94: – were able to establish the laws of gases. The situation with respect to "social physics" is reversed... If Robert Boyle had taken the attitude of many social scientists, he would not have been willing to measure the pressure and volume of a sample of air until an encyclopedic history of its molecules had been compiled. Boyle did not even know that air contained argon and helium but he found a very important law.
666:
44:
behaviour for large numbers of human beings. A basic conception within it is that large numbers of people, in a city for example, actually behave as an attractive force for other people to migrate there. It has been related to W. J.
102:
formulae of gravitation to that of "the average interrelations of people" on a wide geographic scale, elucidating such notions as "the demographic force of attraction," demographic energy, force, potential and gradient.
487:
392:
175:
297:
237:
340:
914:, 1950. Potential of Population and its Relationship to Marketing. In: Theory in Marketing, R. Cox and W. Alderson (Eds) ( Richard D. Irwin, Inc., Homewood, Illinois).
848:
768:
735:
702:
552:
524:
828:
808:
788:
544:
957:
1021:
Higgins, Benjamin, and Savoie, David J. "Regional development theories and their application", pp. 151–155, Transaction
Publishers, New Jersey, 1997.
859:
46:
908:, 1947. Empirical Mathematical Rules Concerning the Distribution and Equilibrium of Population, Geographical Review, Vol 37, 461–486.
404:
The potential of population at any point is equivalent to the measure of proximity of people at that point (this also has relevance to
424:
953:
John Q. Stewart Papers (C0571) 1907–1970s A Finding Aid, Manuscripts
Division Department of Rare Books and Special Collections
881:
355:
86:
Fortunately for physics, the macroscopic approach was the commonsense one, and the early investigators –
244:
Demographic energy = (population 1, multiplied by population 2) divided by distance; this is also Zipf's determinant
121:
1032:
Reilly, W.J. “Methods for the Study of Retail
Relationships” University of Texas, Bulletin No 2944, November 1929.
920:, 1946. The P1 P2/D Hypothesis: On the Intercity Movement of Persons. American Sociological Review, vol. 11, Oct
252:
190:
961:
1022:
1011:
942:
Stewart, J.Q. "The
Development of Social Physics", American Journal of Physics, Vol 18 (1950), pp. 239-253
494:
Population 1 divided by (distance to balance, squared) = Population 2 / (distance to balance, squared)
312:
888:
876:
870:
50:
23:
1081:
911:
905:
99:
29:
1063:
Rybski, Ros, Kropp "Distance-weighted city growth", Physical Review E, Vol 87 (2013), p. 042114,
991:
111:
The following are some of the key equations (with plain
English paraphrases) from his article in
418:
For comparison, Reilly's retail gravity equilibrium (or
Balance/Break Point) is paraphrased as:
1064:
864:
661:{\displaystyle p_{j}=C{\frac {\sum _{k}w_{k}d_{j,k}^{-\gamma }}{\sum _{k}d_{j,k}^{-\gamma }}}}
54:
33:
833:
740:
707:
674:
502:
304:
Demographic potential of population at point 1 = population at point 2, divided by distance
182:
Demographic force = (population 1 multiplied by population 2) divided by (distance squared)
79:
813:
793:
773:
529:
26:
347:
Demographic potential in general = population divided by distance, in persons per mile
1075:
899:
412:
408:
75:
499:
Recently, a stochastic version has been proposed according to which the probability
893:
87:
923:
917:
71:
67:
41:
112:
91:
62:
1006:
Reiser, Oliver L. "Technology and
Society" in Kostelanetz, Richard (Ed.),
405:
986:
Stewart, John Q., "Demographic
Gravitation: Evidence and Applications,"
926:, 1949. Human Behaviour and the Principle of Least Effort. Massachusetts
995:
37:
1050:
Stewart, J.Q. “Demographic
Gravitation: Evidence and Application”
399:
Demographic gradient = persons per (i.e. divided by) square mile
66:, Stewart set out an "agenda for social physics." Comparing the
1041:
Reilly, W.J. "The Law of Retail
Gravitation", New York, 1931.
482:{\displaystyle {\frac {N_{1}}{d^{2}}}={\frac {N_{2}}{d^{2}}}}
32:
in 1947. It is an attempt to use equations and notions of
836:
816:
796:
776:
743:
710:
677:
555:
532:
505:
427:
358:
315:
255:
193:
124:
1008:
Beyond Left and Right: Radical Thought for Our Times
990:, Vol. 11, No. 1/2. (February–May 1948), pp. 31–58.
