ON THE INDUCTION-COIL. 



203 



will increase numerically towards eittier end. The factor of réduction 



on this account will be j ^ x 1 dx, or jlj, so that we may take as the 



value of q in (6) about 22 cm., probably rather an underestimate. Cal- 

 culating froin thèse data, we get in (6) 



F= 2600. 



This is in electrostatic measure. The corresponding volts are 7*9 X 

 If we reckon 33,000 volts to the cm., the sparklength will stand at 

 24 cm. The coil in question is supposed to be capable of an S or 10 cm. 

 spark, and doubtless was capable when new. It is remarkable that the 

 limit, fixed by the iron and secondary capacity alone, should exceed so 

 moderately the actual capability of the coil. 



The limiting formula (6). in which neither the value of the primary 

 current nor the number of secondary windings appears, is arrived at by 

 supposing the iron to be magnetically satnrated. It illustrâtes, no doubt 

 with much exaggeration, the disadvantage of too great a length. If a 

 be given, while c varies, v and q are both proportional to c, so that 

 V ce \/N. And \/N co c~ x nearly. In somewhat the same way the in- 

 crease of effective capacity exjDlains the comparative failure of attempts 

 to increase spark-length by combiiiing similar coils in séries, in spite 

 of the augmented energy at the moment of break ] ). 



If the object be a rough estimate rather than a limit, a more practical 

 formula will be obtained by substituting for 3 in (6) its approximate 

 value fy\N -, so that 



ff denoting the external magnetizing force, due to the primary current. 

 The actual magnetizing force, required to magnetize the soft iron, is 

 here regarded as relatively negligible. Àccording to (7) the spark-length 

 is proportional, cœleris paribus, to the primary current; and it increases 

 with the length of the coil, since N now occurs in the denominator. 

 The application must not be pushed into the région where the iron 

 becomes approximately saturated. 



a ) I am indebted to Mr. Swinton for the détails of some experiments in this 

 direction made for Lord Armstrong. 



