> THE AIM AND ACHIEVEMENTS OF SCIENTIFIC METHOD. 105 



notions were employed it might not necessarily be implied in 

 the resulting system of mechanics. Hertz's mechanics* is 

 a system in which the notion of geometrical connections 

 between the mass-particles (supplemented when occasion 

 demands by hypothetical " concealed masses ") replaces the 

 " forces " of the Newtonian secondary construction. For this 

 reason Mach regards the Hertzian mechanics as an attempt to 

 substitute integral laws for the differential laws that make up 

 the ordinary science of mechanics.f 



That this does not imply that the motion of a particle is 

 determined by consideration of only one configuration of the 

 system to which it belongs instead of by two, as in the 

 Newtonian mechanics, follows from the consideration that 

 Hertz's principles lead us to the assertion that under any given 

 set of conditions supplied in the " integral " form of geometrical 

 connections the particle will take the path of the least possible 

 curvature. But to specify the " curvature " of a path we must 

 make use of a second differential coefficient, just as we must to 

 specify an acceleration. Thus, by an argument closely 

 analogous to that of the preceding section it may be made clear 

 that in this case also one configuration of the particles of the 

 system must be thought of as determined by at least two 

 previous configurations. 



47. 



A very little consideration will show that this concept of 

 the " notice " which one part of the universe takes of the rest 

 must be applicable to other elements of the warp and woof of 

 Nature besides the obvious movements of matter. "We have 

 seen, for example, that the science of Heat is built up upon 

 a basis of correlation of the number series with the observed 

 series of states of bodies which are called temperatures. We 



* Hertz, Principles of Mechanics, Eng. trans, by D. E. Jones, 

 t Mach, Science of Mechanics, 2nd Eng. ed.. p. 255. 



