the Winding of Voltmeters, 113 



an outside resistance-coil of any resistance and of any volume 

 can be calculated from (20). 



It is obvious that as V becomes greater the error becomes 

 less and less, but there is a practical inconvenience in largely 

 adding to the weight of the instrument. 



VI. To determine the best resistance to give to the outside 

 coil of given volume, — When V is fixed, e is a maximum or 



inimum, when 

 ow 



dy 



B 9 , r. B . 



de V^ +2 V^- A 



id 



dy {1+yf ' 



A 2 (T +A ) 



dy 2 (1+y) 3 ' 



y must be positive, therefore (1 +y) B is positive, also A and 



d 2 e 

 B are both positive, therefore -=-3 is positive, and therefore e 



is a minimum, when 



d l-0 

 dy-°' 



that is, when 



B / + 2 | i?/ -A=0, 



or 



y— l±\/i+^; 



but y cannot be negative, therefore only the positive sign can 

 be used, or 



y 



-XA+TT- 1 ( 21 ) 



makes e a minimum. 



Substituting this value of y in (20), we find that 



/ 1+ A 



:2 Y V " B 



v/= 



VII. To determine the best volume, and the best resistance to 

 give to the outside coil for a given permissible error, — From the 

 Phil. Mag. S. 5. Vol. 21. No. 129. Feb, 1886.- I 



