390 Notices respecting New Books. 



trouble, or which might be imperfectly apprehended unless atten- 

 tion were distinctly drawn to it. 



Beginning with the case in which a movable point is acted on 

 by any forces, he first limits the question to the case in which the 

 resultant force can be expressed by means of a force-function, then 

 by a further limitation to the case in which the forces con- 

 cerned are central, and finally to the case in which the force-func- 

 tion becomes the potential function. From this point the subject 

 is treated with great minuteness in regard to all that relates to the 

 determination of the function itself and its first and second 

 differential coefficients. The case in which the point is within the 

 attracting body comes in for very detailed notice, such as its im- 

 portance deserves and requires ; for then, as is well known, the 

 function under the integral sign becomes infinite within the limits 

 of integration. Accordingly, for example, the fundamental 

 equation 



A 2 V=-47re& (1) 



is first proved, in what we may call the usual manner, both for a 

 homogeneous body and for a body not homogeneous. Not content 

 with this, however, the author reproduces a proof, which he first 

 published in Liouville's Journal in the year 1858, and which, as he 

 says, " seems to me to avoid in the simplest manner the difficulty 

 arising from the function under the integral sign becoming 

 infinite " (p. 37). The method adopted, it may be added, depends 

 in the first place on effecting a certain transformation of the ex- 

 pressions for the force-components, and then on proving the pro- 

 position in question by means of these expressions, first for a 

 homogeneous body and then for a body not homogeneous. At the 

 end of the proof the author adds the remark, which expresses the 

 spirit of the whole book, " We have thus arrived at the equation to 

 be proved by means of a series of perfectly simple mathematical 

 operations which depend only on the fundamental principles of the 

 differential and integral calculus " (p. 48). 



The author makes great use of certain terms which he has intro- 

 duced, and which call for notice. In the simplest view of the sub- 

 ject the potential function is merely a function frcm which can be 

 easily derived the attraction exerted by a number of particles — 

 whether forming a continuous body or not — on a particle in any 

 assigned position in space. Under this point of view, to speak of 

 the potential at any point of space of a given distribution of matter 

 is not open to objection ; but when the properties of the potential 

 function are applied to questions of magnetism or electricity, there 

 is a certain impropriety in speaking of a distribution of electricity 

 as a distribution of matter. Professor Clausius proposes to avoid 

 this impropriety by using the terms Agens and Menge. The word 

 Agens is used as the genus of which ponderable matter, electricity, 

 magnetism, &c, are the species. The word Menge is used instead 

 of the word mass or quantity of matter, in order to avoid intro- 

 ducing the notion of inertia, which is inextricably bound up with 



