576 Proceedings of Royal Society of Edinburgh. [sess. 
with the same instrument. There is a clear indication that the 
preliminary tremors outrace the large waves by intervals of time 
which are proportional to the arcual distances between the place 
where the record is taken and the place where the earthquake 
shock is most violent — or, what amounts to very nearly the same 
thing, proportional to the average depth of the chords connecting 
these places. 
Again, from a knowledge of the instant at which the earthquake 
really occurred, the approximate times of propagation of the 
preliminary tremors and of the large waves can be calculated. 
From the data given by Milne I have deduced a simple 
formula * for the speed of propagation of the preliminary tremors 
in terms of the average depth of chord, on the assumption that the 
line of propagation is that of the chord. It is 
z; 2 = 2-9 + ’02 Qd, 
where v is the speed in miles per second, and d the average depth 
of chord in miles. Expressed in kilometres, the formula becomes 
^2 = 7*5 + -042c?. 
For large depths of chord, this formula approximates to Milne’s 
own statement that the speed varies as the square root of the depth 
of chord. 
When a like calculation is made for the larger waves, the speed 
is found to be practically constant for arcual distances greater than 
60°, its value being 1*7 miles per second. 
The formula just given may be used to obtain an approximation 
to the form of the wave-front of simultaneous disturbance as it 
passes through the earth. The problem, mathematically stated, is 
similar in essence to finding the wave-front in a crystal, the differ- 
ence being that in the optical problem the speed of propagation has 
a value depending on certain directions in the crystal and is other- 
wise the same at every point, whereas in the present problem the 
speed depends on the distance from the earth’s centre. 
In Nature Professor Milne reproduced a rough sketch in which 
I gave the forms of successive wave-fronts drawn by aid of the 
See Scottish Geographical Magazine, January 1899, p. 9. 
