March 28, 1889] 



NATURE 



523 



Morgan's remark is easily verified by turning to Potts's Note on 

 Euc. i. io(p.49). Turningnagain to BooIeC'L. of T.," p. 91), it 

 would seem that, the logician does not completely detach himself 

 from the notion of infinity : he has to interpret I : o as well 

 as o :o.^ 



Bacon differs from Plato, who considered forms as absolutely 

 abstracted from matter, and not as confined and determined by 

 it, and agrees with Aristotle in saying that words are the images 

 of thoughts ; - so that the agreement of the views of Bacon with 

 those of Prof. Max Miiller would seem to be tolerably close. It 

 is easy to find cases in which a doubtful meaning of a word may 

 give rise to disagreement on matters of substance. Boole {" L. of 

 T.," pp. 407, 408) observes that the term " necessary " may be 

 applied either to the observed constancy of nature or to the 

 logical connection of propositions. He expresses no decided pre- 

 ference for either meaning. The meanings should be kept care- 

 lully apart. If an axiom be a necessary truth, in thestrictei-t sense, 

 then Newton's laws of motion are laws a priori, viz. giving 

 Kant's meaning to the term (" Prol.," p. 103) ; they are known 

 independently of all experience. But Laplace (" Mec. Cel.," 

 pp. 14-18*) treats them as results of experience. Moreover, he 

 treats (pp. 65-69) the laws of motion under all the relations 

 mathematically possible between force and velocity. Newton, 

 in fact, usually speaks of " law," and gives the term "axiom " 

 Bacon's meaning. 



Boo'e's chapter xx. (" L. of T.," pp. 320-75) relates to 

 problems on causes, but his use of the word " cause " has given 

 rise to much discussion. He proposed a question on causes in 

 1851, which was answered by Prof. Cayley in 1853. The solu- 

 tion was criticized by Boole in 1854, who arrived at a different 

 result, and in 1854, Mr. H. Wilbraham examined both solu- 

 tions. Prof. Cayley returned to the subject in I^62, and Boole 

 thereupon admitted that it would have been better, in stating 

 his problem, not to have employed the word "cau.se" at all."* 

 One mode of stating the nature of the relation between " cause " 

 and "effect" may be this, viz. when a certain (antecedent) 

 change is immediately and invariably followed by a certain other 

 (subsequent) change, then the relation in which the antecedent 

 stands to the subsequent (which may now be called the 

 consequent) change is that of cause and effect. This is, in sub- 

 stance, if not in form, a view common to A,lgazel, Glanvil,'' 

 Hume," Brown," Kant, and, as I believe, Reid ; for the question 

 seems to be one about words. It differs but slightly from the 

 view (C. T., vol. x., part 2, p. 300) of iJe Morgan. Perhaps 

 "unvarying" might be a better word than " invariable," for 

 one instant of time is the immediate and invariable antecedent 

 of its consecutive instant ; but the idea of "cause" does not 

 seem to arise. When " cause" is used in the above sense, the 

 solutions of Boole and Prof. Cayley agree. Boole's question has 

 been dealt with in our Proceedings (vol. xi. p. 118) by Mr. 

 McCoIl. 



The import of the word "principle" is not the same when 

 we speak of the principle of contradiction or of excluded middle, 

 as when we speak of the principle of the permanence of equi- 

 valent forms, or of the sufficient reason, or of continuity. That 

 of sufficient reason has been assailed by Brown ("C. and E.," 



' See the last footnote but one. 



■^ Bacon, 'Advancement of Learning," p. 143; conf. pp. 130, 140. See 

 also pp. 192, 209. 



3 My pagings refer to the 2nd ed. of the " Mecanique Celeste," vol. i. 

 (Paris, 1829). 



4 lio le, C. and D. M. J., vol. vi. p. 286; " L. of T.," pp 321-26; 

 Phit. Mag., S. 4, vol. vu. pP- 29-32; vol. xxiii., pp. 361-63; Wilbraham, 

 Phil. Mag., S. 4. vol. vii. pp. 465-76 ; Cayley, Phil. Mag , S. 4, vol. vi. 

 p. 259; S. 4, vol. xxiii. pp. 352-65, and 470. A sh rt letter by Bole {Phil. 

 Mag., S. 4, vol xxiv. (1862), p. 80, concludes the discussion. 



5 Glanvil (Jo.seph), "Scepsis Scientifica," &c. (Lend.. 1665, 4to) : 

 Lond., 1885, 8vo. On Causation, I have only mentioned compara- 

 tively recent authors. But. going further back, we find Thales (with his 

 elemental aralysis), Xenophanes (with his one cosmic substance), and 

 Pythagoras ^with his arithmetical and geometrical combinations), all recog- 

 nizing invariable sequences in nature ; and Socrates admitted a class of 

 phenomena wherein the connection of antecedent and consequent was 

 invariable and ascertainable by human study (Grote, "History of Greece," 

 vol. i., 1846, pp. 495-98). Socrates applied similar scientific reasonings to 

 moral and social pnenomena (/A, p. 504). 



6 David Hume, " A Treatise of Human Nature," &c. (Lond., vols. 1. and 

 ii., 1739; vol. iii., 1740: his name does not appear on the title-pages). 

