278 



within a cone of small angle, cutting off but a small portion 

 of terrestrial surface near the oscillator, true diffraction-band* 

 are found, arising ultimately from terms, now important, in 

 which order and argument are nearly equal. These bands 

 are also in accord with expectation. But within the shadow, 

 beyond the extreme generators of the cone, the extinction of 

 the waves is very complete. The harmonics of high order 

 are found to be so disposed as to neutralize one another in a 

 remarkable way, and the intensity of the diffracted light, at a 

 distance of a few thousand miles round the surface, sinks to 

 a minute fraction of its value when the sphere is absent. 

 Thus it is improbable that diffraction can explain the effects, 

 unassisted by reflexion from an ionized layer in the upper 

 atmosphere, or by some other cause. The use of directive 

 oscillators in practice, can cause a change, and Sommerfeld* 

 has shown that the finite conductivity of the earth may be 

 sufficient. 



There is one other point of importance in which M. Poincare's 

 investigation may be criticised. The harmonic series is, 

 at one point, replaced by a definite integral in the ordinary 

 way, in order to obtain its first approximation. But there is 

 a special class of series, to which this belongs, for which this 

 integral is not valid. This is the class whose general term 

 contains an exponential of very large argument. The proper 

 formula, expressed as in the integral, for this case is very 

 different, and has been given by the writer t to a high degree 

 of approximation, having also been originally suggested to 

 him by problems of diffraction by large obstacles. 



The proof of the physical results mentioned in the course 

 of this note will be given in a later communication. 



XXVI. Some Variations observed in Electroscopic Measure- 

 ments and their Prevention. By A. S. Russell, M.A. r 

 J3.Sc., Carnegie Research Scholar and 1851 Exhibition 

 Scholar^. 



THE curious varying-leak effect observed in working with 

 the 7 rays of radium and uranium X already described 

 (Soddy and Russell, Phil. Mag. Oct. 1909, p. 635, last 

 paragraph), has now been investigated in some detail and 

 has been traced primarily to the use of too long a stick of 

 sulphur in insulating the leaf system. 



As the work shows clearly a possible source of error to be 



* Ann. der Phys. lGtli March, 1909. 



t Messenger of Mathematics, October 1907. 



X Communicated by F. Soddy, M.A. 





