fundamental Equation in general Theory of Relativity. 285 



which the graphite plate is covered, give bands of similar 

 appearance and likewise sensitive to thermo-electrical ex- 

 citation. The strontium bands are situated in the red and the 

 blue, and those of barium in the green. With the oxide o£ 

 the last named metal the colour of the fringe is green. If 

 none of these compounds is present in appreciable quantities 

 the fringe has a bluish-violet tint. 



The spiral and helical paths observed when a magnetic 

 field is acting downwards are caused by the motions of 

 positively charged particles emitted by the alkali metals. 

 The temperature at which emission of positive particles 

 begins varies inversely as the atomic weights of these 

 elements. The deflexion of the positive streamer by a 

 magnetic field provides a very sure guide as to the presence 

 of these elements in minerals, &c; and this method of 

 detection is more rapid and convenient than the spectro-' 

 scopic test. There are also indications of the emission of 

 negative particles at higher temperatures and with stronger 

 magnetic fields. It seems likely that the phenomena ob- 

 served are analogous to those discovered by Sir J. J. 

 Thomson in connexion with the emission of rays of positive 

 electricity by gases at low pressures*. Thus the emission 

 of positive particles by the alkali metals might possibly be 

 caused by the breaking up of the molecular or atomic systems 

 of these elements, which according to preliminary deter- 

 minations would set in at approximately the following tem- 

 peratures: lithium at 2700° C. ; sodium, 2550°; potassium, 

 2300°; rubidium, 2200° ; and caesium, 1900°. 



XXYI. Parametric Solutions for a Fundamental Equation in 

 the general Theory of Relativity, with a Note on similar 

 Equations in Dynamics. By E. T. Bell f . 



1. TT may be of interest to note that we can solve 



A ds 2 = ta lJ dx i d.r j (i,j=l, 2,3,4), . . . (1) 



which is the point of departure for much recent work in 

 the theories of generalized relativity and gravitation, very 

 simply if we assume that s, x\, a' 2 , x 3i # 4 are functions of four 



* J. J. Thomson, Phil. Mag. vol. xxi. p. 22o (1911). 

 t Communicated, by the Author. 



