318 Mr. C. Godfrey. On the Application of 



No iodine or bromine could be detected in the small quantity of 

 water available for examination. 



' Spectroscopic examination revealed the presence of a trace of 

 barium. The quantity present would have been quite unweighable, 

 and although estimated with the calcium could not have vitiated the 

 results. 



The results given under the heading B are regarded as those which 

 most nearly represent the true condition of the lake, and consequently 

 no attempt has been made to strike an average between the two series 

 of results. The A results are given in extenso in order to demonstrate 

 the degree of reliability of the B results, a matter which will be of 

 importance in the future, when, after an interval of some years, 

 another investigation of the water of Lake Urmi is made. 



" On the Application of Fourier's Double Integrals to Optical 

 Problems." By Charles Godfrey, B.A., Scholar of Trinity 

 College, Isaac Newton Student in the University of Cam- 

 bridge. Communicated by Professor J. J. Thomson, F.R.S. 

 Received June 12, — Bead June 15, 1899. 



(Abstract.) 



The propagation of plane plane-polarised light in the direction of z 

 is governed by the equation Y 2 ^ = where V k is the velocity 



of light. 



The most simple solution of this equation is — 



(!)• 



This may be interpreted as a train of waves of amplitude R, period 

 2ir/u, and phase ^, travelling with velocity V. This train of waves is 

 without beginning or end. Most of the results of physical optics have 

 direct application to a disturbance of the above form. 



No radiation is found in nature which has the properties of the 

 above function. The fact alone that all natural radiations have 

 beginning and end would suffice to render (1) an inadequate repre- 

 sentation. 



It is required to solve the problem how to represent any natural 

 radiation faithfully without losing the conveniences connected with 

 the form (1). The problem recalls the familiar process of harmonic 

 analysis. This p-ocess is applicable only to periodic functions, 

 whereas such a motion of the aether as constitutes white light is 

 non-periodic. In this connection it has been pointed out by Gouy 



