NATURE 



[March 6, 1919 



firmed dyspeptic, he will be spent in her service. 

 But the memory of these services will survive, 

 and the little book to which we direct attention 

 will serve to perpetuate it. 



T. E. Thorpe. 



GRAVITATION AND RELATIVITY. 

 The Physical Society of London. Report on the 



Relativity Theory of Gravitation. By Prof. 



A. S. Eddington. Pp. vii + gi. (London: 



Fleetway Press, Ltd., 1918.) Price 6s. net. 

 T N the year 1905 a paper was published by 

 -*• Dr. A. Einstein which gave to the world of 

 physical science a new subject for controversy 

 under the title of "The Principle of Relativity." 

 For ten years discussion reigned between those 

 who held to the aether as a firm basis to the uni- 

 verse, and those who, treading more mathe- 

 matically, felt a safer foothold on Einstein's 

 elegant abstraction, little caring that aether, space, 

 and time all trembled. 



While men talked, the author of the disturb- 

 ance was quietly preparing a greater. His first 

 effort had left to the materialist a little comfort 

 and cause for self-conceit in that it had not suc- 

 ceeded in resolving the old contradiction between 

 a metaphysical theory of the relativity of space 

 and time and the apparent existence of an absolute 

 standard of rotational motion. The new theory, 

 however, claims, not only that the complete rela- 

 tivity of space and time is true to the facts, but 

 also that it can throw light on gravitational 

 phenomena which was not shed by the more 

 limited principle. To quote the author of this 

 report: ^' Eifi stein's theory has been successful in 

 explaining the celebrated astronomical discordance 

 of the motion of the perihelion of Mercury with- 

 out introducing any arbitrary constant; there is 

 no trace of forced agreement about this predic- 

 tion." 



Any theory of gravitation which succeeded, in 

 doing this would be worthy of serious considera- 

 tion, but what words should be applied to one 

 which transcends the limitations of Newton's 

 marvellous achievement through the acceptance 

 of the doctrine of complete relativity of space and 

 time ? 



In the earlier theory the one essential constant 

 and invariant magnitude was the velocity of light 

 (c). In mathematical signs, dx^ + dy^ + 'dz* ~ c^dt* 

 was invariant. It is obvious that this cannot be so 

 for a complete relativity, but a general quadratic 

 expression in dx, dy, dz, dt will remain through 

 all changes an expression of the same type, though 

 the coefficfents of the several terms will be func- 

 tions of position and time instead of constants. 

 In the new theory it is assumed that the physical 

 properties of space are such that there is a quad- 

 ratic form of this kind which remains invariant. 

 The physical state at any point and instant is 

 summarised in the values of the coefficients. It is 

 Einstein's achievement to have been able to apply 

 the work of the pure mathematician to find equa- 

 NO. 2575, VOL. 1031 



tions between these quantities which, while re- 

 ducing to the equations of Newtonian gravitation 

 for all frames of reference to which the old prin- 

 ciple of relativity applies, have a completely in- 

 variant form. 



While we wonder at the feat, and at the vision 

 of a hitherto uncomprehended unity of thought, 

 there remain some obstinate questionings. If this 

 dream of complete relativity be true we are get- 

 ting near the point at which it is so general as to 

 lose touch with common experience. The new- 

 law of gravitation has not that astounding sim- 

 plicity of expression which distinguishes that of 

 Newton. The old problem of absolute rotation is 

 thrown further back ; but it remains true that 

 there are systems of reference for which dynami- 

 cal phenomena present their greatest simplicity. 

 We ask why our first naive choice of a system 

 of measurement ready to hand is such that within 

 it material bodies have a nearly permanent con- 

 figuration, and light has an approximately con- 

 stant velocity.' 



Generalisation is the supreme intellectual 

 achievement, but it may leave us thirsting for the 

 particular and for simplicity. This report on 

 what may be the most remarkable publication 

 during the war leaves us wondering in which 

 direction the greater satisfaction is given. 



OUR BOOKSHELF. 

 Mnemonic Notation for Engineering FormtUae, 

 Report of the Science Committee of the Con- 

 crete Institute. With explanatory notes by 



E. F. Etchells. Pp. 116. (London: E. and 



F. N. Spon, Ltd., 1918.) Price 6s. net. 



This book contains a series of miscellaneous 

 papers dealing with the application of mnemonic 

 notation to various branches of pure and applied 

 science, and especially to structural engineer- 

 ing. The formulae of science should not be ex- 

 pressed in misleading symbols which are not sug- 

 gestive of the quantities concerned, but in a 

 notation which is the "embodiment of organised 

 common sense." The key to the notation adopted 

 is to be found in the abbreviation of the significant 

 words in any term until only the initial Jetter 

 remains. In a few instances the second, or even 

 the final, letter may be retained to form a subscript 

 to the initial letter. "The ^rea/e; letters are used 

 to indicate greaterness of quantity or greaterness 

 of complexity." 



There is no doubt that the scheme proposed is 

 founded on sound principles, which have been long- 

 recognised by competent teachers. To some it 

 may seem that in parts of the present volume there 

 is a tendency to elaborate the obvious, and that 

 the report would have been more convincing if 

 there had been fewer repetitions and less frequent 

 use of odd and unfamiliar language. A series of 

 useful appendices dealing with various practical 

 questions, such as calculations for business pur- 

 poses and the printing of mathematical formula, 

 occupies more than two-thirds of the book. 



