40:
500:
166:, wherein once a month they read a range of essays on varying subjects, this society met frequently until 1804. After this, Spence visited many places in England, he lived in London for a few months where, in 1809, he published his first work. In 1814, he published his second work, getting married in the same year – Spence intended to live in London, and began his journey back before becoming ill, having travelled as far as
577:
to edit Spence's manuscripts. Spence was held in such high regard by Galt, and later
Herschel that they published a collection of his individual essays in 1819. Posthumously, his work was met with appreciation from his contemporaries, with a review in the ninety-fourth number of the
899:
453:
308:
569:
Spence's work was noted to be remarkable at the time, with John
Herschel, his acquaintance and one of Britain's leading mathematicians at the time, had referenced it in one of his later publications
590:" first formal essay in our language on any distinct and considerable branch of the integral calculus, which has appeared since… Hellinsʼs papers on the ‘Rectification of the Conic Sections".
151:, who documented much of his life and his works posthumously. Despite having received a formal education until he was a teenager, Spence never attended university, instead he moved to
187:
An Essay on the Theory of the
Various Orders of Logarithmic Transcendents: With an Inquiry Into Their Applications to the Integral Calculus and the Summation of Series in 1809.
353:
94:
A D D Craik, The 'Mathematical Essays' of
William Spence (1777–1815), Historia Mathematica 40: 4 (2013), 386–422. Image accredited to the Watt Institute, Inverclyde Council
541:
147:
From an early age, Spence was characterised as having a docile and reasonable nature, with him being mature for his age. At school he formed a life-long friendship with
757:
An Essay on the Theory of the
Various Orders of Logarithmic Transcendents: With an Inquiry Into Their Applications to the Integral Calculus and the Summation of Series
548:
Outlines of a theory of
Algebraical Equations, deduced from the principles of Harriott, and extended to the fluxional or differential calculus was published in 1814.
486:
364:
815:
Outlines of a theory of
Algebraical Equations, deduced from the principles of Harriott, and extended to the fluxional or differential calculus
986:
838:
Mathematical Essays, by the Late
William Spence, Esq. Edited by John F. W. Herschel, Esq. With a Biographical Sketch of the Author
207:
550:
In which he took a systematic approach to solving equations up to the fourth degree using symmetrical functions of the roots.
194:
925:
991:
20:
996:
197:, which is notable since at the time very few were familiar with their works. In his preface he derived the
981:
316:
636:"Polylogarithms, functional equations and more: The elusive essays of William Spence (1777–1815)"
510:
706:
667:
125:
113:
785:
136:
Spence was the second son to Ninian Spence and his wife Sarah
Townsend. Ninian Spence ran a
1006:
1001:
493:
148:
8:
465:
174:
958:
881:
117:
105:
962:
885:
841:
818:
760:
155:
where he lodged with a friend of his fathers, learning the skills of a manufacturer.
121:
109:
355:. He went on further to derive nine general properties of this function in a table.
950:
871:
647:
579:
198:
163:
448:{\displaystyle L_{2}(x)=-\int _{0}^{x}{\frac {\ln(1-t)}{t}}\operatorname {d} \!t}
39:
488:
from 1 to 100, the first ever of its kind. These functions became known as the
845:
822:
710:
201:
and mainly focused on the properties and analytic applications of the series:
112:, Scotland) was a Scottish mathematician who published works on the fields of
975:
728:
652:
635:
574:
561:, which was published in 1819, with John Galt writing a biography on Spence.
554:
489:
764:
503:
Spence's numerical calculation of the dilogarithm from (Spence, 1809, p. 24)
954:
876:
859:
499:
459:
137:
668:"Greenock - Towns - Scottish Directories - National Library of Scotland"
162:
in 1797. With the support of Galt and others, he established a small
190:
159:
141:
189:
Throughout his work, he displayed a familiarity with the work of
167:
152:
462:) to nine decimal places, in a table, for all integer values of
158:
Two years after his father's death in 1795, Spence returned to
140:
business, and the Spence family were a prominent family in
303:{\displaystyle \pm x/1^{n}-x^{2}/2^{n}\pm x^{3}/3^{n}-...}
943:
864:
Philosophical Transactions of the Royal Society of London
131:
584:
The Literary and Miscellanies of John Galt, Volume 1)
513:
468:
367:
319:
210:
941:"XVIL. Of the rectification of the conic sections".
697:
Galt, J. (May 1819). "THE LATE MR. WILLIAM SPENCE".
860:"XXII. Consideration of various points of analysis"
759:. John Murray and Archibald Constable and Company.
535:
492:functions, with this particular case often called
480:
447:
347:
302:
840:. Thomas and George Underwood, 32, Fleet Street.
