large and very small Alternating Currents. 273 



Unfortunately, in practice we cannot quite attain to the 



condition ~ = <x> , but we can get near enough to make the 



error quite small. In the following table are given (approxi- 





mately), for different values of^-, the values of the ratio ^ 



for frequencies of n = 80 ~ per sec, and n = A0 ~ per sec, if 

 the ratio =1 when n = x) . 



Table I. — Transformation Ratios. 



R 2 



»=au . 



»==80. 



n=40. 



100 



1-00 



1-02 



1-08 



50 



1-000 



1-005 



1-02 



25 



1000 



1-001 



1005 



10 



1-000 



1-0002 



1-0008 



By this it will be seen that if *J> = 50, the error in the 



transformation ratio from n = 80 to w = oo becomes insignifi- 



cant ; and that if ^J = 25 the ratio is approximately constant 

 down to ?i = 40. -d T> 



In practice it is easy to make — =50, but to get ^J =25 



would require a rather lavish expenditure of copper wire. 



Instead of finding the ratio of a particular transformer 

 (with ammeter) once for all, a simple way is to find it each 

 time for the frequency to be used, the strength of the primary 

 current being chosen so as to lie within the range of the 

 instruments available. 



The following instance will make the method clearer. 

 Suppose we want to measure currents up to 1000 amperes 

 with an electrodynamometer and a Kelvin balance, each up 

 to 100 amperes. Let the transformer have a " current ratio " 

 of about 10 when the balance is the only load on the secondary. 

 The electrodynamometer is inserted in tlie primary circuit, and 

 a primary current of (say) 98*2 amperes is found to produce 

 (say) 10 amperes in the secondary. If the electrodynamometer 

 be now taken out of circuit, any\ primary current up to 1000 

 amperes can be measured by reading the balance in the 

 secondary and multiplying by 9*82. 



Phil Mag. S. 5. Vol. 42. No. 256. Sept. 1896. X 



