170 Proceedings of the Royal Society of Edinburgh. [Sess. 
B. The Secondary Wave. 
From R = 6300 to R = 5700 
velocity = 17*37 - '00208 R. 
From R = 5620 to R = 5040 
velocity = 15*93 - '00181 R. 
In the great majority of cases the values of the velocity calculated from 
these formulae differ from the given values by less than 1 in 200. In the 
few cases in which the differences are of the order of 1 to 2 per cent., the 
differences are well within the errors of the data on which the original 
calculations are based. 
For values of R less than about 5000 the velocities of both the Primary 
wave and the Secondary wave become practically constant, the former 
having the value 12'8 and the latter 6*85 km. per second. It should be 
remembered that the data for arcual distances greater than 110° or 120° 
are very uncertain. 
Determination of the Rays. 
In accordance with equation (4) the path or ray depends on the value 
of the integral 
This might be evaluated in parts by means of the empirical relations 
just given between the velocity and the radial distance; but difficulties 
would arise in passing properly from the one linear relation to the other. 
The only certain way is to work out a sufficient number of points on the 
paths by means of quadratures from the Tables IV and V suitably 
prepared. 
For any one ray the quantity p is constant, and the other important 
quantities are the radius r and the ratio (r/v) 2 = rj 2 . The first step is 
obviously to tabulate corresponding values of r and yj 2 from the data given 
in Tables IV and V. Let these then be plotted on a suitable scale, the 
relative scales of the ordinates being adjusted in the various parts so as 
to give well-conditioned graphs. From each of these graphs a new table 
is then to be constructed giving the values of rj 2 for successive equal 
differences of r. The numerical values of p and of rj depend on the unit 
of arc employed ; and in Table VI, containing the data for both the 
Primary and Secondary waves, rj 2 involves the radian as the unit of arc. 
