350 VIII. NEWTONIAN POTENTIAL FUNCTION. 



The parameter z/F is often called the Laplacian of V. 



div. P = AV^ 



Fig. 124 c. 



div.P=AV = 



Fig. 124 b. 



In Fig. 124 a, b, c, are graphically 

 represented regions of divergent, solenoi- 

 dal, and convergent vector s, with the 

 level surfaces of the functions V of which 

 they are the vector parameters. The 

 arrows on the vector lines show the 

 direction of increase of V, and it is 

 evident that Fhas positive concentration 

 (and a maximum value) where P is 

 convergent, negative concentration (and 

 a minimum value) where P is divergent, 

 and no concentration (nor maximum) 

 where P is solenoidal. 



118. Reciprocal Distance. Gauss's Theorem. Consider the 

 scalar point -function, F= > where r is the distance from a fixed 



point or pole 0. Then the level surfaces are spheres, and the para- 

 meter is 



and since h r = 1, 



- dr\r 



drawn toward ( 110). 



Consider the surface integral of the normal component of E 



directed into the volume bounded by a closed surface S not con- 



taining 0, or as we have called it, the flux of E into S, 



40) 



C CE cos (En) dS = - fC cos (rn) dS. 



