:
480:
477:
472:
451:
448:
428:
420:
417:
414:
411:
408:
405:
402:
399:
396:
391:
384:
381:
378:
375:
372:
369:
366:
363:
360:
355:
349:
344:
341:
315:
312:
292:
289:
277:
274:
201:, also called
175:
174:
158:
153:
149:
143:
136:
133:
130:
127:
124:
121:
116:
110:
104:
101:
98:
95:
90:
86:
76:
71:
68:
67:
64:
58:
57:
52:
50:Common symbols
49:
46:
45:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
7492:
7481:
7478:
7476:
7473:
7471:
7468:
7467:
7465:
7452:
7451:
7438:
7432:
7429:
7427:
7424:
7422:
7419:
7417:
7414:
7412:
7409:
7407:
7404:
7402:
7401:Crystal habit
7399:
7397:
7394:
7393:
7390:
7386:
7379:
7374:
7372:
7367:
7365:
7360:
7359:
7356:
7346:
7341:
7327:
7324:
7322:
7319:
7317:
7314:
7312:
7309:
7307:
7304:
7302:
7299:
7298:
7296:
7292:
7282:
7279:
7277:
7274:
7272:
7269:
7267:
7264:
7262:
7259:
7257:
7254:
7252:
7249:
7248:
7246:
7242:
7236:
7235:Safety shower
7233:
7231:
7228:
7226:
7223:
7221:
7218:
7216:
7213:
7212:
7209:
7206:
7203:
7196:
7192:
7185:
7181:
7167:
7164:
7162:
7159:
7158:
7156:
7152:
7146:
7145:Wire stripper
7143:
7141:
7138:
7136:
7133:
7131:
7128:
7127:
7125:
7121:
7115:
7112:
7110:
7107:
7105:
7102:
7100:
7097:
7095:
7092:
7090:
7087:
7085:
7082:
7080:
7077:
7075:
7072:
7071:
7069:
7065:
7059:
7056:
7054:
7051:
7049:
7046:
7044:
7041:
7037:
7034:
7032:
7029:
7028:
7027:
7024:
7023:
7021:
7017:
7013:
7009:
7004:
7000:
6986:
6983:
6981:
6978:
6976:
6975:Spiral plater
6973:
6971:
6968:
6966:
6963:
6962:
6960:
6956:
6950:
6947:
6945:
6942:
6940:
6937:
6933:
6930:
6929:
6928:
6925:
6924:
6922:
6920:
6916:
6910:
6907:
6905:
6902:
6901:
6899:
6897:
6893:
6887:
6884:
6882:
6879:
6877:
6874:
6872:
6869:
6867:
6864:
6862:
6859:
6857:
6854:
6852:
6849:
6847:
6844:
6843:
6841:
6839:Compositional
6837:
6833:
6829:
6824:
6820:
6806:
6803:
6801:
6798:
6796:
6793:
6791:
6788:
6787:
6785:
6781:
6775:
6772:
6770:
6767:
6765:
6762:
6760:
6757:
6755:
6752:
6750:
6747:
6746:
6744:
6742:
6738:
6732:
6729:
6727:
6724:
6722:
6719:
6717:
6714:
6712:
6709:
6707:
6704:
6702:
6699:
6697:
6694:
6693:
6691:
6687:
6681:
6678:
6676:
6673:
6671:
6668:
6666:
6663:
6662:
6660:
6656:
6650:
6647:
6645:
6642:
6640:
6637:
6635:
6632:
6630:
6627:
6625:
6622:
6620:
6617:
6615:
6612:
6610:
6607:
6605:
6602:
6601:
6599:
6597:
6593:
6587:
6584:
6582:
6579:
6577:
6574:
6572:
6569:
6568:
6566:
6562:
6556:
6553:
6551:
6548:
6547:
6545:
6543:
6539:
6533:
6530:
6529:
6527:
6523:
6517:
6514:
6512:
6509:
6507:
6504:
6503:
6501:
6497:
6493:
6489:
6484:
6480:
6466:
6463:
6461:
6458:
6456:
6453:
6451:
6448:
6446:
6443:
6441:
6438:
6436:
6433:
6431:
6428:
6426:
6423:
6421:
6418:
6416:
6413:
6411:
6408:
6406:
6403:
6401:
6398:
6396:
6393:
