272 Mr. Louis Schwendler on Differential Galvanometers. 



differential coil should consist of separate coils connected with a 

 commutator in such a manner that it is convenient to alter the 

 resistance of each coil according to circumstances, i. e. connect- 

 ing all the separate coils in each differential coil parallel when 

 the resistances to be measured are comparatively low, and all the 

 separate coils consecutively if the resistances to be measured are 

 high &c, fulfilling in each case the law of maximum sensitive- 

 ness for certain resistances, which are to be determined under 

 different circumstances differently, but always bearing in mind 

 that it is more desirable to fulfil the law of maximum sensitive- 

 ness for high resistances (when the testing current in itself is 

 obviously weak) than for low resistances. 



An example will show this clearer. Say, for instance, a dif- 

 ferential galvanometer has to be constructed for measuring 

 resistances between I and 10,000. A Siemens' s comparison box 



of the usual kind f m J being at disposal, it will be conve- 

 nient and practical to decide that the two differential coils should 

 be of equal magnetic momentum; from which, it follows that C 

 as well as p must be unity, or, in other words, that the two coils 

 must be of equal size, shape, and distance from the needle, and 

 must also have equal resistances, i. e. must be filled with copper 

 wire of the same diameter. The resistance of each coil is then 

 found by 



9=t ~ ^ + I ^*** + W°+f*> 



where / is the resistance of the battery, and iv a certain value 

 between 1 and 10,000, the two limits of measurement. The 

 question now remains to determine w. 



It is clear that the law of maximum sensitiveness has not to 

 be fulfilled for either limit, because they represent only one of 

 the 10,000 different resistances which have to be measured ; but 

 it is also clear that to fulfil the law for the average of the two 

 given limits would be equally wrong, inasmuch as the maximum 

 sensitiveness is far more required towards the highest than the 

 lowest limit. We may assume, therefore, that it is desirable to 

 fulfil the law for the average of the average and the highest limit, 

 which gives 



w=7500, 

 against which the resistance of the battery may always be neg- 

 lected. 



Consequently we have 



f =2500 



O 



for each coil. 



