OP ARTS AND SCIENCES. 4G3 



T = tem2:)orary part of B. 



iV^ = total number of coils on the riag magnet. 



a = mean radius of the rinjr. 



r = radius of cross-section of the rinor. 



y = strength of the current. 



N = number of coils on the helix. 



N'=z number of coils on the earth inductor. 



li = radius of earth inductor. 



C = deflection of earth inductor. 



h = deflection of the helix when the current is reversed. 



h' = deflection of the helix when the current is broken. 



V = vertical force of tiie earth's maanetisra. 



S = deilectiou of the tangent galvanometer. 



The magnetic potential inside of a ring solenoid is 



Q=—2N^ye* 



where 6 is the azimuth angle about the axis of the ring. 

 Differentiating, we have 



do. „ ,^ dd 



d s . 



but — = p, the distance from the axis ; hence the magnetic force 



_ _ Jo _ 2N^y 

 ds p 



To find the total number of lines of force passing through any area, 

 we find an expression for the force at a single point, and then integrate 

 this expression all over the surface between the proper limits. 



If we take a section of the ring and divide it into bars of length B C 

 and width d x, we shall have BC=2 ^/r'^ — x% and we shall find the 

 total number of lines of force through the section to be equal. 



a \ ' 4 a- ' 8 a* ' / a 



since in the rings used the parenthesis differs but little from unity. 

 * Maxwell's Elect and Mag., sect. G81. 



