1895.] Conductivities of Badly Conducting Substances. 259 



Thus until S is less than 



2E 

 the maximum current through the primary is less than 



U 



which is the maximum value of the current when 8 is infinite or 

 when the secondary circuit is broken. Thus we get the somewhat 

 curious result that the current through the primary of a trans- 

 former is less when the transformer has a slight load than when it 

 has no load at all. 



The work absorbed by the transformer in unit time is 

 J E^ cos a 

 '^ '^L'Y + R'^ 

 ^ , E'R' 



_^ E'[S (Ly - R') + p'R {2LN - M')] My ^ E'R 



~2 (8'+]sry){L'y+R"){Ly+R') '^^ly+R'' 



The second term on the right-hand side of this equation is the 

 work absorbed when the secondary circuit is open; if Xp is greater 

 than R, the first term is positive for all values of S; hence the work 

 absorbed in the primary is in this case always greater when the 

 secondary is closed than when it is open. 



If R is small compared with Lp, we find from the preceding 

 expression that the absorption of energy is greatest when 



a /at ^^ 



Thus if there is any magnetic leakage between the primary and 

 secondary, i.e. if LN does not equal M^, there is a definite resistance 

 for which the work expended in the primary is greatest. 



We shall now consider the case when the currents which 

 circulate through the primary are those produced by discharging 

 a Leyden jar; we shall suppose that the primary circuit connects 

 the inside and outside coatings of a jar whose capacity is C. Let 

 X now denote the charge in this jar at any time, the rest of the 

 notation being the same as before ; then the equations giving the 

 currents through the coats are, 



^l?+^f +^s + 5=« ■•■■«■ 



20—2 