387:{\displaystyle {\text{gradient}}={\frac {N}{m^{2}}}}
842:
822:
802:
782:
762:
729:
696:
660:
538:
518:
481:
386:
334:
291:
231:
169:
1010:p. 85, William Morrow & Co., New York, 1968.
830:controls the overall growth-rate. The parameter
22:is a concept of "social physics", introduced by
40:, to seek simplified insights and even laws of
170:{\displaystyle F={\frac {N_{1}N_{2}}{d^{2}}}}
74:viewpoints in the methodology of formulating
8:
53:'s Demographic Energy, and to the theory of
982:
980:
978:
835:
815:
795:
775:
748:
742:
715:
709:
682:
676:
646:
635:
625:
610:
599:
589:
579:
572:
560:
554:
531:
510:
504:
471:
461:
455:
444:
434:
428:
426:
376:
367:
359:
357:
322:
314:
292:{\displaystyle PN_{1}={\frac {N_{2}}{d}}}
278:
272:
263:
254:
232:{\displaystyle E={\frac {N_{1}N_{2}}{d}}}
217:
207:
200:
192:
159:
148:
138:
131:
123:
1054:, vol. XI, February–May 1948, pp. 31–58.
55:trip distribution through gravity models
935:
850:determines the degree of compactness.
955:, Princeton University Library, 2004
7:
860:Reilly's law of retail gravitation
47:Reilly's law of retail gravitation
14:
335:{\displaystyle P={\frac {N}{d}}}
1065:doi:10.1103/PhysRevE.87.042114
896:'s least cost location theory.
770:is the distance between sites
78:, he made an analogy with the
1:
546:to become urban is given by
98:Stewart proceeded to apply
1098:
882:Johann Heinrich von ThĂĽnen
958:"John Q. Stewart Papers"
843:{\displaystyle \gamma }
763:{\displaystyle d_{j,k}}
730:{\displaystyle w_{k}=0}
697:{\displaystyle w_{k}=1}
413:Economic rent#Land rent
60:Writing in the journal
20:Demographic gravitation
887:Walther Christaller's
844:
824:
804:
784:
764:
731:
698:
662:
540:
520:
483:
388:
336:
293:
233:
171:
96:
873:'s demographic energy
845:
825:
805:
785:
765:
732:
699:
663:
541:
521:
519:{\displaystyle p_{j}}
484:
389:
337:
294:
234:
172:
84:
889:central place theory
884:'s spatial economics
877:Central place theory
871:George Kingsley Zipf
834:
814:
794:
774:
741:
708:
704:for urban sites and
675:
553:
530:
503:
425:
356:
313:
253:
191:
122:
51:George Kingsley Zipf
24:Princeton University
951:Vecchia, Karla J.,
912:John Quincy Stewart
906:John Quincy Stewart
654:
618:
30:John Quincy Stewart
840:
820:
800:
780:
760:
727:
694:
658:
631:
630:
595:
584:
536:
516:
479:
384:
332:
289:
229:
167:
865:Trip distribution
823:{\displaystyle C}
803:{\displaystyle k}
783:{\displaystyle j}
656:
621:
575:
539:{\displaystyle j}
477:
450:
382:
362:
330:
287:
227:
165:
34:classical physics
1089:
1067:
1061:
1055:
1048:
1042:
1039:
1033:
1030:
1024:
1019:
1013:
1004:
998:
984:
973:
972:
970:
969:
960:. Archived from
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943:
940:
849:
847:
846:
841:
829:
827:
826:
821:
809:
807:
806:
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645:
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393:
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385:
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341:
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323:
298:
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273:
268:
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238:
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201:
176:
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163:
154:
153:
152:
143:
142:
132:
1097:
1096:
1092:
1091:
1090:
1088:
1087:
1086:
1072:
1071:
1070:
1062:
1058:
1049:
1045:
1040:
1036:
1031:
1027:
1020:
1016:
1005:
1001:
985:
976:
967:
965:
956:
950:
946:
941:
937:
933:
867:: gravity model
856:
832:
831:
812:
811:
792:
791:
772:
771:
744:
739:
738:
711:
706:
705:
678:
673:
672:
620:
585:
574:
556:
551:
550:
528:
527:
506:
501:
500:
467:
457:
440:
430:
423:
422:
372:
354:
353:
