416 JOURNAL OF THE WASHINGTON ACADEMY OF SCIENCES VOL. 13, No. 19 
obtained by comparing their times of arrival at various points on the 
surface with the corresponding distances from the origin) should 
vary with the distance, whereas the velocity of the surface-waves 
should be constant. The data obtained from seismograms indicate 
that the material of the earth, except at the surface, may be treated 
as (megascopically) isotropic. It is fortunate that this is the case, 
since otherwise the mathematical treatment of seismologic data would 
be extremely difficult. 
Starting from a time-distance curve, that is, the times of arrival 
of a disturbance at given distances along the surface, by a compara- 
tively simple process one can calculate the elastic constants of the 
material of the earth at various depths. The steps in the process are 
as follows: (a) from the slopes of the time-distance curves the ap- 
parent surface velocities of each of the varieties of through-waves is , 
obtained; (b) by graphical integration of a certain function of the 
surface-velocity there is obtained the maximum depth for a wave 
traveling between two points separated by a specified distance; 
(c) from a very simple relation the true velocity at this depth is 
determined; (d) and finally, the bulk modulus K and the rigidity R 
are calculated from the equations: 
R/p = Vs? (5) 
K/p = wt — 509 6) 
obtained directly from (3) and (A). 
With the time-distance curve given by Turner! the velocity-depth 
curve shown in Fig. 1 was obtained.’ In this figure the abscissae 
represent depth in kilometers and the ordinates the velocity in km/sec. 
This curve closely resembles that obtained by Wiechert® and by 
Knott.?7. The velocity of both kinds of waves increases rapidly at 
first, and then steadily and almost linearly until a depth of 1600 km 
is reached, after which the velocity, although nearly constant, shows 
a tendency to fall off, especially at about 3000 km. By the use of 
equations (5) and (6) it is evident that these curves could be con- 
verted into a compressibility-depth and a rigidity-depth curve—pro- 
vided that the density were known. 
4See Davison, Manual of Seismology, p. 145. 
5 further details will be given in a subsequent communication. 
6 Nachr. Kgl. Ges. Wiss. Géttingen. 1907, pp. 415-549. 
7 Proce. Roy. Soc. Edinburgh, 39: 167. 1918. 