6391:
6388:
6386:
6383:
6381:Balance brush
6380:
6378:
6375:
6373:
6370:
6369:
6367:
6363:
6357:Weighing dish
6356:
6354:Weighing boat
6353:
6351:
6348:
6346:
6343:
6341:
6338:
6336:
6333:
6331:
6328:
6326:
6323:
6321:
6318:
6316:
6313:
6312:
6310:
6304:
6301:
6300:
6297:
6291:
6288:
6286:
6283:
6281:
6278:
6276:
6273:
6270:
6268:
6265:
6262:
6260:
6257:
6254:
6251:
6248:
6246:
6245:Burette clamp
6243:
6241:
6238:
6236:
6233:
6230:
6229:
6227:
6221:
6219:
6216:
6213:
6212:
6209:
6203:
6200:
6198:
6195:
6193:
6190:
6188:
6185:
6183:
6180:
6178:
6175:
6173:
6170:
6168:
6165:
6163:
6160:
6158:
6155:
6153:
6150:
6149:
6147:
6141:
6138:
6137:
6134:
6128:
6125:
6123:
6120:
6118:
6115:
6112:
6110:
6107:
6105:
6102:
6100:
6097:
6095:
6092:
6090:
6087:
6085:
6082:
6080:
6079:Bunsen burner
6077:
6075:
6072:
6071:
6069:
6063:
6060:
6059:
6056:
6052:
6045:
6041:
6037:
6030:
6025:
6023:
6018:
6016:
6011:
6010:
6007:
6000:
5997:
5996:
5992:
5986:
5984:0-471-20231-2
5980:
5976:
5971:
5967:
5961:
5957:
5952:
5949:
5946:
5943:
5940:
5937:
5934:
5933:
5929:
5921:
5917:
5911:
5908:
5897:
5893:
5886:
5883:
5878:
5872:
5864:
5860:
5856:
5850:
5846:
5839:
5837:
5833:
5828:
5824:
5818:
5816:
5812:
5803:
5797:
5794:
5782:
5778:
5771:
5768:
5755:
5754:
5746:
5743:
5737:
5732:
5728:
5724:
5720:
5713:
5710:
5706:
5701:
5698:
5694:
5689:
5686:
5680:
5677:
5673:
5667:
5665:
5661:
5655:
5653:
5649:
5644:
5640:
5636:
5632:
5628:
5621:
5619:
5615:
5610:
5607:(in German).
5606:
5605:
5597:
5595:
5591:
5588:
5587:0-412-16590-2
5584:
5578:
5576:
5574:
5570:
5565:
5564:
5563:Metric Manual
5556:
5553:
5548:
5546:0-471-34856-2
5542:
5538:
5537:
5529:
5526:
5521:
5520:
5512:
5509:
5503:
5498:
5495:
5493:
5492:Jolly balance
5490:
5488:
5485:
5483:
5480:
5478:
5475:
5473:
5470:
5468:
5465:
5463:
5460:
5459:
5454:
5449:
5446:
5443:
5440:
5437:
5433:
5429:
5424:
5421:
5420:
5419:
5417:
5413:
5409:
5396:
5393:
5390:
5387:
5374:
5364:
5331:
5325:
5314:
5304:
5300:
5291:
5289:
5284:
5276:
5274:
5271:
5270:
5266:
5264:
5261:
5260:
5256:
5254:
5251:
5250:
5246:
5244:
5241:
5240:
5236:
5234:
5231:
5230:
5226:
5224:
5221:
5220:
5216:
5214:
5211:
5210:
5206:
5204:
5201:
5200:
5196:
5194:
5191:
5190:
5186:
5184:
5181:
5180:
5176:
5174:
5171:
5170:
5166:
5164:
5161:
5160:
5156:
5154:
5151:
5150:
5146:
5144:
5141:
5140:
5136:
5134:
5131:
5130:
5126:
5123:
5120:
5119:
5115:
5113:
5110:
5109:
5105:
5102:
5101:
5095:
5093:
5091:
5082:
5080:
5066:
5032:
5028:
5011:
4987:
4984:
4964:
4960:
4943:
4937:
4934:
4917:
4910:
4899:
4869:
4856:
4854:
4852:
4848:
4846:
4842:
4838:
4836:
4832:
4829:
4825:
4821:
4819:
4812:
4807:
4804:
4801:
4797:
4793:
4790:Hubbard, for
4789:
4786:
