10 Louis Schwendler — On Differential Galvanometers. [No. 1, 



1 and 10,000, the two limits of measurement. The question now remainia 

 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 



IV = 7500 

 against which the resistance of the battery may always be neglected, 



Consequently we have 



^=^==2500 



for each coil. 



Now if the coil be small, and consequently the wire to be used for filling 

 it is thin, the value g = 2500 wants a correction to make allowance for the 

 thickness of the insulating material, by which g becomes somewhat smaller.* 



Before concluding I may remark that the question of the best resistance 

 of the coil, when the resistance to be measured varies between two fixed or 

 variable limits, can be solved mathematically by the application of the 

 Variation Calculus. 



* These expressions for g and g ' must be corrected, if the thickness of the 

 insulating covering of the wire cannot be neglected against its diameter. ThQ 

 formula by which this correction can be made was given by me in the Philosophical 

 Magazine, January, 1866, namely 



z=^cg il — ^ / g wi^ I 



corrected g 

 where g =5 the resista^ce to be corrected and expressed in Siemen's Units, 



/ c -K K 

 and m == 5* V —r^ 



8 = radial thickness of the insulating covering expressed in millimetres. 



c = a co-eflBicient expressing the arrangement adopted for filling the available 

 space uniformly with wire. Namely, if we suppose that the cross section of the coil, 

 by filling it up with wire, is divided into squares we have c == 4, if in hexagons 

 c s= 3.4. &c., &c. 



A == absolute conductivity of the wire material (Hgr = 1 at freezing point). 



A = half the section of the coil in question when cut normal to the direction of 

 the convolutions, and always expressed in square millimetres. 



B = length of an average convolution in the coil, and expressed in metres. 



