Messrs. Lodge and Howard on Electric Radiation. 65 



(log -j — something), for what we have called the character- 

 istic factor. It is easy to subtract 1 from it if that is the 

 proper thing to do, as our calculation indicates it is. But the 

 violent constriction at the spark, in the case of an oscillator, 

 must cause a considerable increase of self-induction. 



It may be interesting just to quote in similar form the self- 

 induction of the same rod bent into a circle, viz. 



U 



n(bg;-*-hg5) f 



if the currents keep to its periphery. When they penetrate 

 its section uniformly the 4 becomes 5*14, and that is all the 

 change unless it is made of magnetic material. 



It thus approaches the same value as the straight rod for 

 infinite length, but is always distinctly less. 



There is one point on which we find ourselves differing 

 from Hertz. We regret to say that our calculation of 

 radiation-intensity comes out four times as great as his. We 

 get the same formula as he does, so there is no slip in the 

 working there ; but, in the application, a 2 or a s/2 comes in 

 wrongly in one or other of our calculations. His using 

 half-wave lengths is a natural source of confusion, but we 

 have avoided all that ; and it must be that it is owing to a 

 different calculation of the effective capacity concerned in an 

 oscillator that the discrepancy arises. If an oscillator has 

 spheres 30 centim. diameter at either end, Hertz calls its 

 capacity 15 centim. ; we call it 7-^. We feel bound to call 

 it 7 J according to any method of calculation ; although the 

 radius of either sphere is the natural thing to write down at 

 first thought. The charge which surges into either sphere 

 has had to come from the other, not from the earth or any- 

 thing of infinite capacity. The two spheres are therefore like 

 two condensers in series. Hence our wave-lengths are 

 l/x/2 of Hertz's wave-lengths (or rather >/2 times what he 

 calls his wave-length) ; and since X occurs to the fourth power 

 in radiation intensity, it makes our radiation 4 times as strong 

 for a given oscillator as that which he would calculate. 

 This discrepancy we by no means view lightly, and it is not 

 without many qualms that we find ourselves differing, even 

 about a 2, with a man so splendidly careful in his work as 

 Hertz has shown himself. It is more than probable that he 

 is right after all, so we explain what will then turn out to be 

 our error in this note. 



Phil. Mag. S. 5. Vol. 28. No. 170. July 1889. F 



