Permanent Magnets. 187 



this case extra resistance had to be added from the resistance 

 box to keep the readings on the scale. 



Calculation of Results. 



The formula for the ballistic galvanometer is 



n 



Q=k sin — 



2 



in which Q is the quantity of electricity ; Jc, a constant factor ; 

 and 6, the angular throw of the needle. The observations 

 were made with telescope and scale. Letting d represent the 

 observed throw and r the distance of the mirror from the scale, 



tan 20= — 



Expanding sin — we have 



8 , !=!.[.-»,«(!)',] 



This formula was used in reducing the large readings. 



The earth inductor readings were taken frequently and 

 varied but little throughout the experiment. The throw due 

 to the earth inductor when both magnets were at 14° C. was 

 39*5 scale divisions; when one magnet was at 99°*5 C. and 

 the other at 14° C, it was 37*8. Corresponding throws of the 

 needle due to the slipping of the exploring coils over various 

 portions of the magnets were averaged. The average throws 

 taken when one magnet was hot and the other cold was multi- 



39'5 



plied by = 1*045 to reduce to the same scale as the read- 



f J 37 . 8 



ings taken when both magnets were at 14° C. Correspond- 

 ing^ measurements were then subtracted to get the difference of 

 distribution caused by change in temperature in terms of the 

 scale divisions. The reduction to absolute measurement was as 

 follows : The effective area of the earth inductor, as determined 

 by previous observers, was 20,716 sq cm . The total number of 

 lines of induction cut by turning the earth inductor was 

 2HA= 8,286*4. The throw was 39*5 scale divisions, therefore 

 each scale division of throw caused by the movement of the 

 exploring coils corresponded to 8,286*4-i-(39*5Xl50)=l*398 

 C.G.S. lines of induction. The factor 150 is due to the 150 

 turns of the exploring coils. The change in distribution as 

 given in scale divisions was then multiplied by 1*398, giving 

 the change in distribution in C.G.S. lines of induction for 

 each 2*17 cm of length, that being the distance the coils were 

 moved at each step. In determining the difference of distri- 

 bution the angles observed were quite small ; the largest was 



