356 Mr. S. D. Chalmers on the Sine Condition 



Summary of Results. 



(1) The corpuscular radiation excited in different metals 

 by homogeneous beams possessing a wide range of penetrating 

 power is absorbed in every case according to an exponential 

 law. 



(2) The absorbability of the homogeneous corpuscular 

 radiation from a tertiary radiator depends solely upon the 

 degree of " hardness " of the exciting homogeneous secondary 

 beam, and not at all upon the nature of the tertiary radiator. 



(3) The absorption coefficient of the corpuscular radiation 

 from any metal is a linear function of the atomic weight of 

 the metal which acts as the source of the homogeneous exciting 

 beam. 



(4) In the case of those metals which emit a characteristic 

 homogeneous Rontgen radiation when subjected to a suitable 

 exciting beam of Rontgen rays, it is found that whenever the 

 homogeneous Rontgen radiation is produced it is always 

 accompanied by a special increase in the corpuscular type of 

 radiation. Where the homogeneous type of radiation is not 

 produced, we still have a portion of the exciting radiation 

 scattered by the metal, while the intensity of the corpuscular 

 radiation is quite considerable. It is probable that the cor- 

 puscular radiation emitted in such cases is intimately con- 

 nected with this scattering. 



In conclusion I wish to express my indebtedness to Pro- 

 fessor Wilberforce for the interest he has shown throughout 

 this research, and for the ready help and advice he has accorded 

 me. I wish also to thank Dr. Barkla for his advice in the 

 early stages of the work. 



George Holt Physics Laboratory, 



University of Liverpool. 



29th January, 1910. 



XXXVI. The Sine Condition in Relation to the Coma of 

 Optical Systems. By S. D. Chalmers, M.A* 



THE condition for the correction of coma in a centred 

 optical system is the well-known Sine Condition. This 

 has been proved by Clausius, Helmholtz, Hockin, and others, 

 and the importance of this condition in the design of optical 

 systems has been pointed out by Abbe, Steinheil, Conrady, 

 and others ; but so far as I am aware no discussion of the 

 effects of failure to satisfy this condition has been published. 



* Communicated by the Physical Society : read June 25 1909. 



