Maech 11, 1898.] 



SCIENCE. 



355 



sky are indispensable to every active astro- 

 nomical observatory and to every astronomer 

 who wishes to study the fainter stars. Unfor- 

 tunately, the original edition of this work is 

 exhausted, so that copies can no longer be sup- 

 plied. A new edition is being prepared by the 

 Bonn Observatory, and will be published 

 shortly, provided that subscriptions for a hun- 

 dred copies, at seventy Marks each, are prom- 

 ised before May 1, 1898. The price is very low, 

 considering the amount of material furnished. 

 After that date the price will be raised to one 

 hundred and twenty Marks. The Astronomical 

 Conference held at the dedication of the 

 Yerkes Observatory appointed the under- 

 signed a committee to aid this project. Or- 

 ders for copies may be sent to the publishers, 

 Messrs. A. Marcus and E. Weber, Bonn, Ger- 

 many, or will be transmitted to them by any 

 member of the committee. It is proposed to 

 publish a list of American subscribers, and it is 

 hoped that at least fifty copies will be taken by 

 American astronomers. Since charts deterior- 

 ate rapidly by constant use several copies 

 should be taken by each of the larger observa- 

 tories. The members of the committee have 

 shown their appreciation of the value of this 

 work by ordering twelve copies for use in the 

 institutions under their direction. It is of the 

 greatest importance that the subscription list 

 should be filled, as it is probable that in the fu- 

 ture many similar enterprises may be under- 

 taken, whose success will depend upon that 

 now attained. 



Edward C. Pickering, 

 J. H. Hagen, S. J., 

 M. B. Snyder, 



Committee. 



SCIENTIFIC LITERATURE. 

 Theoretical and Practical Graphics. By Fred- 

 erick N. WiLLSON, C.E., A.M., Professor in 

 the School of Science, Princeton University. 

 (Author's Edition.) 1897. 4to. Pp. viii + 

 264 + Appendix. 



This is a most attractive work, not only con- 

 quering elementary graphics entire, but con- 

 taining much more of highest geometric interest, 

 including a fairly complete course on higher 

 plane curves. 



The part of the subject where Church so long 

 held supremacy in America, with his Descriptive 

 Geometry, justly appreciated for its elegance, is 

 paralleled by Professor Willson in his chapter 

 I. and chapters IX.-XII., 117 pages in all, in- 

 cluding 219 figures in the text, where he not 

 only covers with equal conciseness and elegance 

 the matter of Church's 138 pages of text and 21 

 pages of illustration (102 figures), but in addi- 

 tion has treated many new and important mat- 

 ters, such as the Conoid of Pluecker (articles 

 333, 356, 477), a favorite surface of Sir Robert 

 Ball, applied in his Theory of Screws, which 

 itself may be looked upon as in part an applica- 

 tion of non-Euclidean geometrj', also the Cylin- 

 droid of Frezier (§§ 333, 360, 489), the corne de 

 vache (§361, 475-6), and some special helicoids 

 (§ 480-4), and also has covered the Third Angle 

 (or 'shop ') method of employing descriptive 

 geometry, and given a very full treatment of 

 development (§§ 405-20). The mathematical 

 surfaces are beautifully illustrated. 



The, general plan of the book, while providing 

 a comprehensive graphical training in the form 

 of a progressive course, admits of specialization, 

 of shorter courses, with noticeable flexibility. 

 In fact, eight sub-groupings are indicated for 

 independent courses. Comparison with the 

 special treatises scrupulously cited shows the 

 extent of matter on all topics usually treated to 

 be surprisingly great. Professor Willson has a 

 gift for condensing without loss of clearness. 



With this power, he does well to restate for 

 convenient reference many of the fundamental 

 definitions which he presumes already in some 

 form previously mastered — for example, the de- 

 finition of the trigonometric functions on p. 31. 



But I still prefer the definition in the note 

 on p. 121, " A straight line is the line which is 

 completely determined by two points:'' to the 

 author's second thought given in the preface, 

 " The line that is completely determined by any 

 two of its points." The spheric space of non- 

 Euclidean geometry, though movable as a 

 whole in itself, is such that two geodetic lines 

 in it always cut in two points. 



Of course, no spherical trigonometry is em- 

 ployed in the author's solution of the problems 

 of trihedrals, purely a graphic process, as it 

 should be. We are glad to find as an appendix 