441:
973:
927:The Literary Life and Miscellanies of John Galt
559:Mathematical Essays by the late William Spence
507:Later on he also created a similar table for
571:Consideration of various points of analysis,
358:Spence goes on to calculate the values of:
19:For other people named William Spence, see
586:that described his first work in 1809 as:
38:
875:
651:
498:
170:, he died in his sleep due to illness.
974:
835:
812:
754:
633:
629:
627:
625:
623:
132:Early life, family, and personal life
987:19th-century Scottish mathematicians
923:
808:
806:
780:
778:
776:
774:
750:
748:
746:
744:
742:
740:
726:
722:
720:
696:
692:
690:
688:
621:
619:
617:
615:
613:
611:
609:
607:
605:
603:
13:
438:
180:
16:Scottish mathematician (1777–1815)
14:
1018:
829:
803:
771:
737:
717:
685:
634:Craik, Alex D.D. (October 2013).
600:
108:, Scotland – died 22 May 1815 in
546:Spence published his last work,
934:
917:
892:
21:William Spence (disambiguation)
904:historydb.adlerplanetarium.org
900:"John Herschel Correspondence"
852:
730:The autobiography of John Galt
660:
429:
417:
384:
378:
342:
330:
1:
949:: 448–476. 31 December 1802.
870:: 440–468. 31 December 1814.
594:
348:{\displaystyle L_{n}(1\pm x)}
786:"William Spence – Biography"
7:
536:{\displaystyle \tan ^{-1}x}
173:Spence held an interest in
10:
1023:
18:
564:
92:
87:
70:
58:
46:
37:
30:
836:Spence, William (1819).
813:Spence, William (1814).
755:Spence, William (1809).
653:10.1016/j.hm.2013.06.002
177:, and played the flute.
992:Scientists from Glasgow
80:Sarah Townsend (mother)
955:10.1098/rstl.1802.0020
877:10.1098/rstl.1814.0023
582:(reproduced in Galt's
553:After Spence's death,
537:
504:
482:
449:
349:
313:which he denoted with
304:
120:and their relation to
104:(born 31 July 1777 in
77:Ninian Spence (father)
538:
502:
483:
450:
350:
305:
126:differential calculus
114:logarithmic functions
62:20 May 1815 (aged 37)
997:People from Greenock
699:The Monthly Magazine
640:Historia Mathematica
511:
466:
365:
317:
208:
924:Galt, John (1834).
733:. Key & Biddle.
727:Galt, John (1833).
481:{\displaystyle 1+x}
407:
175:musical composition
118:algebraic equations
982:Scottish flautists
533:
505:
478:
445:
393:
345:
300:
53:Greenock, Scotland
494:Spence's function
436:
185:Spence published
99:
98:
65:Glasgow, Scotland
1014:
967:
966:
938:
932:
931:
921:
915:
914:
912:
910:
896:
890:
889:
879:
856:
850:
849:
833:
827:
826:
810:
801:
800:
798:
796:
782:
769:
768:
752:
735:
734:
724:
715:
714:
705:(325): 373–375.
694:
683:
682:
680:
678:
664:
658:
657:
655:
631:
580:Quarterly Review
542:
540:
539:
534:
526:
525:
487:
485:
484:
479:
454:
452:
451:
446:
437:
432:
409:
406:
401:
377:
376:
354:
352:
351:
346:
329:
328:
309:
307:
306:
301:
287:
286:
277:
272:
271:
259:
258:
249:
244:
243:
231:
230:
221:
199:binomial theorem
164:literary society
42:
28:
27:
1022:
1021:
1017:
1016:
1015:
1013:
1012:
1011:
972:
971:
970:
940:
939:
935:
930:. W. Blackwood.
922:
918:
908:
906:
898:
897:
893:
858:
857:
853:
834:
830:
811:
804:
794:
792:
784:
783:
772:
753:
738:
725:
718:
695:
686:
676:
674:
666:
665:
661:
632:
601:
597:
573:which prompted
567:
518:
514:
512:
509:
508:
467:
464:
463:
410:
408:
402:
397:
372:
368:
366:
363:
362:
324:
320:
318:
315:
314:
282:
278:
273:
267:
263:
254:
250:
245:
239:
235:
226:
222:
217:
209:
206:
205:
183:
181:Published works
134:
95:
83:
66:
63:
54:
51:
33:
24:
17:
12:
11:
5:
1020:
1010:
1009:
1004:
999:
994:
989:
984:
969:
968:
933:
916:
891:
851:
828:
802:
770:
736:
716:
684:
672:digital.nls.uk
659:
646:(4): 386–422.
