Notices respecting New Books. 489 



We see now that the quantities which seemed absolutely 

 independent of each other are united by relations all very 

 simple, rendering unnecessary the employment of long empiric 

 formulas, which often rest only on more or less questionable 

 observations. 



Finally, if we compare the results of this investigation with 

 Dulong and Petit's law on specific heats, we can establish one 

 relation more, and say that the latent heats of all liquids are 

 multiples of the specific heats. 



In a memoir to be published shortly, we shall more com- 

 pletely develop these questions, of which these few lines are 

 only a succinct epitome. 



LYII. Notices respecting New Books. 



The Theory of Screws: A study in the Dynamics of a rigid body. By 

 Eobert Stawell Ball, LL.D., F.B.S., Andrews' Professor of 

 Astronomy in the University of Dublin, and Astronomer Royal of 

 Ireland. Dublin : Hodges, Foster & Co., Grafton Street. 1876 

 (8vo, pp. 194). 



HPHIS book contains the substance of various previously published 

 J- papers, which the author has rewritten and systematically 

 arranged. It is in fact a treatise on the equilibrium and motion 

 of a rigid body, regarded from a point of view quite different from 

 that of other writers. 



The theory is worked out with great completeness and in a 

 manner that bears conspicuous testimony to the extent of the 

 author's acquirements and to his power as a mathematician. 



For several reasons it is difficult to convey any idea of the con- 

 tents of the work within the limits of a short notice. Thus, to men- 

 tion only one — very many technical terms are used, which need 

 definition for the purposes of the discussion in hand ; a list of 

 fifty-five of these terms is given in a separate index. "We will, 

 however, endeavour to state, as briefly as possible, some of the 

 fundamental points of the theory, and to show by an example or 

 two how they apply to the exposition of the subject. It will be 

 proper to premise that the discussion is conducted under certain 

 restrictions ; e. g. the body is supposed to be acted on by the same 

 forces whenever it occupies the same position — a restriction which 

 excludes such forces as those arising from a resisting medium, or 

 from friction. Again, it is assumed that the body while under ex- 

 amination continues indefinitely adjacent to its original position, so 

 that all displacements are supposed to be small. Though this re- 

 stricts the field of inquiry, it still leaves it wide enough to include 

 the theory of equilibrium, of impulsive forces, and of small 

 oscillations. 



It is well known that any displacement which a rigid body under- 

 goes may be reduced to a rotation round an axis and a translation 



