Section- III., 1913. [97] Trans. R.S.C. 



On the Gradient of the Penetrating Radiation from the Earth 



By Louis V. King, B.A., Asst. Prof, of Physics, McGill 

 University, Montreal. 



(Presented by Prof. H. T. Barnes, F.R.S.) 



(Read May 28, 1913) 



Sect. 1. Introduction. 



It was first shown by Eve* that if the penetrating radiation is due 

 to 7-rays from the radio-active constituents of the soil, the intensity 

 should decrease rapidly with height above the earth's surfaces and 

 should be easily measurable. 



The analysis was extended by the writerf and the gradient expressed 

 in terms of a transcendental function denoted by 



f (x)= e-^ + Ei (-X) 

 Ei ( — x) representing Glaisher's exponential integral. The function 

 Ei ( — x) is of special importance in all problems relating to radiation 

 from plates which radiate from each element of volume and also 

 absorb their own radiations exponentially. J 



The object of the present note, undertaken at the suggestion of 

 Professor A. S. Eve, is to set forward the formulae for the gradient of the 

 penetrating radiation and interpret them numerically in terms of the 

 constants which have been determined since the papers above referred 

 to were published. A brief account of experiments bearing on the 

 subject is also given and the results discussed. 



Sect. 2. — Calculation of the Gradients of the Penetrating Radiation. 



The following notation is employed in the sequel: 



ni=number of ions produced per second per c.c. at a height z^ 

 above the earth's surface. 



n^ refers to the number of ions produced per c.c. per sec. in a 

 small cavity at a depth 22 below the earth's surface. 



Hi and /i, are the mean coefficients of absorption of 7 -rays by 

 air at ordinary pressure and temperature and of rock respectively. 



*Eve, Phil. Mag. 21, Jan., 1911, pp. 26-46. 

 tKing, Phil. Mag. 23, Feb., 1912, p. 242. 



J Applications to radiation problems are given by the writer, King, Phil. Trans. 

 495A, Vol. 212, p. 375, 1913. 



