lo GWYTHER, Rate of Propagation of an Earth-Tremor. 



In (ii), I write 



7' = log{^ + s-tanh='/3}, 



/=Iog{A'^ + 2=tanhV}, 

 in which X stands for x—x' — qt^ and in which a has been 

 put equal to zero, so that the wave progresses in the 

 direction of the axis of x. 



Then, for the stresses R and 5, we find 



R= - Aoq ^(2Cosh-y - I )|^^-^, ^ ,.tanh^/3^) " (^'^ + 2^tanhV)d' 

 c o. ,0 ^ r 4tanh^/3 (i+tanh^y)^ T 



Except at the points where X = 0, these vanish with ^, 

 and have the appearance of becoming infinite when both 

 X and z vanish. But if we imagine the surface loaded 

 with lines of density (t, all parallel to the axis of j, and 

 compare with the second differential coefificients of the 

 logarithmic potentials due to the attraction of these lines, 

 we may, by analogy, find that R and 5 are finite, but 

 offer discontinuities of the same character as in the similar 

 case of attraction. 



Since these expressions are complicated, I will illus- 

 trate upon the simplest case of the wave of displacement 

 transverse to the direction of its progression, and parallel 

 to the earth's surface, under the conditions given by (8). 



In this case we shall have, for points not quite close to 

 the pole, 



« = 



z;^.e^sinhV ^,_^^,^f^^,^^ (x6) 



7f/ = 0. 



If we draw in the substance of the earth, one-half ot 

 the cylindrical surface of which the equation is 

 A'- + z-tanh'^y = t^sinh^y, 



