﻿152 Notices respecting New Boohs. 



particles of gravitating matter) is taken to be 



the normal flux of force-intensity due to any distribution of 



sources, whether forming a continuous " body " or not, taken at 



all points outwards through any closed surface in the field, is 4 ir 



times the total " mass " (or quantity of source) contaiued within 



the surface. With the above definition of the force between m 



and m, this 47r will enter into many physical expressions : for 



example, the force between two electric charges in a dielectric of 



ee 

 " specific inductive capacity " K is -^-g, and the relation between 



displacemement and electric force-intensity is D = j- . E. This 4?r 



seldom fails to excite the wrath of Mr. Heaviside. It is easy to see 

 that its introduction into certain expressions can be avoided by 

 assuming the force between two elements to be 



mm' 



where, at first, He is undetermined. With this expression, the 

 normal outward or inward flux of force-intensity through any 

 closed surface will be 4/rk times the contained " mass ; " and if we 

 wish to make this flux of force the exact numerical measure of the 



contained mass, we must take 4xrJc=l, i.e. &=t~> ana< then the 

 force between two elements is 



mm' 



where the 4n is no longer irritating to Mr. Heaviside, although the 

 B. A. authorities (quoted by Mr. Heaviside at p. 118) expressly 

 rejected every constant, other than unity, in the expression for 

 the force between two elements as " absurd and useless." 



The unit mass, or source, then, in this system is one which acts 

 on an equal one (both supposed homogeneous spheres) with a force 

 of 47r dynes when their centres are one centimetre apart ; or, 

 again, the unit mass may be defined by saying that it is such that 

 the flux of its force-intensity (i. e. force per same unit) through 

 any closed surface surrounding it is unity. It is, then, ou this 

 characteristic of giving a unit flux of force that Mr. Heaviside 

 founds the unit of quantity. But, however desirable it is to get rid 

 of 47r in the expressions for a large number of physical constants, it 

 is just as well to point out that from the standpoint of funda- 

 mental 'principles a flux of force is not a fundamental entity at all, 

 because it consists of an arithmetical sum of forces which act in all 

 possible directions in space, and therefore it is not of fundamental 

 value — unlike the sum of the components of such forces in a single 

 direction. In fact, the conception of such an indiscriminate sum 