 " Phil /sophical Essays concerning Human Understanding " (_2nd ed., Lond., 

 1750). " An Inquiry concerning Humati Understanding " (Lond , 1861) 

 marks the issue to w hich I refer. 



7 Th .mas Brown, " Inquiry into the Relation of Cause and Effect" (3rd 

 ed., Edinburgh, i8i8). Draper does not admit the construction put upon 

 Algazcl's words by Whewell (" Hist. Ind. Sc," Lond , 1837, i. p. 251). A 

 facsimile reprint of Glanvil has been published within the last few years. 

 Buckle pronounced Brown's to be one of the best books ever written. 



sect. iv. pp. 222, misnumbered 322, to 306), and by De Moi^ark 

 (C. T., X., part 2, pp. 290-304). Clifford {op. cit., p. xl.) was- 

 prepared to sacrifice the principle of continuity, even in the case 

 of space, and the author of anonymous "Strictures" on Pea- 

 cock's " Algebra " (Camb., 1837), who was (so at least I was 

 told many years ago by Davies) Hind, concludes (p. 21) that 

 number is perfectly abstract, that it is the only thing which is 

 so, that it is not rightly denominated a species of quantity, being 

 equally connected with every species. An instance of a striking 

 failure of the principle of the permanence of equivalent forms 

 is given by Dr. |. \V. L. Glaisher in the Messenger of Mathe- 

 matics, N. S., vol, ii. (1872) p. 95. Again, take another word 

 — viz "disparity." Supposing it to be said that there are two 

 persons in a room, whose united ages are twenty-one years, and 

 between whose ages there is the greatest disparity possible. 

 This is intelligible if one be a new-born or nascent infant, and 

 the other a person aged twenty-one. But suppose the same state- 

 ment made of three persons ; the proficient in language might have 

 to inquire of the mathematician what meaning, if any, the state- 

 ment bears. Or, again, the mathematician might be asked 

 what, or whether any, numerically definite meaning can be 

 attached to the words, " triangle of maximum scalenity." 



Prof. Newman (" Logic," 1838, p. 52) says that the truths of 

 arithmetic are verbal. Perhaps this, and the corresponding 

 statements of Dugald Stewart, would not now be insisted on. 

 They are opposed to the views of Kant, Clifford, and De Morgan 

 (C. T., xi., part i, p. 160). The identities 3- -I- ^i^ = 5-, and 

 I 3* + 4^ + 53 = 6'*, seem to be something very different from 

 definitions of words. Kant considers 7-1-5 = 12 to be a 

 synthetical judgment (" Proleg.," pp, 22, 23). 



Metaphysics and mathematics are consorts in the East as well 

 as in the West, Bhascara says that the analytical art is merely 

 sagacity exercised, and is independent of symbols, which do not 

 constitute the art.^ If De Morgan- be right in placing Dio- 

 phantus as late as !he beginning of the seventh century, Arya- 

 bhatta was earlier, by two centuries, than Diophantus. The name 

 certainly seems to have been a very common one. Josephus " 

 relates that Alexander (a son of Herod the Great) said that 

 Diophantus the scribe had imitated his hand. But Mr. Heath's 

 work ■* renders it scarcely possible to sustain De Morgan's 

 contention. 



EXHIBITION OF METEOROLOGICAL 

 INSTRUMENTS. 



^''HE Royal Meteorological Society's tenth annual Exhibition 

 of Instruments was held in the rooins of the Institution of 

 Civil Engineers, 25 Great George Street, Westminster, from the 

 19th to the 22nd instant. This Society's Exhibitions are always 

 interesting and instructive, as each one is devoted to some 

 special class of instruments : this year the instruments consisted 

 principally of actinometers and solar radiation apparatus. 

 Specimens of most of the various forms of these instruments 

 were exhibited ; but when it was not possible to obtain an 

 instrument itself, a photograph or drawing of it was shown, so 

 that the visitors to the Exhibition could readily see what 

 instruments have actually been made. 



Several specimens were exhibited of Sir John Herschel's 

 actinometer, for ascertaining the absolute heating effect of the 

 solar rays, in which time is considered one of the elements of 

 observation. This consists of a large cylindrical thermometer 

 bulb, with a special open scale, so that minute changes may be 

 easily seen. The bulb is of transparent glass filled with a deep 

 blue liquid, which is expanded when the rays of the sun fall on 

 the bulb. When taking an observation, the actinoineter is 

 shaded for one minute and read off ; it is then exposed for one 

 minute to sunshine, and its indication recorded ; it is finally 

 shaded again, and its reading again noted. The inean of the 

 two readings in the .shade, subtracted from that in the sun, 

 indicates the expansion of the liquid produced by the sun's rays 

 in one minute of time. 



The Kew Committee exhibited Hodgkinson's actinometer, 

 the principle of which is the same as that of Sir J. Herschel's, 



' Colebroke, "Algebra," &c. (London, 1817). p. xix. 



* De Morgan, •' Arithmetical Books" (London, 1847), P- 47- 



3 Josephus, "Antiquities of tlie lews" (Burder's TransUiion, vol, i, pp. 

 616, 617). Burder's preface is dated Lend >n. October i, i8ti. 



* T. L. Heath, " Diophantos of Alexandria : a Study in the History of 

 Greek Algebra" (Cambridge University Press, 1885), 