311:
310:
274:
259:
251:
250:
213:
203:
202:
189:
188:
155:
144:
134:
133:
120:
119:
109:
80:social sciences
17:
12:
11:
5:
1095:
1093:
1085:
1084:
1074:
1073:
1069:
1068:
1056:
1043:
1034:
1025:
1014:
999:
974:
944:
934:
932:
929:
928:
927:
921:
915:
909:
903:
897:
891:
885:
879:
874:
868:
862:
855:
852:
839:
819:
799:
779:
757:
754:
751:
747:
726:
723:
718:
714:
693:
690:
685:
681:
669:
668:
652:
649:
644:
641:
638:
634:
628:
624:
616:
613:
608:
605:
602:
598:
592:
588:
582:
578:
571:
568:
563:
559:
535:
513:
509:
490:
489:
474:
470:
464:
460:
454:
447:
443:
437:
433:
395:
394:
379:
375:
371:
366:
343:
342:
329:
326:
321:
318:
300:
299:
286:
281:
277:
271:
266:
262:
258:
240:
239:
226:
220:
216:
210:
206:
199:
196:
178:
177:
162:
158:
151:
147:
141:
137:
130:
127:
108:
105:
27:astrophysicist
15:
13:
10:
9:
6:
4:
3:
2:
1094:
1083:
1080:
1079:
1077:
1066:
1060:
1057:
1053:
1047:
1044:
1038:
1035:
1029:
1026:
1023:
1018:
1015:
1012:
1009:
1003:
1000:
997:
993:
989:
983:
981:
979:
975:
964:on 2007-06-10
963:
959:
954:
948:
945:
939:
936:
930:
925:
922:
919:
916:
913:
910:
907:
904:
901:
900:Economic rent
898:
895:
892:
890:
886:
883:
880:
878:
875:
872:
869:
866:
863:
861:
858:
857:
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851:
837:
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777:
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749:
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724:
721:
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691:
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679:
650:
647:
642:
639:
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632:
626:
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611:
606:
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586:
580:
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569:
566:
561:
557:
549:
548:
547:
533:
511:
507:
497:
495:
472:
468:
462:
458:
452:
445:
441:
435:
431:
421:
420:
419:
416:
414:
410:
409:economic rent
407:
402:
400:
377:
373:
369:
364:
352:
351:
350:
348:
327:
324:
319:
316:
309:
308:
307:
305:
284:
279:
275:
269:
264:
260:
256:
249:
248:
247:
245:
224:
218:
214:
208:
204:
197:
194:
187:
186:
185:
183:
160:
156:
149:
145:
139:
135:
128:
125:
118:
117:
116:
114:
107:Key equations
106:
104:
101:
95:
93:
89:
83:
81:
77:
76:physical laws
73:
69:
65:
64:
58:
56:
52:
48:
43:
39:
35:
31:
28:
25:
21:
16:Social effect
1059:
1051:
1046:
1037:
1028:
1017:
1007:
1002:
987:
966:. Retrieved
962:the original
952:
947:
938:
902:: Land rent.
894:Alfred Weber
670:
498:
493:
491:
417:
403:
398:
396:
346:
344:
303:
301:
243:
241:
181:
179:
110:
97:
85:
61:
59:
19:
18:
924:Zipf, G. K.
918:Zipf, G. K.
737:otherwise,
90:, Charles,
72:macroscopic
68:microscopic
42:demographic
1082:Demography
1052:Sociometry
988:Sociometry
968:2007-10-22
931:References
526:of a site
113:sociometry
92:Gay-Lussac
63:Sociometry
36:, such as
838:γ
651:γ
648:−
623:∑
615:γ
612:−
577:∑
100:Newtonian
1076:Category
854:See also
406:Georgist
361:gradient
996:2785468
411:theory
70:versus
38:gravity
994:
810:, and
671:where
992:JSTOR
88:Boyle
790:and
415:).
1078::
977:^
496:)
401:)
349:)
306:)
246:)
184:)
115::
82::
57:.
49:,
971:.
818:C
798:k
778:j
756:k
753:,
750:j
746:d
725:0
722:=
717:k
713:w
692:1
689:=
684:k
680:w
643:k
640:,
637:j
633:d
627:k
607:k
604:,
601:j
597:d
591:k
587:w
581:k
570:C
567:=
562:j
558:p
534:j
512:j
508:p
492:(
473:2
469:d
463:2
459:N
453:=
446:2
442:d
436:1
432:N
397:(
378:2
374:m
370:N
365:=
345:(
328:d
325:N
320:=
317:P
302:(
285:d
280:2
276:N
270:=
265:1
261:N
257:P
242:(
225:d
219:2
215:N
209:1
205:N
198:=
195:E
180:(
161:2
157:d
150:2
146:N
140:1
136:N
129:=
126:F
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