ELECTRO-CHEMICAL EQUIVALENT OF SILVER. 
415 
There would be some advantage in a disposition of the coils such that B 3 —|A 3 =0, 
for then the attraction would be in a high degree independent of the position of the 
suspended coil. In this case 
“=6^X'2138.(6) 
If, on the other hand, we take B 3 =;jA_ 3 , we find from the first term 
^=6^X‘2862. . .(7) 
showing a not unimportant increase of effect. To the second order of approximation 
the distance between the fixed coils (2B), corresponding to the maximum effect upon 
a small coil suspended at their centre, is given by 
b=4a(i-a|).(8) 
so that when a 2 /A 2 is sensible the fixed coils should be somewhat closer than when 
a 2 /A 2 is negligible. For the actual apparatus used a 2 /A 2 is very sensible, and the ideal 
state of things was only imperfectly approached. The coils of the dynamometer used 
for the “fixed coils” conform to the relation B 3 =^A 3 , and are not adjustable. It will 
be seen later that but little is practically lost by the slight imperfection of the 
arrangements in this respect. 
Formula (7) is sufficient for the preliminary estimate of the attraction to be expected, 
and from (5) we can form an idea of the exactitude necessary in the adjustment of the 
suspended coil. Thus if b be not zero, the correcting factor is, when B = -|A^ 
1-3-2^ .(S) 
With the actual apparatus an error in b of one millimetre alters the attraction by 
on ly AoTooV 1 
§ 7. It may be convenient to carry through the rough theory so as to show the 
dependence of the current upon the quantities actually measured. Thus 
Force of attraction =hnn ihv l /A. 2 , 
where h is written for 67 t 2 X '2862. If the ratio of the galvanometer constants of the 
coils be (3, we have 
« 2 /A 3 =/3 3 n /2 /« 2 , 
whence 
F orce = hf3Hhi s /n, 
and 
%■= f$~ x hr l 7irri~*{ Force) 4 .(10) 
