241 
by reducing K or by increasing 7. The latter alternative, however, 
would soon render the galvanometer less fit; therefore I prefer to 
introduce at once the maximum value of 7’ which we will allow 
in any special case. So we must try to find the maximum of (4) 
for fixed 7’, mirror and external resistance. Moreover [Il assume 
H to be given. From the result it will then be clear in which way 
the resulting sensitivity depends upon H. From (2) and (3) we find: 
Ax Kr 
Tie 
Now suppose the coil to be short cireuited and the mirror removed 
by which Ar= Kr, thus assuming its minimum value for the 
coil in use. 
From (5) we then derive the minimum value of AH with which 
the galvanometer can be made aperiodic. The importance of this 
minimum magnetic field, which I shall represent by Hin, lies in 
the fact that this quantity appears to be independent of the dimensions 
of the coil, the diameter of the wire ete. Indeed, taking only the 
vertical part of the windings into account, it will be easily found that: 
Kr. 
f = 80 
i.e. the product of the density and the specific resistance of the 
metal. The horizontal part of the circuit of the coil, the insulation 
ete. can only crease the value found here and consequently Hi. 
The following relations therefore hold: 
4a Kor, 4286 
EE T f == T (6) 
so that Hi must be considered as a constant in finding the maximum 
sensitivity. 
(5) and (6) give: 
H* Kr 
= ME stil ve Vareansl denpennnGiay 
Fe Ter. a 
in which thus m is a known number > 1. Representing K/K, by 4, 
r/r, = m?/k. Instead of (4) we can write: 
Tike ] me” 
pd ln en a .) 
An? (K—K,) (r—r,) m? k 
In this expression only the two last factors are variable. Their 
product is a maximum for =m. Hence the conditions for maximum 
sensitivity are: 
r Ved 
= oid Se Ee Nee ENEN 
H, min ( ) 
FEO ol 
eee 
