Notices respecting New Books, 391 



that of matter. " No other supposition is made in regard to an 

 Agent {Agens) except that it can be determined as to quantity, 

 and that the force exerted by a certain group of an Agent {Menge 

 eines Agens) is proportional to the group {Menge), other circum- 

 stances being the same " (p. 9). This point is one of considerable 

 importance, as these words, one or both of them, appear in nearly 

 all the leading enunciations of the book ; e. g., it is said of equation 

 (1) that " it expresses the second leading property of the potential 

 function, viz. that from the potential function of an agent we can 

 deduce its density as a function of the space-coordinates, and 

 thereby can determine the way in which the agent is distributed 

 through space" (p. 34). 



It is plain from the titlepage that Professor Clausius draws a 

 distinction between the potential function and the potential : in 

 fact, the work consists of two parts of unequal length, the first 

 and longer being devoted to the former subject, the second to the 

 latter. The potential function is defined thus : — " When an agent 

 acts by attraction or repulsion, according to the inverse square of 

 the distance, its force-function relative to a unit of the same agent, 

 supposed to be concentrated in a point, is called the Potential 

 function " (p. 12) ; and accordingly it is expressed by 



V = eSl or by V=ef^l 



The constant e, which appears throughout the work, is defined to 

 be the force of repulsion which two positive units of the agent 

 exert on each other at the unit of distance ; and if we choose as the 

 unit of the agent that group {Menge) which exerts the unit of force 

 on an equal group {Menge) of the agent at the unit of distance, we 

 shall have e= — 1* for ponderable matter, and e=4-l for electri- 

 city and magnetism (p. 15). 



The potential (W), which forms the subject of the second part 

 of the treatise, is the force -function of one group {Menge) relative 

 to another group, not merely relative to a unit group conceived 

 as concentrated at a point ; it is, accordingly, represented by a 

 double summation, viz. 



W 



where q belongs to the one group and q to the other. It is 

 plain that 



in other words the potential is obtained from the potential function 



* Of course, therefore, in the case of ponderable matter, equation (I.) 

 takes the form V 2 V=47rft; this equation is usually written V 2 V=— Ank ; 

 but then Professor Clausius expresses the components of the force along 



the coordinate axes by — - &c. 