4782:
4779:
4776:
4775:
4774:
4773:
4769:
4767:
4762:
4758:
4745:
4739:
4736:
4725:
4721:
4705:
4693:
4687:
4676:
4672:
4669:
4658:
4654:
4645:
4632:
4616:
4604:
4598:
4595:
4580:
4568:
4562:
4551:
4547:
4541:
4525:
4513:
4507:
4504:
4489:
4477:
4471:
4458:
4446:
4437:
4426:
4422:
4414:
4409:
4402:
4397:
4389:
4384:
4379:
4375:
4371:
4366:
4353:
4339:
4335:
4324:
4310:
4306:
4295:
4288:
4271:
4267:
4256:
4249:
4246:
4230:
4226:
4215:
4208:
4205:
4199:
4188:
4184:
4173:
4157:
4143:
4139:
4128:
4121:
4118:
4115:
4106:
4098:
4089:
4073:
4059:
4055:
4044:
4037:
4034:
4031:
4022:
4014:
4004:
3991:
3987:
3975:
3971:
3968:
3957:
3953:
3950:
3937:
3925:
3911:
3907:
3896:
3891:
3887:
3884:
3873:
3863:
3856:
3849:
3845:
3841:
3834:
3818:
3814:
3800:
3788:
3774:
3770:
3759:
3754:
3750:
3747:
3736:
3727:
3722:
3720:
3715:
3712:
3707:
3705:
3701:
3697:
3693:
3689:
3686:
3682:
3678:
3674:
3670:
3664:
3658:
3652:
3643:
3642:Ancient Greek
3639:
3633:
3624:
3616:
3609:
3607:
3605:
3600:
3587:
3570:
3564:
3560:
3554:
3548:
3545:
3542:
3526:
3511:
3507:
3499:
3498:
3493:
3489:
3485:
3476:
3469:
3467:
3453:
3433:
3427:
3423:
3417:
3411:
3408:
3404:
3399:
3383:
3368:
3364:
3357:
3356:
3353:
3351:
3350:
3341:
3337:
3333:
3328:
3327:
3317:
3310:
3308:
3294:
3288:
3282:
3279:
3276:
3272:
3267:
3248:
3230:
3224:
3208:
3193:
3189:
3182:
3181:
3178:
3176:
3175:
3170:
3169:
3159:
3152:
3150:
3136:
3130:
3124:
3121:
3118:
3098:
3094:
3091:
3084:
3083:
3080:
3078:
3073:
3069:
3065:
3055:
3048:
3046:
3032:
3029:
3012:
3008:
3005:
2998:
2997:
2994:
2991:
2978:
2975:
2958:
2954:
2951:
2948:
2940:
2934:
2930:
2926:
2923:
2919:
2915:
2907:
2904:
2901:
2897:
2893:
2889:
2886:
2882:
2879:
2876:
2873:
2870:
2867:
2861:
2858:
2852:
2849:
2846:
2842:
2835:
2832:
2831:
2830:
2827:
2823:
2821:
2816:
2814:
2809:
2803:
2798:
2790:
2788:
2784:
2779:
2768:
2765:
2762:
2758:
2751:
2748:
2747:
2746:
2732:
2706:
2702:
2685:
2666:
2660:
2657:
2654:
2641:
2639:
2626:
2623:
2606:
2603:
2589:
2573:
2570:
2556:
2550:
2532:
2516:
2498:
2482:
2475:
2466:
2443:
2418:
2395:
2372:
2353:
2326:
2320:
2317:
2314:
2305:
2292:
2251:
2198:
2187:
2174:
2171:
2163:
2158:
2155:
2151:
2142:
2140:
2137:
2120:
2116:
2110:
2108:
2104:
2100:
2096:
2095:mineralogists
2092:
2088:
2084:
2076:
2074:
2051:
2050:
2049:
2046:
2043:
2008:that while SG
2006:
1999:
1992:
1985:
1978:
1970:
1968:
1963:
1962:
1958:
1956:
1953:
1940:
1929:
1919:
1915:
1912:
1909:
1906:
1871:
1861:
1859:
1847:
1843:
1839:
1820:
1815:
1809:
1786:
1748:
1730:
1722:
1715:
1708:
1701:
1697:
1691:
1669:
1595:
1584:
1577:
1573:
1569:
1564:
1551:
1538:
1529:
1520:
1509:
1500:
1494:
1489:
1486:
1471:
1461:
1434:
1428:
1422:
1411:
