PEIRCE. — BALLISTIC GALVANOMETERS OF LONG PERIOD. 313 



S Q - ^T~2 \- e9T to • sin p t ~ p • cos /"") _ fl ( 53 ) 



q = k {l _ e -kry (54) 



.If gr = _ £, a = 0.0125, and p = 0.0450 ; the value of A/A will be 

 0.989, if the current flows until the needle reaches its elongation, say 

 for 29 seconds. 



When the shape of an induced current which is to pass through a 

 ballistic galvanometer of long period is not analytically simple, it is 

 always possible to determine by mechanical integration, with sufficient 

 accuracy, the ratio of the throw caused by the current to the throw 

 which the same total quantity of electricity sent instantaneously through 

 the instrument would give. As an example, we may consider the form 

 of current represented by the curve ODJPW of Figure 0, which is a 

 fairly close copy of an oscillogram. If we assume that the duration of 

 the current is to be 4 seconds and that galvanometer V is to be used, 

 so damped that 



a = 0.0125, P = 0.0450, 



it is easy to measure a number of ordinates of the current curve, mul- 

 tiply each by the corresponding values of e at ■ cos pt, e at • sin pt, and thus 

 compute the ordinates of the curves OUPW and OQW. The areas 

 under these curves obtained by a good planimeter represent RQ and 

 SQ of (35) and (42), and the area under the current curve gives Q 

 on the same scale. An actual trial would show that A falls below A 

 by about one seventh of one per cent. If the galvanometer W were 

 used, it would be quite impossible to detect the difference between A 

 and A, even if the duration of the current, of the form shown, were as 

 much as 16 seconds. 



The galvanometers V and W are to be used in making determina- 

 tions by the " Isthmus Method " of the ultimate values of the intensity 

 of magnetization in a large number of specimens of magnetic metals, in 

 cases where it is necessary to reverse the direction of the exciting cur- 

 rents. When a rather small yoke which weighs about 300 kilograms 

 is used under a fairly high voltage, V works very well : the whole dura- 

 tion of the induced current is practically less than 5 seconds, and the 

 intensity falls off rapidly after the first, so that the difference between 

 A and A is wholly inappreciable. For very high values of the induc- 

 tion a solid yoke of the form shown in Figure B is to be employed. In 

 this case the smallest cross section of the core has an area of 450 square 

 centimeters, and it is not possible sensibly to reverse an excitation of 



