Experiments and Inductions. 197 



tor, and, the distance A B continuing to be 1 inch, let the weight 

 required to raise A be again measured. Let the first weight 

 be denoted by m, and the second by n, and let the charge given to 

 B at first be c unit-jars. The forces at the constant distance 

 A B being as the square of the quantities of engaged electricity 



between the opposite surfaces, we have Vm : \/ n : : 1 : \/ ', 



and c\ / — is the charge which, engaged between two surfaces 

 V m 



of 100 square inches at the distance of 1 inch, engenders the 

 force m of apparent attraction. Now c\ / — upon 100 square 



inches gives electricity of same density as 3*14 c \/ — upon 314 



square inches, the surface of the sphere of 10 inches diameter: 

 compare this charge with g. The force of apparent attraction 

 follows the ratio of the square of the charge ; hence we have 



;a/!L x 3-14 : g : : 3'] 4 x m : ^ a/ 



n 



that is, the value of the weight that, acting through 5 inches, the 

 radius of the sphere, expresses the integral of its electric charge 

 — its work-representative. 



On the Arrangement of Electric Lines into Systems. 



57. From the simplest system, viz. that of lines issuing from 

 the surface of an insulated conducting sphere, we may pass to 

 others where exact mathematical treatment seems hardly possible 

 as yet. But one or two salient points arrest the attention. 



58. Free electricity in a conducting surface of unequal curva- 

 ture, as the solid SB with a sharp and blunt end (fig. 31). 



a. The mechanical equivalent of a line upon such a surface 

 increases in going from the blunt to the sharp end. The lateral 

 force of the roots lying in the small circle a, resolved perpendicular 

 to that circle, must equilibriate the lateral force of those in the 

 larger circle b similarly resolved. This requires closer packing at 

 a than at b. The number in a x their lateral force should be 

 equal to the number in b x their lateral force. Let a be the 

 length of one circle, and b that of the other ; m the number in 



a, and n the number in b. Then ( — j and (-) represents the 



area of each root respectively ; and since the lateral force at the 



root is inversely as the area, we have I —J and ( t) representing 



