96 Mr. H. Barfield on the Experimental 



A the moment of inertia of mirror and needle, 

 Q the quantity passing in each transient current, 

 n the number of such currents per second, 

 </> the permanent deflection due to their passage, 

 6 the throw of the needle due to one transient current. 

 Then Ht 



\JT7T 



nQ= p- tan </>; 

 or, with sufficient accuracy for the purpose of this comparison, 



0=Wt Q > (1) 



</>=|xn.Q (2) 



Thus </> nr /Q . 



I'V (d) 



And it may be observed, in passing, that these "equations hold 

 rigidly true when <f> and 6 become very small ; and thus, in 

 the use of a null method, the equation (3) accurately expresses 

 the relative sensitiveness of the two methods. 



AT • *T /MH L . ■ „, 



JNow, since - = </ — r-> equation (1) may be written 



»=«- G Vn < 4 > 



So that, with Q and G given, to obtain the largest value of 0, 



M 



we must make -r- as large as possible and H as small as pos- 

 sible. The former condition is provided for in the Thomson's 

 galvanometer; and, using such an instrument, we have only 

 to make H as small as we are able. In doing this r is in- 

 creased, and equations (2) and (4) show that, whilst we are 



increasing in the ratio — -=, <j> increases in the square of that 

 ratio. vH 



Now, by diminishing H, r may readily be made as large as 

 2tt, in which case the relative sensitiveness of the two methods 

 would be given by the equation 



4> = 2n6 (5) 



From this it would appear that the value of (f> is only limited 

 by that of n. This latter quantity, again, cannot exceed a 

 limit determined by the duration" of the transient current. 

 This duration Blaserna gives as ^^ second, or thereabouts, in 

 one of the cases investigated by him ; but the capabilities of 



