April i, 1909] 



NATURE 



12- 



SPHEKICAL ASTROXOMY. 

 A Treatise on Spherical Astronomy. By Sir Robert 

 Ball, F.R.S. Pp. xii + 506. (Cambridge: Uni- 

 \ersity Press, 1908.) Price 12s. net. 



IT is difficult to decide what limits an author should 

 set himself in writing a text-book on this subject. 

 Gravitational astronomy on the one hand and descrip- 

 tive and general astronomy on the other should be, 

 for the most part, omitted. A more difficult question 

 arises as to what details of practical astronomy should 

 be included. It seems to us that the aim of such 

 a book should be to show how the geometrical 

 |)Ositions of stars and other heavenly bodies are 

 defined and accurately determined, and how these 

 [xjsitions vary with the place and time of observation, 

 and from such causes as refraction and aberration. 

 Some description of the more important instruments, 

 e.g. the transit circle, the equatorial, theodolite, and 

 sextant, should be included, and preferably in connec- 

 tion with the class of astronomical problem to which 

 thev are applied, and the geometrical problems to 

 which they give rise or which arise in connection 

 with them. The excellent little book, written by 

 Sir Robert Ball in 1877, fulfils this condition. 

 Godfray's "Astronomy" is incomplete and anti- 

 quated, but in this way is an admirable manual for 

 students. 



In the work under review the instruments are con- 

 sidered as particular cases of the " generalised 

 instrument." This mode of treatment is of consider- 

 able geometrical interest, but it does not give the 

 student an adequate idea of the use of astronomical 

 instruments or the parts they play in astronomical 

 investigations. As the author explains in the preface 

 that he proposes to avoid the multitudinous details 

 of practical astronomy, this criticism is perhaps 

 beside- the mark, but the student will, we think, need 

 to read concurrently with this work one on the out- 

 lines of practical astronomy. The most striking 

 illustration of the difliculties which arise from the 

 separation of the geometrical problems from the 

 instruments which furnish their data is found in the 

 scanty treatment of the determination of latitude and 

 longitude. With the exception of Sumner's method, 

 only incidental references are made to a subject 

 which requires at least one chapter for an account 

 of the various methods applicable under different 

 conditions. 



Within the limits the author has imposed on him- 

 self, the book will be found very useful by students 

 whose mathematical attainments are sufficient to 

 obtain a first class in the mathematical tripos at 

 Cambridge. The author usually treats questions 

 generally and analytically, and then proceeds to 

 transform, simplify, and approximate. This method 

 is naturally and necessarily employed in treatises, such 

 as Chauvenet's, intended for the actual requirements 

 of astronomers, and is the simplest for students to 

 whom the mathematics does not present difficult v. 

 For other students more elementary methods applied 

 to the simplest cases will be found necessary. 



A valuable feature of the work is the constant 

 introduction of the numerical values of the astro- 

 XO. 2057, ^'OL. 80] 



nomical constants, and the frequent solution of 

 numerical examples. The short exjxisition of the art 

 of interpolation properly finds a place in the book. 



In the chapter dealing with the use of spherical 

 coordinates, it is pointed out that the direction of 

 graduation of a circle enables the two poles to be 

 distinguished, and the use of the word nole is 

 suggested for the one generally called the North Pole. 

 Such a term is a useful one, as the words North 

 Pole can then be restricted to the actual North Pole of 

 the heavens. 



We are glad to see that a short account is given 

 of the theory of map-making. It is very desirable 

 that a knowledge of the principles on which maps are 

 constructed should be more widely known, and not 

 confined to students of pure mathematics. 



Attention may be directed to the chapter on refrac- 

 tion. This subject presents difficulties both to the 

 astronomer and the teacher. The theories of Bessel, 

 Gylden, and Radau are too complicated for a text- 

 book, and yet the importance of the subject demands 

 more than is usually given when these are omitted. 

 The author, who gives a simple approximate 

 integration of the differential equation of refraction 

 (for which he expresses his indebtedness to Prof. 

 E. T. Whittaker), has presented the whole question 

 in a satisfactory and adequate manner. 



The geometry of such questions as aberration, 

 parallax, and occultations is well presented. Generally 

 speaking, the book will be found very useful both 

 by teachers and students in all applications of 

 spherical trigonometry to astronomy. The collection 

 of exercises is well chosen, and the numerical applica- 

 tions, both in the text and among the exercises, serve 

 to give a real connection between the mathematical 

 formulae arvd astronomical phenomena. F. W. D. 



THE CELL AND ITS WORK. 

 The Cell as the Unit of Life, and other Lectures de- 

 livered at the Royal Institution, London, 1899-1902. 

 .In Introduction to Biology. By the late Allan 

 Macfadyen. Edited by Prof. R. Tanner Hewlett. 

 Pp. xvi + 381. (London : J. and A. Churchill, 1908.) 

 Price ys. 6d. net. 



THE volume before us is the outcome of courses 

 of lectures delivered some years ago by the 

 late Dr. .Allan Macfadyen in his capacity of Fullerian 

 professor of physiology in the Royal Institution. 

 Naturally, owing to the time that has elapsed since 

 they were delivered, some modification must have been 

 rendered necessary, and Prof. Hewlett, who has under- 

 taken the task of editing the book, is to be con- 

 gratulated on the way in which he has performed his 

 part. 



The lectures themselves deal principally with the 

 cell as the morphological and physiological unit of 

 organic life. The author strongly emphasises this 

 point of view. It is one which, in our judgment also, 

 still affords the most comprehensive as well as the 

 most effective grasp of the problems presented by 

 living beings, notwithstanding the attacks that have 

 been from time to time directed against it. The 



