GENERAL MEETINGS. 
19 
mately represented in the diagram, and the curve will have a point 
of inflexion at which the decrease in the value of 2 / as E P in¬ 
creases will be a maximum. Differentiating the equation twice 
and equating the value of the second differential coefficient to zero 
will give us the co-ordinates of this point of inflexion. The value 
of the abscissa of this point will be 
1 / 3 
From this value the constant a has disappeared, showing that it 
is independent of the intensity of the original shock and dependent 
upon the depth alone. The application of this analysis to the 
problem is as follows : As we recede from the epicentrum the inten¬ 
sity diminishes, but it does not diminish at a uniform rate with the 
distance. There is some critical distance from the epicentrum at 
which the rate of decrease of intensity has a maximum value. 
This critical distance depends upon the depth of the focus and 
upon nothing else, and the magnitude of this distance is equal to 
the depth divided by V 3, and, conversely, the depth of the focus 
is equal to the critical distance multiplied by i/3. If, then, we can 
locate the epicentrum and the points where the intensity diminishes 
with greatest rapidity, we have at once the means of determining 
the depth of the focus. In the case of the Charleston earthquake 
this location has been approximately made and a depth of about 
twelve miles has been deduced for the focus of the principal shock. 
After a description of Mallet’s second method of investigation by 
the observation of the overturning power of earthquakes, the sub¬ 
ject was discussed by the President and by Messrs. H. Farquhar, 
Gilbert, and Dutton. 
Mr. F. 'W. Clarke made an oral communication on the 
MANCHESTER MEETING OF THE BRITISH . ASSOCI AT TON FOR THE 
ADVANCEMENT OF SCIENCE, 1887. 
Remarks upon this communication were made by Mr. Abbe. 
