610 



SCIENCE 



[N. S. Vol. XXXVII. No. 955 



search arrives at more positive results, indi- 

 cating a different origin for -{-. He shows 

 that in Widman's printed arithmetic of 1489, 

 4- had not yet become a purely mathematical 

 sign, that with Widman + meant simply 

 "und" (and), in conformity with a practise 

 of the middle ages, according to which a sym- 

 bol closely resembling + was used for " et." " 

 It is now known that Widman possessed a 

 manuscript algebra in which + is used for 

 " et," even in cases where " et " does not mean 

 addition.* Widman in 1849 sometimes indi- 

 cated subtraction by the special symbol — , a 

 usage found somewhat earlier in a Dresden 

 manuscript of the year 1481. 



Halsted attributes decimal fractions to 

 Stevin (1585), but makes no mention of the 

 earlier use of decimals by Vieta" (1579) and 

 EudoW (1530). Halsted mentions Napier 

 (1617) as the first to use the decimal point, 

 but the period (or the comma) was used by 

 Biirgi as early as 1592,' by Pratorius in 1599' 

 and by Kepler in 1616. 



Flokian Cajori 



Colorado College, 

 Colorado Springs 



Treatise on Light. By Christuan Huygens. 



Eendered into English by Silvanus P. 



Thompson. London, Macmillan & Com- 

 pany. 1912. Pp. vii +128. 



Ever since its birth, in 1690, the wave theory 

 of light has been adapting itself to environ- 

 ment. Just at the present moment, when the 

 completeness and perhaps the competency of 

 the wave theory is being called in question by 

 certain phenomena of radiation and radioac- 

 tivity,' an English translation of Huygens's 



'Bibliotheca matliematica, 3 F., Bd. 9, 1908-09, 

 pp. 155-157, 248. 



* Bibliotheca mathematica, 3 F., Bd. 10, 1909- 

 10, p. 182, 183. 



' Biiliotheca mathematica, 3 F., Bd. 11, 1911, 

 p. 340. 



" Bibliotheca mathematica, 3 F., Bd. 10, 1909- 

 10, p. 243. 



' Teachers College Bulletin, 1910-11, No. 5, p. 

 19. 



•Cantor, op. cit.. Vol. II. (2), 1900, p. 619. 



»W. H. Bragg, evening discourse before the 



great " Treatise on Light " is particularly op- 

 portune. The fact that this translation has 

 been made by Professor Silvanus P. Thomp- 

 son is an ample guarantee that it has been 

 done in a scholarly and sympathetic manner. 

 Two distinct courses are open to one who 

 wishes to transfer into English the thought of 

 a foreign author who lived more than two 

 hundred years ago — either he may employ the 

 English phraseology of our own day, or he may 

 use that which he conceives to have been the 

 current diction of the period in which the 

 work was composed. In either case he must 

 avoid anachronisms, and in either case the 

 problem is difficult. So many modes of expres- 

 sion are common to the languages of western 

 civilization and so many of these forms have 

 disappeared from our language during the last 

 two hundred years, that a certain quaintness 

 is inevitably given to any translation of old 

 French, German, or Italian, in which partic- 

 ular pains is not taken to avoid these obsolete 

 phrases. It is the second of these alternatives 

 which Professor Thompson has chosen. The 

 result is that the volume including its title 

 page, table of contents, text, paper, binding, 

 typography, size, and English style, is as nearly 

 as possible what it would have been if Huy- 

 gens had lived and worked and published on 

 the other side of the English Channel. This is 

 not to be understood as meaning that the 

 translation is in any sense a literal one, for it 

 is precisely the spirit of the work which Pro- 

 fessor Thompson has caught and has faith- 

 fully reproduced. In brief the volume is in 

 every way worthy of the great contributions to 

 science which it contains. The first three 

 chapters in which Huygens's principle is enun- 

 ciated had already been made available to 

 English readers through Harper's Scientific 

 Memoirs. But the full evidence for Huygens's 

 principle can only be obtained by understand- 

 ing Chapters 4, 5 and 6. Atmospheric refrac- 

 tion is explained in Chapter 4 practically ^a 

 we have it to-day. In Chapter 5 the wave sur- 

 British Association at Dundee, Nature, 90: 559 

 (1913); R. A. Millikan, vice-presidential address 

 before the American Association for the Advance- 

 ment of Science, Science, January, 1913. 



