Septembek 27, 1912] 



SCIENCE 



407 



the relatively extensive knovcledge whicli 

 we have of its properties, seem to com- 

 mend it as tlie most useful curve to repre- 

 sent the type of distribution to which scholar- 

 ship marks should conform. If it is desirable 

 to have the grades express significant local 

 factors, this can always be done by adding 

 some constant value to these grades, and the 

 constants so found will also give an index as 

 to the scholarship of a particular institution. 

 A. P. Weiss 

 TJniveesity op Missouri 



SCIENTIFIC BOOKS 

 Nature's Harmonic Unity. By Samuel 



CoLMAN, N.A. Edited by C. Arthur Coan, 



LL.B. New York, G. P. Putnam's Sons. 



1912. Cloth, 8X9i in. Pp. viii + 32Y; 



302 illustrations. $3.50 net. 



The purpose of this book appeals to the 

 scientist and ought to be a matter of serious 

 study for every beginner in the vocation of 

 arts. 



It contends to prove that pleasing forms of 

 nature, as well as of human creation, are 

 ruled by mathematical laws. 



That this is true to a certain extent has 

 been shown by the reviewer in an article on 

 " Mathematical Principles of Esthetic Forms," 

 which in October, 1900, appeared in the 

 Monist, and in various other publications, 

 where also a number of important references 

 may be foimd. The fact that the author does 

 not seem to be familiar with these accounts 

 for some serious defects in the presentation 

 of the subject. A writer who attempts to ex- 

 plain the principles of esthetic forms in na- 

 ture should not neglect to study, for example, 

 Schwender's " Vorlesungen iiber Mechanische 

 Probleme der Botanik." ' Furthermore, what 



' ' ' Mathematik in Natur und Kunst, ' ' Mitteil- 

 ungen der Naturforschenden Gesellschaft in Solo- 

 thurn, Vol. XV., 1906. "Sur quelques exemples 

 math^matiques dans les sciences naturelles, " 

 L'Enseignement MatMmatique, Vol. XII., Paris, 

 1910. "Wiskunde en Natuurlijke Historie," 

 Wiskundig Tijdschrift, Vol. 10, Haarlem, 1910. 

 ' ' Mathematics and Engineering in Nature, ' ' Pop- 

 ular Science Monthly, November, 1911. 



'Engelmann, Leipzig, 1909. 



a rich source of beautiful natural forms might 

 he find in Haeckel's " Kunstf ormen der Na- 

 tur." ' 



In neglecting the physiological and psycho- 

 logical factors of the problem, the treatment 

 must necessarily become antiquated and, 

 from the standpoint of the exact scientist, in 

 many parts shrouded by a semi-mathematical 

 mythology and naively stated principles. 



The book contains, nevertheless, a number 

 of very readable chapters which will be of 

 value to any one interested in the problem. 

 The examples chosen from biology are by far 

 the most interesting, while some of those in 

 architecture are of questionable value. See, 

 for instance, on page 79, the combined figure 

 of a snow crystal and the Parthenon. It is 

 evident that a hexagonal figure may always be 

 drawn to fit the tinted square and resembling 

 a snow crystal. But what about the exact 

 dimensions? Again, the paraphrase of a vase, 

 p. 273, designed according to, what in this 

 and similar cases I call mathematical mythol- 

 ogy, is certainly no object of universal ad- 

 miration. Notice the paiirfully weak points 

 in the foot. 



The Greeks did not know the logarithmic 

 spiral as would appear from a statement in 

 connection with the discussion of the Ionic 

 volute in the chapter on conehology. This 

 particular spiral, expressed by the polar equa- 

 tion p != 6°^, was discovered by Descartes in 

 1638. When writing about the Ionic order, 

 why not mention the Lituus (p" = a/6) dis- 

 covered by Cotes in 1722. It seems strange 

 too, that the catenary should be given the prize 

 as the most beautiful curve. Those algebraic 

 lines which pass through the circular points 

 are generally considered as the beauties 

 among the curves. 



The technical aspect of the book is gener- 

 ally pleasing. It is, however, to be regretted 

 that in a treatise with esthetic purposes most 

 of the geometric figures should be so crudely 

 drawn. They are clumsy-looking and lack 

 neatness and precision of execution. 



= Leipzig, 1899-1903. 