598:
596:
593:
566:
563:
532:
529:
524:
521:
517:
496:after Spence.
477:
474:
471:
456:
455:
444:
440:
435:
431:
428:
425:
422:
419:
416:
413:
405:
400:
396:
392:
389:
386:
383:
380:
375:
371:
344:
341:
338:
335:
332:
327:
323:
311:
310:
299:
296:
293:
290:
285:
281:
276:
270:
266:
262:
257:
253:
248:
242:
238:
234:
229:
225:
220:
216:
213:
182:
179:
133:
130:
128:respectively.
102:William Spence
97:
96:
93:
90:
89:
85:
84:
82:
81:
78:
74:
72:
68:
67:
64:
60:
56:
55:
52:
48:
44:
43:
35:
34:
32:William Spence
31:
15:
9:
6:
4:
3:
2:
1019:
1008:
1005:
1003:
1000:
998:
995:
993:
990:
988:
985:
983:
980:
979:
977:
964:
960:
956:
952:
948:
944:
937:
929:
928:
920:
905:
901:
895:
887:
883:
878:
873:
869:
865:
861:
855:
847:
843:
839:
832:
824:
820:
816:
809:
807:
791:
790:Maths History
787:
781:
779:
777:
775:
766:
762:
758:
751:
749:
747:
745:
743:
741:
732:
731:
723:
721:
712:
708:
704:
700:
693:
691:
689:
673:
669:
663:
654:
649:
645:
641:
637:
630:
628:
626:
624:
622:
620:
618:
616:
614:
612:
610:
608:
606:
604:
599:
592:
591:
587:
585:
581:
576:
572:
562:
560:
556:
555:John Herschel
551:
549:
544:
530:
527:
522:
519:
515:
501:
497:
495:
491:
490:polylogarithm
475:
472:
469:
461:
442:
433:
426:
423:
420:
414:
411:
403:
398:
394:
390:
387:
381:
373:
369:
361:
360:
359:
356:
339:
336:
333:
325:
321:
297:
294:
291:
288:
283:
279:
274:
268:
264:
260:
255:
251:
246:
240:
236:
232:
227:
223:
218:
214:
211:
204:
203:
202:
200:
196:
192:
188:
178:
176:
171:
169:
165:
161:
156:
154:
150:
145:
144:at the time.
143:
139:
129:
127:
123:
119:
115:
111:
107:
103:
91:
86:
79:
76:
75:
73:
69:
61:
57:
49:
45:
41:
36:
29:
26:
22:
946:
942:
936:
926:
919:
907:. Retrieved
903:
894:
867:
863:
854:
837:
831:
814:
793:. Retrieved
789:
756:
729:
702:
698:
675:. Retrieved
671:
662:
643:
639:
589:
588:
583:
570:
568:
558:
552:
547:
545:
506:
457:
357:
312:
186:
184:
172:
157:
146:
135:
101:
100:
50:31 July 1777
25:
1007:1815 deaths
1002:1777 births
460:dilogarithm
138:coppersmith
976:Categories
846:1021878949
823:1063204490
595:References
963:110222385
886:111328500
528:
520:−
424:−
415:
395:∫
391:−
337:±
289:−
261:±
233:−
212:±
149:John Galt
765:10156665
707:ProQuest
575:Herschel
195:Arbogast
191:Lagrange
160:Greenock
142:Greenock
122:integral
106:Greenock
909:28 June
795:24 June
711:4520067
677:24 June
557:edited
168:Glasgow
153:Glasgow
110:Glasgow
71:Parents
961:
884:
844:
821:
763:
709:
565:Legacy
959:S2CID
882:S2CID
458:(the
88:Notes
911:2022
842:OCLC
819:OCLC
797:2022
761:OCLC
679:2022
193:and
124:and
59:Died
47:Born
951:doi
872:doi
868:104
648:doi
516:tan
978::
957:.
947:92
945:.
902:.
880:.
866:.
862:.
817:.
805:^
788:.
773:^
739:^
719:^
703:47
701:.
687:^
670:.
644:40
642:.
638:.
602:^
543:.
412:ln
116:,
965:.
953::
913:.
888:.
874::
848:.
825:.
799:.
767:.
713:.
681:.
656:.
650::
531:x
523:1
476:x
473:+
470:1
443:t
439:d
434:t
430:)
427:t
421:1
418:(
404:x
399:0
388:=
385:)
382:x
379:(
374:2
370:L
343:)
340:x
334:1
331:(
326:n
322:L
298:.
295:.
292:.
284:n
280:3
275:/
269:3
265:x
256:n
252:2
247:/
241:2
237:x
228:n
224:1
219:/
215:x
23:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
.png)
