426 



Prof. A. W. llucker on the Magnetic 



may increase and then diminish or vice versa, but the total 

 range of the magnitude of the horizontal disturbing couple 

 (supposed to be small) depends only on the current LI and 

 the distance of the observatory from the line (if). It is equal 

 to Ll/y. 



In the case of a line of Unite length the car may not reach 

 one of both of the points at which the disturbance is a maxi- 

 mum or a minimum, and the range of the disturbance may 

 therefore be reduced. 



If, now, a be the length of the line (taken as straight and 

 as the axis of #), if y be the length of the perpendicular 

 from the observatory on the line, b and b + a the distances 

 of the ends of the line from the foot of the perpendicular 

 from the observatory on the line, and I the total current, 

 the disturbing forces parallel to «r, y, and z (vertical) are 



F*= LI y J ^72 - (b + a y + V 2f 



F,= LI { 



b 2 +y 2 

 b 



b 2 +y 2 

 2 y I \/b 2 +y 2 



b + a 

 (b + a) 2 +y 2 



b + a 



} 



^(b + af+fi 



disturbance of 

 The calculated 



Experiments were made at Stockton by placing self- 

 registering instruments at a distance of 0'4 mile from a 

 tramway 2 miles in length, when a current of about 150 

 amperes was flowing along the trolley-wire over the whole 

 length of the line. 



The Vertical- force instrument showed a 

 7ry(ryz=10 -5 c.G.s. units of magnetic force), 

 disturbance due to the trolley-wire was 437. 



Hence L = 7/43 = 16*3 p. cent. 



The Horizontal-force instrument gave 



L = 3*5/22 = 15-9 p. cent. 



These results were in satisfactory accord, and showed that 

 the effects produced were the same as if about 84 p. cent, of 

 the current returned through the rails as a uniform current, 

 and 1(5 p. cent, entered and left the earth at the ends of 

 the line. 



The current thus determined is such that if a uniform 

 current of this magnitude (*84 1) flowed in the rails the 

 disturbance produced would be equal to that actually caused 

 by the real current in the rails which, owing to leakage, 

 varies from point to point. It may be called the equivalent 



