188 Proceedings of Royal Society of Edinburgh. [sess. 
properties unlike those of the other half of the world. If it were 
possible to show that one half of the earth’s surface was subjected 
to a compressive stress from which the other half was free during 
the period of plasticity, the magnitude of the pressure would be 
measured hydrostatically by the mass elevated over the free half. 
Except the pressure of the hydrosphere on the abysmal area, no 
such force is at present at work, and that pressure is certainly quite 
inadequate to the result. 
A Geometrical Method, dependent on the Principle of 
Translation. By David Maver. (With Plate.) 
(Read March 3, 1890.) 
The properties of generating lines and surfaces often afford an 
easy and beautiful mode of demonstrating geometrical theorems 
which, if done by the ordinary method, would be long and tedious. 
As the subject, so far as the writer is aware, is new, a short paper 
upon it may not be unacceptable. 
The following principles will readily be admitted : — 
1. Let AB and CD be two parallel straight lines, and EF, GK 
any lines whatever drawn from the line AB to the line CD. If 
these lines EF, GK advance equal distances along AB and CD, 
each keeping parallel to itself, the spaces passed over by these lines 
will evidently be equal. Let these spaces be represented by sEF 
and sGK, which may be read space generated by EF and space 
generated by GK, then we have sEF = sGK. From this it follows 
that if one side of a triangle be the direction of motion the spaces 
generated by the other two sides are equal, that is if ABC be a 
triangle and BC the direction of motion sAB = sAC. 
2. If there be two lines EF, GK standing upon the straight 
line FK, and if FK be the direction of motion, and sEF = sGK, 
then the lines EF, GK are between the same parallels, that is if 
EG be joined, EG is parallel to FK. 
- 3. If AB and CD be two equal straight lines, and equally in- 
clined to their respective directions of motion, we plainly have 
sAB = sCD. 
