302 MEANING or mi. FUNCTION T. 



ti"u . f tlic tan-cut t. this line at /'; 7i tlie attraction 



resolved along this tangent ; then 



dV dV d 



v. if we restrict ourselves to points lying on tin- line s r 

 I'M ill become a function of 8 alone; for V is a function of 

 a, J, and c, and each of these may be regard <<! as a function 

 of*; thus we shall have by the differential calculus, 



dVdb 



= t 



ds da ds db ds dc </.s ' 



, . da , db Jc 



and since -j- = h :r~ m > j ~ n > we ^ et 



dV 



236. To examine the meaning of the function V. 



This function is of so much importance that it will be well 

 to dwell a little on its meaning. 



In the first place it may be observed that the equation (1) 

 contains a physical definition of F, which has nothing to do 

 with the system of co-ordinates, rectangular, polar, or anv 

 other, -which may be used to define algebraically the posit 

 of P and of the attracting particles. Thus !' is to be con- 

 templated as a function of the position of Pin sjiac.-, if such 

 xpression may be allowed, rather than as a function of 

 the co-ordinates of P; although, in consequence of its de- 

 pending upon the position of 1\ I' will be a function of the 

 co-ordinates of P, of whatever kincl they may be. 



Secondly, it may be remarked that although an nftr.; 



le has hitherto been conceived as situate. 1 at /'. 

 nas a definite meaning depending upon tl n of the 



point P. whether any attracted matter exist there or not. 

 Thus V is to be contemplated as having a definite val 

 each point of space, irrespective of the attracted matter which 

 may exist at some places. 



The function V is called the potential of the attracting 

 mass. 



