A POCKET GALVANOMETER. 



293 



there is only one variation of sign among the coefficients of a what- 

 ever h or c may be. Hence this equation has only one pair of real 

 roots. Putting a=—y=h, and «=-^ ^ successively the expression 

 changes sign once, so that the positive root of this equation lies 

 between .5 and .71 whatever be the values of c/b. Dividing the 

 equation by its last term we see that the higher powers of a rapidly 

 converge when c increases. When c = oo the equation reduces to 



which agrees with the previous result. When h = c = 1 it reduces to 



4 {a"" + ly (Ga« + 18fi* + lia'- - 5) = 



as might be found by an independent calculation. 



Since a knowledge of the solution of this equation will serve as a 

 guide in the construction of such galvanometers, I give the following 

 table of its roots for several values of c/b together with the values of 

 the field and the proportional decrement of force at the point "ex = 

 7^rt. From these numbers we can at once judge of the uniformity of 

 the field. 



Value 



of c;6. ' 



I (root). 



2ian--^^. 



l'a V ■'\ H ' 



j2J';Poata; = èci. 



1 



54451 



57° 8' 



8.144 



.00085 



Vl=lA 



G0040 



61° 58' 



7.151 



.00081 



2 



5973G 



or 4L' 



G.G81 



.00077 



3 



58393 



G0° 34' 



G.3G5 



.00074 



4 



57983 



ßü° 13' 



G. 222 



.00074 



5 



578 J 3 



GO" G' 



G.148 



.00074 



10 



57742 



GO" Ü' 



G.039 



.00074 



00 



57735 



GO" 0' 



G.OOO 



.00075 '■■- 



For Helmboltz's airaugem ut â^P¥ç,= .0007 