1401:
1395:
1369:
1362:
1349:
1339:
1312:
1306:
1286:
1282:
1273:
1250:
1241:
1232:
1203:
1200:
1196:
1175:
1162:
1153:
1144:
1133:
1124:
1118:
1086:
1082:
1073:
1051:
1041:
997:
976:
963:
953:
926:
920:
900:
896:
887:
884:
879:
877:
873:
869:
865:
849:
829:
810:
792:
786:
767:
749:
743:
725:
720:
718:
714:
710:
706:
702:
698:
694:
690:
686:
639:
606:
602:
593:
591:
575:
523:
470:
449:
446:
426:
389:
353:
347:
329:
313:
310:
290:
287:
275:
273:
271:
267:
263:
259:
255:
251:
247:
242:
238:
236:
232:
228:
224:
220:
216:
212:
208:
204:
200:
193:
189:
186:
181:
151:
141:
114:
108:
88:
84:
77:
69:
65:
63:
59:
56:
53:
47:
42:
37:
33:
19:
7470:Mass density
7441:
7425:
7306:Fire blanket
7244:Eye and hand
7230:Rubber apron
7094:Oscilloscope
7058:Potentiostat
6985:Plate reader
6881:pH indicator
6851:CHN analyzer
6846:AutoAnalyzer
6639:Round-bottom
6532:Boston round
6395:Filter paper
6350:Refrigerator
6267:Retort stand
6235:Clamp holder
6231:Beaker clamp
6197:Vortex mixer
6192:Stirring rod
6187:Static mixer
6117:Teclu burner
5974:
5955:
5947:
5941:
5935:
5919:
5910:
5899:. Retrieved
5895:
5885:
5844:
5826:
5796:
5784:. Retrieved
5780:
5770:
5758:. Retrieved
5752:
5745:
5726:
5722:
5712:
5700:
5688:
5679:
5671:
5634:
5630:
5608:
5602:
5562:
5555:
5535:
5528:
5518:
5511:
5410:
5292:
5285:
5282:
5086:
4860:
4850:
4849:
4840:
4839:
4834:
4833:
4823:
4822:
4817:
4816:
4771:
4770:
4763:
4759:
4646:
4415:
4407:
4400:
4387:
4385:
4377:
4369:
4367:
4171:
4087:
4005:
3854:
3847:
3839:
3832:
3725:
3723:
3716:
3708:
3685:ground glass
3672:
3668:
3637:
3635:
3603:
3601:
3495:
3483:
3481:
3470:
3347:
3339:
3335:
3331:
3324:
3322:
3311:
3172:
3166:
3164:
3153:
3076:
3071:
3067:
3063:
3060:
3049:
2992:
2938:
2932:
2928:
2917:
2911:
2905:
2902:is negative.
2899:
2895:
2891:
2880:
2874:
2868:
2859:
2850:
2833:
2828:
2824:
2819:
2817:
2813:displacement
2810:
2807:
2785:
2777:
2775:
2766:
2761:pounds-force
2749:
2645:
2452:Displacement
2404:Displacement
2306:
2216:Displacement
2161:
2159:
2146:
2118:
2111:
2080:
2072:
2047:
2001:
1994:
1987:
1980:
1976:
1973:
1964:
1954:
1862:
1818:
1810:
1746:
1728:
1727:that, while
1720:
1713:
1706:
1699:
1695:
1692:
1593:
1582:
1575:
1571:
1567:
1565:
1274:
1074:
888:
880:
721:
688:
684:
594:
279:
243:
239:
230:
226:
202:
198:
197:
62:SI unit
54:
7294:Other items
7220:Face shield
7067:Measurement
7048:Galvanostat
7008:Electronics
6958:Other items
6944:Thermometer
6927:Calorimeter
6856:Colorimeter
6800:Gas syringe
6783:Other items
6711:Eye dropper
6586:Watch glass
6571:Evaporating
6550:Cold finger
6365:Other items
6271:Screw clamp
6263:Pinch clamp
6252:Flask clamp
6202:Wash bottle
6157:Homogenizer
5729:: 349–392.
