932, REPORT—1899. 
of the movements is a linear function of the average depth, which7corre- 
sponds, as already indicated, with observation.! 
The result at which Knott arrives indicates that the square of the. 
speed increases at 0-9 per cent. per mile of descent in the earth, the. 
formula being 
v?=2°9+°026d in mile second units. 
With an initial velocity of 1-7 mile per second the velocities at depths 
of 400, 800, 1,200, . . . . 4,000 miles, are 3-7, 4-9, 5-8, 6-7, 7-4, 8-1, 8-7, 
9:3, 9°8 and 10°3 miles per second. The times taken for wave fronts to 
Fic. 5, 
BCH 
SFE 
i 
V 
i. 
ee 
</ 
gq 
reach the positions shown are indicated in the diagram, the time takem 
to pass through the earth being twenty-two minutes. 
I assume that when a wave has passed from its origin beyond the 
region vaguely referred to as the crust of our earth, it then spreads in all 
directions through a mass in which there is only an extremely gradual 
change in elasticity and density with regard to its centre. All wave 
paths, however, before they emerge at the surface, encounter at varying 
obliquities the under surface of this crust. For purposes of illustration 
we will assume this region of abrupt change to lie on the 400-mile circle. 
The path P, meets this nearly at right angles, whilst P, P, meet the same 
at decreasing angles less than right angles. After each of these incidences 
a condensational wave will be refracted and split up into condensational 
and distortional rays. Now it will be observed that these two waves, 
which I will call c and d, will have different distances to travel before 
1 See Lrtt, Assoc. Report, 1898, p, 221, 
