the Winding of Voltmeters. 105 



p cannot be of the simple character here assumed; but inas- 

 much as our results are only applied in cases where the wind- 

 ings are either of German silver or of copper, or of the two 

 together, and in these cases the expressions used are quite 

 correct, there is no practical objection to the use of such a 

 law. The law is very nearly the same as the assumption that 

 a wire of any material, lying electrically between German 

 silver and copper, is made up of wires of German silver and 

 copper. 



Since from (7), 



p—2+b— ia + c, 



it follows, using (13), that 



^=2 + 1-1436-4^ (14) 



and the values of m and n are given respectively in terms of 

 a, b, and d in (5) and (6), and are 



m=2 + b-2a (14) 



n — d—a + l (14) 



In our Solenoid Voltmeter, r equals 1, r x equals 8, and d 

 equals —1; and since the greatest value of p is 13p , it follows 

 that r b cannot be greater than J 3, but & is a constant, and 

 the greatest value of r is 8, therefore b must be less than 

 2. From (14), since b is always small, we see, after a has 

 reached a certain large value, that p, m } and n increase 

 numerically as a increases, and are positive when a is nega- 

 tive, and vice versa ; also that, finally, p equals 2m or 4n. 



Substituting the values for r and r\, the error (9) may be 

 written 



^fe) V8^l) 



P 

 8*-l 



and it may be seen by inspection that each of the factors of 

 which it is composed is always positive, whether m, n, and p 

 be positive or negative. Therefore the error is always positive. 

 For large values of m, n, and p, the error may be written 



\8 n -l)\& n -l) 



An 



8 4 "-l 