5497:Plato scale
5467:Baumé scale
5462:API gravity
5432:albuminuria
5083:Limitations
4845:caesium-137
4802:D 70, 24 mL
4785:thermometer
3702:, using an
3165:Combining (
2920:. From the
2143:Measurement
2115:Plato table
2103:Gemologists
1814:Plato table
872:ideal gases
695:at 4 °
258:must weight
7464:Categories
7421:Mohs scale
7225:Respirator
7166:Test probe
7084:Multimeter
6896:Microscopy
6716:Eudiometer
6680:Separatory
6649:Volumetric
6614:Erlenmeyer
6542:Condensers
6506:Dean–Stark
6455:Wire brush
6415:Microscope
6410:Centrifuge
6385:Cork borer
6340:Petri dish
6315:Agar plate
6302:Containers
6285:Wire gauze
6122:Water bath
6084:Desiccator
5901:2022-01-23
5637:: 97–105.
5611:: 195–196.
5504:References
5487:Hydrometer
5436:glycosuria
5183:Table salt
5112:Balsa wood
4778:Gay-Lussac
4374:hydrometer
3669:pyknometer
3638:pycnometer
3630:See also:
3610:Pycnometer
3494:equation (
3329:) we have
3323:But from (
2922:Archimedes
2797:hydrometer
2791:Hydrometer
2429:Deflection
2381:Deflection
2195:Deflection
2091:geologists
1834: g/cm
864:molar mass
711:or 1
7316:Fume hood
7261:Glove box
7114:Voltmeter
6499:Apparatus
6488:Glassware
6377:Autoclave
6372:Aspirator
6325:Incubator
6259:Iron ring
6182:Sonicator
6152:Chemostat
6094:Hot plate
5871:cite book
5863:228373703
5365:ρ
5332:ρ
5293:Example:
5193:Aluminium
5143:Olive oil
5003:in which
4991:%
4985:×
4961:−
4935:−
4737:−
4706:ρ
4694:ρ
4688:−
4617:ρ
4605:ρ
4599:−
4581:ρ
4569:ρ
4563:−
4526:ρ
4514:ρ
4508:−
4490:ρ
4478:ρ
4472:−
4459:ρ
4447:ρ
4340:ρ
4336:−
4325:ρ
4311:ρ
4307:−
4296:ρ
4272:ρ
4268:−
4257:ρ
4231:ρ
4227:−
4216:ρ
4144:ρ
4140:−
4129:ρ
4060:ρ
4056:−
4045:ρ
3976:ρ
3969:−
3958:ρ
3938:ρ
3912:ρ
3908:−
3801:ρ
3775:ρ
3771:−
3651:romanized
3571:ρ
3558:Δ
3543:≈
3434:ρ
3421:Δ
3412:−
3286:Δ
3280:−
3249:ρ
3231:ρ
3177:) yields
3128:Δ
3122:−
3099:ρ
3079:). Thus,
3013:ρ
2959:ρ
2843:per unit
2703:−
2604:×
2571:×
2354:ρ
2327:ρ
2252:×
2199:×
2172:ρ
2107:gemstones
2057:4 °C
2035:0.9999720
2029:0.9982008
1920:ρ
1916:×
1872:ρ
1838:cgs units
1340:ρ
1313:ρ
1042:ρ
998:ρ
954:ρ
927:ρ
787:≈
768:ρ
750:ρ
689:reference
685:substance
576:ρ
524:ρ
471:ρ
390:ρ
354:ρ
248:(101.325
142:ρ
115:ρ
7411:Fracture
7396:Cleavage
7215:Lab coat
7140:Tweezers
7130:Heat gun
6886:pH meter
6795:Bell jar
6675:Dropping
6629:Florence
6619:Fernbach
6581:Syracuse
6440:Scoopula
6390:Crucible
6099:Lab oven
5672:op. cit.
