On the Spark-Length of an Induction- Coil. 189 



while J 3 &c. are o£ higher powers in a than a 2 . Thus i£ we 

 stop at the first power of s, we are concerned only with the 

 multiples of t represented by 



p, p-q, p+qi 



while if we include a? we have 



p, p-q, p + q. p-'2q, p + 2q. 



But when a is not small, the convergence is slow, and a 

 large number of terms will be required even for a moderately 

 close approximation. The preceding table, due to Meissel, is 

 condensed from Gray and Mathew's ' Bessel's Functions.' 

 So far as ir can be identified with 3, the values of a equal to 

 3, 6, 12, 18, 24 correspond to maximum deviations of phase 

 (in both directions) equal to \, 1, 2, 3, 4 periods respectively. 

 It appears that the largest value of J„(a) occurs for a value 

 of n somewhat less than a. Indeed, it is at once evident 

 from (12) that frequencies in the neighbourhood of p±qcc 

 will be important elements. 



VIII. J he Spark-Length of an Induction-Coil. 

 By E. Beattie, B.Sc* 



IN an ordinary induction-coil the relationship of the 

 secondary spark-length to the conditions which obtain 

 at the primary break has, at one time or another, received a 

 good deal of attention ; and most of the facts which are likely 

 to have any bearing on the action of the coil are well enough 

 known. On one or two minor points, however, no very 

 accurate or detailed data appear to exist. For instance, 

 although Rijke f has studied the effect on the secondary 

 spark-length of using different materials as the primary poles, 

 and although he has indicated in a general way the influence 

 of rate of separation of the primary poles, yet his experiments 

 were incomplete in many respects. In making the experi- 

 ments described in the present paper 3 the object was to 

 extend Rijke's results, and to examine more fully how the 

 length of the secondary spark depends upon the nature of 

 the primary poles, the rate of break, and the electromotive 

 foi*ce in the primary circuit (1) with no condenser across the 

 break, (2) with condensers of various capacities across the 

 break. 



Apparatus. — The eoil used for the purpose of the experi- 

 ments was one by Apps, giving normally a 25 cm. spark. 



Throughout the experiments the current made or broken 



* Communicated by the Author. 



t Rijke, Pogg. Ann. vol. xcvii. p. 7o. 



