312 



SCIENCE. 



[N. S. Vol. V. No. 112. 



only by measurements of absolute exactness. 

 Just as we are content to accept a small piece 

 of smooth water as level, although we know 

 from measurements of large surfaces of it that 

 it is curved, so we must be content to take 

 Euclid's geometry as true within the limits of 

 error of ordinary measurements. It may be 

 that we shall be able to arrive at such a pre- 

 cision of measurement of the very large or the 

 very small as to prove Euclid's geometry false ; 

 we can only prove it true by arriving at infinite 

 precision of measurement, which can never be. 



It is interesting to note the effect of this dis- 

 covery upon the position of Euclid as a math- 

 ematician of ability. It has raised him to a posi- 

 tion higher than it had ever been supposed 

 possible to place him, for his work shows that 

 he knew something of this science of absolute 

 space — how much may never appear, but cer- 

 tainly enough to make him the original pro- 

 genitor of it. Certain portions of Euclid have 

 long been considered as blemishes in an other- 

 wise remarkable book. His treatment of pro- 

 portion has been discarded in modern geome- 

 tries as too prolix and heavy. His treatment 

 of parallels has been regarded as unscientific, 

 and would-be authors, bent on showing their 

 ingenuity and superiority to Euclid, have ad- 

 opted other methods which they claimed were 

 more satisfactory. But when a man like Bolyai 

 appears, whose genius is comparable with that 

 of Euclid, he brushes the dust of ages from 

 these blots, and behold, they shine as gems of 

 purest thought, whose brightness and depth 

 confound and dazzle his would-be improvei-s! 

 After all, it takes a long time for scientific 

 knowledge to spread, aud doubtless there will 

 continue to be many authors who will write 

 geometries with so-called modern improvements 

 that proclaim simply their authors' ignorance 

 of the elements of Euclid and the science of 

 space. 



Many editions and different points of view of 

 Non-Euclidean gometry have been presented 

 by modern authors, such as Cayley, Clifford, 

 Riemann and others. Of American workers 

 on the subject we have Dr. Halsted who has 

 been interested on the historical side, dating 

 probably from his Bibliography of the subject 

 prepared for the American Journal of Mathe- 



matics, while a Fellow of the Johns Hopkins TJni^ 

 versity. We may expect much more new and val- 

 uable material from him in this line. Dr. Story, of 

 Clark University, has also written for the same 

 journal in line with the labors of Cayley, Clif- 

 ford and other European mathematicians. One 

 remarkable feature of the later developments is 

 that the various non-Euclidean geometries may 

 be interpreted as the forms in which Euclidean 

 geometry itself would appear, depending upon 

 the meaning of those vexatious quantities ' dis- 

 tances, ' ' angular measurements, ' etc. 



A. S. Hathaway. 

 Rose Polytechnic Institute, 

 Teeee Haute, Ind. 



Elementary Meteorology for High Schools and Col- 

 leges. ByFEANK Waldo, Ph.D. New York, 

 Cincinnati and Chicago, The American Book 

 Company. 1896. Pp. 372. 

 Another Elementary Meteorology is added to 

 the list of recent works under that same title. 

 This one is by Dr. Frank Waldo, of Princeton, 

 N. J. Dr. Waldo was formerly connected with 

 our Signal Service (the predecessor of the pres- 

 ent Weather Bureau) as Junior Professor of 

 Meteorology, and in that capacity gave instruc- 

 tion in meteorology to the officers and men of 

 the Service. His experience then gained, and 

 his intimate acquaintance with the modern 

 German writings in this science, should have 

 qualified him well for the preparation of a text- 

 book of meteorology. This volume is designed, 

 as is stated on the title-page, ' for High Schools 

 and Colleges,' and, as appears in the preface, 

 ' is intended to serve as a text-book of the ele- 

 ments of the science for general students, and 

 must not be considered as a manual for practis- 

 ing meteorologists.' The book will doubtless 

 have a large sale. It gives a good general view 

 of the science ; it is of convenient size, well 

 printed, fairly well illustrated and, a very im- 

 portant matter, it is published at a moderate 

 price. The general plan of the book is similar 

 to that of most of the other text-books, so that 

 there is no occasion for comment on this score, 

 but the chapter on the general circulation of 

 the atmosphere is more complete than usual. 

 Dr. Waldo has succeeded in putting Ferrel's 

 ideas on this subject into tolerably simple Ian-, 