5472:Buoyancy
5455:See also
5177:1.9–2.3
5173:Graphite
5163:Ironwood
5103:Material
5096:Examples
4396:in vacuo
3352:) gives
2993:or just
2925:buoyancy
2083:buoyancy
1977:in vacuo
1712:), with
1696:in vacuo
66:Unitless
7154:General
7074:Ammeter
6774:Thistle
6731:Pipette
6706:Cuvette
6696:Burette
6665:Büchner
6658:Funnels
6644:Schlenk
6624:Fleaker
6604:Büchner
6525:Bottles
6445:Spatula
6435:Stopper
6405:Forceps
6305:Storage
6222:Holders
6142:Shakers
6113:Striker
6061:Heaters
6048:General
5786:Sep 15,
5760:Sep 15,
5243:Mercury
5133:Ethanol
5090:bubbles
4792:bitumen
4399:), for
3700:mercury
3690:with a
3688:stopper
3677:density
3665:
3653::
3490:of the
3171:) and (
2883:is the
2863:new/ref
2757:newtons
2207:Gravity
2099:mineral
2038:
2026:
1993:) with
1967:Density
1858:A. Brix
1844:). The
1766:⁄
862:is the
326:) is a
215:density
213:of the
205:, is a
7480:Ratios
7431:Streak
7416:Lustre
7188:Safety
6790:Beaker
6769:Thiele
6754:Cragie
6749:Drying
6670:Hirsch
6634:Retort
6596:Flasks
6564:Dishes
6555:Liebig
6516:Kipp's
6430:Splint
6240:Tripod
6218:Clamps
6214:Stands
6177:Shaker
6139:Mixers
6064:Dryers
5981:
5962:
5861:
5851:
5807:
5585:
5543:
5412:Helium
5277:22.59
5273:Osmium
5247:13.56
5237:11.35
5223:Copper
5203:Cement
5059:, and
4170:where
3831:where
3657:puknos
3646:πυκνός
3640:(from
2845:volume
2745:where
2610:
2593:
2577:
2560:
2536:
2520:
2502:
2486:
2183:Volume
2042:ITS-90
1785:ITS-90
1579:sample
1566:where
1514:sample
1208:sample
1188:where
1138:sample
989:where
842:where
439:where
262:syrups
254:brines
7123:Tools
6741:Tubes
6576:Petri
5448:Vodka
5442:Blood
5423:Urine
5267:19.3
5257:19.1
5227:8.96
5217:7.87
5207:3.15
5187:2.17
5153:Water
5147:0.91
5137:0.78
5127:0.75
4772:Types
3696:water
3681:glass
2781:water
2770:water
2627:1.02.
2087:fluid
1851:0.998
1830:0.999
1803:0.998
1796:0.999
1789:0.998
1778:0.998
1769:0.999
1760:0.998
1740:1.000
693:water
219:water
211:ratio
6805:Vial
6764:Test
6400:File
6104:Kiln
5979:ISBN
5960:ISBN
5877:link
5859:OCLC
5849:ISBN
5788:2024
5762:2024
5583:ISBN
5541:ISBN
5263:Gold
5233:Lead
5213:Iron
5197:2.7
5167:1.5
5124:wood
5116:0.2
4800:ASTM
4794:and
4766:ASTM
3842:the
3663:lit.
2841:mass
2257:Area
2180:Mass
2136:ASBC
2093:and
2077:Uses
1965:See
1853:2343
1846:ASBC
1798:9720
1794:and
1791:2041
1780:2288
1771:9720
1762:2008
270:must
266:wort
227:r.d.
194:fuel
192:JP-5
5731:doi
5727:216
5639:doi
5609:100
5434:or
5416:air
5122:Oak
4988:100
3698:or
3671:or
3343:ref
2936:ref
2854:new
2837:ref
2753:air
1836:in
1832:972
1805:232
1742:000
868:mol
724:air
590:rho
250:kPa
246:atm
229:or
7466::
5918:.
5894:.
5873:}}
5869:{{
5857:.
5835:^
5825:.
5814:^
5779:.
5725:.
5721:.
5663:^
5651:^
5635:20
5633:.
5629:.
5617:^
5593:^
5572:^
5157:1
4388:RD
4378:RD
3717:A
3706:.
3660:,
3648:,
3644::
3636:A
3334:=
3066:−
2939:Vg
2918:mg
2860:RD
2759:,
2607:20
2574:34
2533:34
2499:20
2024:=
1808:.
1776:=
1756:=
1747:SG
1738:=
1729:SG
717:cm
705:kg
701:SI
268:,
256:,
235:SI
231:RD
183:A
55:SG
7377:e
7370:t
7363:v
6028:e
6021:t
6014:v
5987:.
5968:.
5922:.
5904:.
5879:)
5865:.
5829:.
5790:.
5764:.
5739:.
