on Galvanometers. 85 



tively proportional to the steady deflexion per micro-ampere 

 and the first swing per micro-coulomb for the same con- 

 trolling-moments for all galvanometers, we must multiply 

 D by I and S by VI* Now the stability of the zero of any 

 galvanometer depends on the controlling-moment per unit 

 angle of deflexion ; hence columns 7 and 8 give numbers pro- 

 portional to the angular deflexion per micro-ampere and the 

 angular swing per micro-coulomb for the same amount of 

 stability of the zero for all the instruments. The periodic 

 times, however, will be very different for the different numbers 

 either in column 7 or for the different numbers in column 8, 

 the periodic time corresponding with any particular number 

 being equal to 10 VI seconds, w T here I is the moment of 

 inertia given in column 6 for the particular instrument 

 in question. For example, the numbers 3200 and 283, given 

 in columns 7 and 8 for Profs. T. and A. Gray's galvano- 

 meter, correspond with a periodic time of 10 y/50, or about 

 70 seconds ; while the numbers 542 and 3400, given in the 

 same columns for the 360,000-ohm galvanometer at the 

 Central Institution, correspond with a periodic time of only 

 10 VO'01, or 1 second. The numbers, then, in columns 7 

 and 8 give a fair comparison between the various galvano- 

 meters when the time required to take an observation is 

 unimportant. 



The influence of resistance has next to be considered. If 

 two galvanometers differ only in the gauges of wire with 

 which they are wound, and the convolutions are similarly 

 distributed, then the sensibilities should be proportional to the 

 number of turns. If, again, the thickness of the insulating 

 covering bears a constant proportion to that of the wire, then 

 the resistance of the coils would be proportional to the square 



of the number of turns ; so that the values of D/r*, S/r 1 

 would be constants for the same pattern of instrument, where 

 D and S are the number of scale-divisions per micro-ampere 

 and micro-coulomb respectively, and r is the resistance of the 

 galvanometer. The proportion in question, however, varies 

 not only for coils of different resistances, but also in the same 

 coil, for several different gauges are generally used in winding 

 the various portions. To get some idea of the relation between 

 resistance and sensibility, we have made tests on galvanometers 

 of the same pattern but of different resistances, the same sus- 

 pended system of magnets being used successively in each 

 instrument, the controlling magnet being adjusted to produce 

 the same periodic time in each experiment, and, when the gal- 

 vanometers were reflecting ones, the scale being placed at the 



