26 Proceedings of the Royal Society of Victoria. 



the u'ou losses are equal, we find, taking the figures for the 10 

 K.W. transformer discussed in § 23, that /? will be given by the 

 equation 



/ 10,000 X 



Cot/3 = tan8n +z ,oQ ) 



where z is the fraction of full load and 8 = 50' for the closed- 

 circuit, and =4° for the open-circuit transformer. 



The figures in the following table, calculated from the above 

 formula, show the relative approach to opposition of C^ and C^ 

 in 10 K.W. transformers of the two types. 



In V)oth cases the approach to opposition will be quicker for 

 larger transformers, as in them the iron loss is a smaller fraction 

 of the full load output. 



For inductive loads having a constant power factor Cos<^ 



P.,Sin8 



Cot^ = tan(8 + <^) + g^^^^^^^^^g^^ 



7r 

 SO that at no-load /? = ?, — (S + 0) or C^ and C, at the beginning of 



the range are nearer to opposition for both types than when the 

 load is non-inductive, and as Cos<^Cos(8 + <^) is less than unity, 

 the successive increments to Cot/3 for definite fractions of the 

 load will be greater ; hence for both types of transformers the 

 approacli to opposition of C^ and C, will be more marked with 

 inductive than with non-inductive loads. 



Section II. 



27. The theory developed in Section I. is easily applicable to 

 the design of a closed-circuit transformer, when the full load, 

 power factor of the load, periodicity, and e.m.f.'s are given. 



In the first place we would select the form of the magnetic 

 circuit, and after consideration of the probable cooling surface, 