5733::
5645:.
5641::
5549:.
5438:.
5397:,
5394:D
5391:R
5388:=
5380:O
5375:2
5371:H
5358:l
5355:a
5352:i
5349:r
5346:e
5343:t
5340:a
5337:M
5326:=
5320:O
5315:2
5311:H
5305:D
5301:R
5067:e
5044:n
5041:i
5038:m
5033:e
5029:,
5023:x
5020:a
5017:m
5012:e
4976:n
4973:i
4970:m
4965:e
4955:x
4952:a
4949:m
4944:e
4938:e
4929:x
4926:a
4923:m
4918:e
4911:=
4905:R
4900:D
4875:R
4870:D
4746:.
4743:)
4740:1
4731:A
4726:D
4722:R
4719:(
4711:w
4699:a
4682:A
4677:D
4673:R
4670:=
4664:V
4659:D
4655:R
4633:.
4622:w
4610:a
4596:1
4586:w
4574:a
4557:V
4552:D
4548:R
4542:=
4531:w
4519:a
4505:1
4495:w
4483:a
4464:w
4452:s
4438:=
4432:A
4427:D
4423:R
4411:w
4408:ρ
4406:/
4404:s
4401:ρ
4391:V
4381:A
4354:.
4345:a
4330:w
4316:a
4301:s
4289:=
4283:)
4277:a
4262:w
4253:(
4250:V
4247:g
4242:)
4236:a
4221:s
4212:(
4209:V
4206:g
4200:=
4194:A
4189:G
4185:S
4175:s
4172:ρ
4158:,
4155:)
4149:a
4134:s
4125:(
4122:V
4119:g
4116:=
4110:n
4107:,
4104:s
4099:F
4088:n
4074:,
4071:)
4065:a
4050:w
4041:(
4038:V
4035:g
4032:=
4026:n
4023:,
4020:w
4015:F
3992:.
3988:)
3981:a
3972:V
3963:w
3954:V
3951:+
3943:b
3931:b
3926:m
3917:a
3902:b
3897:m
3892:(
3888:g
3885:=
3879:w
3874:F
3858:b
3855:ρ
3851:a
3848:ρ
3840:g
3836:b
3833:m
3819:,
3815:)
3806:b
3794:b
3789:m
3780:a
3765:b
3760:m
3755:(
3751:g
3748:=
3742:b
3737:F
3726:V
3604:x
3588:.
3582:f
3579:e
3576:r
3565:m
3561:x
3555:A
3549:+
3546:1
3537:f
3534:e
3531:r
3527:/
3523:w
3520:e
3517:n
3512:D
3508:R
3497:4
3484:x
3475:)
3473:4
3471:(
3454:.
3445:f
3442:e
3439:r
3428:m
3424:x
3418:A
3409:1
3405:1
3400:=
3394:f
3391:e
3388:r
3384:/
3380:w
3377:e
3374:n
3369:D
3365:R
3349:3
3340:ρ
3338:/
3336:m
3332:V
3326:1
3316:)
3314:3
3312:(
3295:.
3289:x
3283:A
3277:V
3273:V
3268:=
3260:f
3257:e
3254:r
3242:w
3239:e
3236:n
3225:=
3219:f
3216:e
3213:r
3209:/
3205:w
3202:e
3199:n
3194:D
3190:R
3174:2
3168:1
3158:)
3156:2
3154:(
3137:.
3134:)
3131:x
3125:A
3119:V
3116:(
3110:w
3107:e
3104:n
3095:=
3092:m
3077:x
3072:x
3070:Δ
3068:A
3064:V
3054:)
3052:1
3050:(
3033:.
3030:V
3024:f
3021:e
3018:r
3009:=
3006:m
2979:g
2976:V
2970:f
2967:e
2964:r
2955:=
2952:g
2949:m
2933:ρ
2929:g
2906:A
2900:x
2896:x
2892:x
2890:Δ
2887:.
2881:g
2875:m
2869:V
2851:ρ
2834:ρ
2820:x
2778:W
2767:W
2750:W
2733:,
2724:r
2721:e
2718:t
2715:a
2712:w
2707:W
2697:r
2694:i
2691:a
2686:W
2678:r
2675:i
2672:a
2667:W
2661:=
2658:D
2655:R
2624:=
2617:m
2614:m
2600:n
2597:i
2590:5
2584:m
2581:m
2567:n
2564:i
2557:3
2551:=
2543:m
2540:m
2527:n
2524:i
2517:5
2509:m
2506:m
2493:n
2490:i
2483:3
2476:=
2467:.
