NATURE 



[September 4, 1919 



the needs of such students, and suggests com- 

 parison with the work on astronomy by the late 

 Hugh Godfray, which has held the field in our 

 universities for so many years. A good deal of 

 space is wisely devoted to the chapter on time, 

 for the experience of teachers generally will con- 

 firm the remark made in the preface that "this 

 subject seems to cause the student more difficulty 

 than any other branch of practical astronomy." 



The young student of spherical trigonometry, 

 entering upon the practical solution of triangles, 

 is sometimes a little bewildered by the number 

 and variety of the formula put before him for 

 the determination of an angle from three given 

 sides, by means of the halved sine, cosine, tan- 

 gent, etc. A somewhat novel feature of Prof. 

 Hosmer's work is a short discussion of the con- 

 ditions under which one of these is to be pre- 

 ferred to the others." 



To each chapter is appended a small collection 

 of examples, some numerical, some calculated to 

 test the grasp obtained upon the subject-matter 

 of the chapter. These should be of great assist- 

 ance to the student. H. B. G. 

 History of the Theory of Numbers. Vol. i. 



Divisibility and Primality. Publication No. 256. 



By Prof. L. E. Dickson. Pp. xii + 486. (Wash- 

 ington : Carnegie Institution of Washington, 



1919.) 

 This work appears to be a chronological encyclo- 

 paedia rather than a history as that word is 

 usually understood. Prof. Dickson has aimed 

 at giving references to all papers bearing on the 

 subject, and in most cases he has given a sum- 

 mary of the contents. 



These papers are so numerous that the need 

 for brevity has forced the author into a style 

 which is often abrupt and occasionally irritating, 

 but the subject-matter will be found invaluable 

 by all who aim at original work in the theory of 

 numbers. 



The volume begins with an account of the 

 theory of perfect numbers ^ ; these are now of 

 historical interest only, but the quest for all per- 

 fect numbers has proved one of the greatest 

 driving forces in the general theory of numbers. 



The next topic includes the theorems of Fermat 

 and of Wilson ; it is remarkable that the first proof 

 known of the one and the first enunciation of the 

 other are both due to Leibniz. 



The section on indices, binomial congruences, 

 and circulating decimals includes a large number 

 of writings of an unusually miscellaneous char- 

 acter, and the reader will find that this source 

 contains much information which has not been 

 easily accessible hitherto. 



The most elaborate chapter bears the title 

 "Sum and Number of Divisors"; and this 

 chapter contains many references to the analytical 

 theory of numbers, which has grown so rapidly 

 of late years. On the other hand, recent work 



1 Th« Greeki called a namhtr perfect if the number happens to be equal 

 to the sum of its divisors. For example, we have 

 6=1+3 + 3, 

 28=1+2 + 4+7+14. 



NO. 2601, VOL'. 104] 



on prime number theory is but lightly sketched, 

 and rightly so, inasmuch as the treatise by 

 Landau and subsequent reports have provided all 

 the necessary material. 



Physical Laboratory Experiments for Engineer- 

 ing Students. By Prof. Samuel Sheldon and 

 Prof. Erich Hausmann. Part i. Mechanics, 

 Sound, Heat, and Light. Pp. v+134. (Lon- 

 don : Constable and Co., Ltd., 1919.) Price 

 65. net. 

 This book, prepared for use in the Polytechnic 

 Institute of Brooklyn, is suitable for candidates 

 for engineering degrees who have already pur- 

 sued laboratory courses in physics. " Each ex- 

 periment has been chosen because of its close 

 connection with engineering work, and in many 

 cases the theoretical result may be calculated 

 from the constants of the apparatus with which 

 that result obtained by experiment may readily 

 be compared. As these two results approach to 

 an equality the student gains confidence in the 

 apparatus, confidence in the theory, and con- 

 fidence in himself." This is well said. There 

 can be no doubt that many students lose not only 

 confidence but also interest in physics when they 

 find that owing to inefficient apparatus results of 

 reasonable accuracy cannot be obtained. The 

 experiments here described are well selected, and 

 as apparatus of engineering design has been 

 chosen, the equipment with ordinary care in use 

 should continue to give sufficient accuracy. 

 Special mention may be made of the apparatus 

 for the study of the harmonic motion of a rotat- 

 ing system, which appears to be unknown t<:> 

 British instrument makers. The book is printed 

 on good paper, and is well illustrated. 



H. S. A. 

 The North Riding of Yorkshire. By Capt. W. J. 

 Weston. Pp. viii+i6i. (Cambridge: At the 

 University Press, 1919.) Price 2^. 6d. net. 

 In view of the time which has elapsed since the 

 greater proportion of these well-known county 

 geographies were issued, one had almost feared 

 that the greatest county had been overlooked. It 

 is now apparent that three volumes will be issued 

 for Yorkshire, one for each Riding, and the first 

 of these, dealing with the North Riding, has 

 just appeared. As we are fairly familiar with all 

 that have previously been published, it is a pleasure 

 to be able to state that this is one of the best ; 

 the author seems to have had a ;better grasp of 

 the object of the work he has had in hand, result- 

 ing in a volume which is much more a geography 

 than a guide-book. The illustrations are numer- 

 ous and well chosen ; misprints, as usual, are few 

 • — which makes that ,in the word "Montreal " on 

 p. 58 all the more glaring. The only statement 

 we cannot agree with is in reference to the 

 "raised beach " ^at Saltburn, which is now known 

 to be a "kitchen midden." The colouring of the 

 geological map at the end, for which the author 

 is not responsible, does not seem quite so success- 

 ful as with the maps in the earlier volumes. 



T. S. 



