SOME APPLICATIONS OF PHYSICS AND MATHEMATICS 
TO GEOLOGY.* 
By C. CHREE, M. A. 
I.—SOME PHYSICAL AND MATHEMATICAL DATA. 
Many of the terms employed in treating of the properties and condi- 
tions of matter have in common use a somewhat vague meaning. The 
meaning, so far as clearly outlined, is also only too often different from 
that which the physicist intends to convey. As regards terms such as 
rigid, solid, plastic, viscous, etc., it seems to me that even eminent 
geologists are apt to be misled by the popular usage, so that they fall 
into error respecting the data which mathematical and physical science 
places at their disposal. It thus seems advisable on the present occa- 
sion to clear the ground by briefly considering the sense attached to 
these terms by the more exact school of physicists. To render the fol- 
lowing statements intelligible it is necessary to explain the meaning 
scientifically attached to the terms stress and strain. By stress is 
meant a force referred to unit of area of the surface across which it 
acts; by strain the increase in the distance between two material points 
divided by the original distance. For instance, if a vertical bar n 
square inches in cross section fixed at the upper end, sustain a load of 
t tons, and the load be uniformly distributed over the cross section, the 
longitudinal stress is tn, taking the square inch as unit of area and the 
weight of 1 ton as unit of force. Ifa portion of the bar increase in 
length from 100 to 100.01 inches, and the increase be uniformly distrib- 
uted over the portion lengthened, the longitudinal strain is (100,01— 
100) x 10—, or .0001. 
The writers who have had most influence on the present scientific 
usage of English terms dealing with physical properties are unquestion- 
ably Prof. Clerk Maxwell and Sir William Thomson. The former 
gives the following definitions in his Theory of Heatt: ‘‘A body which 
when subjected to a stress experiences no strain would, if it existed, be 
called a perfectly rigid body. There are no such bodies. = 
“From the L. E. D. Phil. Maa., September and October, 1891; vol. XXXII, pp. 
233-252, and 342-353. 
t Fifth edition, chapter xxi, 
127 