2464:f
2461:e
2458:R
2444:.
2441:f
2438:e
2435:R
2419:.
2416:j
2413:b
2410:O
2396:.
2393:j
2390:b
2387:O
2373:=
2365:f
2362:e
2359:r
2347:t
2344:c
2341:e
2338:j
2335:b
2332:o
2321:=
2318:D
2315:R
2293:.
2284:r
2281:e
2278:d
2275:n
2272:i
2269:l
2266:y
2263:C
2246:e
2243:n
2240:i
2237:L
2234:r
2231:e
2228:t
2225:a
2222:W
2188:=
2175:=
2162:ρ
2132:O
2128:2
2123:H
2121:(
2119:ρ
2066:0
2032:/
2022:O
2020:2
2018:H
2014:O
2012:2
2010:H
2004:r
2002:T
1997:s
1995:T
1990:r
1988:T
1986:/
1983:s
1981:T
1941:.
1935:O
1930:2
1926:H
1913:G
1910:S
1907:=
1901:e
1898:c
1895:n
1892:a
1889:t
1886:s
1883:b
1880:u
1877:s
1826:O
1824:2
1822:H
1819:ρ
1754:O
1752:2
1750:H
1736:O
1734:2
1732:H
1724:r
1721:T
1717:s
1714:T
1710:r
1707:T
1705:/
1703:s
1700:T
1675:O
1670:2
1666:H
1658:m
1632:e
1629:l
1626:p
1623:m
1620:a
1617:s
1610:m
1597:V
1594:W
1590:O
1588:2
1586:H
1583:ρ
1576:ρ
1572:V
1568:g
1552:,
1544:O
1539:2
1535:H
1530:,
1526:V
1521:W
1510:,
1506:V
1501:W
1495:=
1490:g
1487:g
1477:O
1472:2
1468:H
1462:m
1455:e
1452:l
1449:p
1446:m
1443:a
1440:s
1435:m
1429:=
1423:V
1417:O
1412:2
1408:H
1402:m
1396:V
1390:e
1387:l
1384:p
1381:m
1378:a
1375:s
1370:m
1363:=
1355:O
1350:2
1346:H
1333:e
1330:l
1327:p
1324:m
1321:a
1318:s
1307:=
1301:e
1298:u
1295:r
1292:t
1287:G
1283:S
1256:O
1251:2
1247:H
1242:,
1238:A
1233:W
1204:,
1201:A
1197:W
1176:,
1168:O
1163:2
1159:H
1154:,
1150:A
1145:W
1134:,
1130:A
1125:W
1119:=
1113:t
1110:n
1107:e
1104:r
1101:a
1098:p
1095:p
1092:a
1087:G
1083:S
1057:O
1052:2
1048:H
1018:e
1015:l
1012:p
1009:m
1006:a
1003:s
977:,
969:O
964:2
960:H
947:e
944:l
941:p
938:m
935:a
932:s
921:=
915:e
912:u
909:r
906:t
901:G
897:S
850:M
830:,
822:r
819:i
816:a
811:M
804:s
801:a
798:g
793:M
779:r
776:i
773:a
761:s
758:a
755:g
744:=
739:D
736:R
715:/
713:g
709:m
707:/
697:C
668:e
665:c
662:n
659:e
656:r
653:e
650:f
647:e
644:r
640:/
636:e
633:c
630:n
627:a
624:t
621:s
618:b
615:u
612:s
607:D
603:R
553:e
550:c
547:n
544:e
541:r
538:e
535:f
532:e
529:r
500:e
497:c
494:n
491:a
488:t
485:s
482:b
479:u
476:s
450:D
447:R
427:,
419:e
416:c
413:n
410:e
407:r
404:e
401:f
398:e
395:r
383:e
380:c
377:n
374:a
371:t
368:s
365:b
362:u
359:s
348:=
343:D
340:R
314:G
311:S
291:D
288:R
260:(
157:O
152:2
148:H
135:e
132:l
129:p
126:m
123:a
120:s
109:=
103:e
100:u
97:r
94:t
89:G
85:S
38:.
20:)
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