86 
Proceedings of Boy al Society of Edinburgh. [jan. 31 , 
might be said to depend upon the mathematical artifice of finding 
the resultant force due to the mutual action of the earth mass, and 
the wall a maximum, the earth being supposed to yield incipient^ 
under the action of its weight, and in opposition to friction and the 
reaction in question, along an inclined plane determined so as to 
fulfil that imposed condition. Coulomb’s method has been de- 
veloped by various writers, and may be regarded as complete. 
The second method is due to Rankine. It is based upon two 
general dynamical principles, both of which are really involved in 
Coulomb’s treatment, but which are there drawn upon as it were 
incidentally rather than appealed to as fundamental principles. 
Rankine’s first principle is merely a statement that the well-known 
propositions in regard to the laws of static friction apply in the 
interior of a granular mass of earth ; and, in particular, that there 
is a coefficient of friction for earth upon earth of any given kind. 
That some sort of physical datum of this nature with respect to any 
given kind of earth may be properly assumed does not admit of 
question ; but how far it answers to an ordinary physical constant, 
or even an ordinary coefficient of friction, is by no means certain. 
However, objections of this kind apply to Coulomb’s method with 
even greater force, and the author proposes to attempt to push 
Rankine’s theory farther on its present bases, rather than to discuss 
preliminary difficulties. If, therefore, he shall be fortunate enough 
to arrive by a path not altogether mistaken at certain results, he 
would merely say that such are the consequences of adopting these 
fundamental principles. 
The first of the principles just referred to enabled Rankine to 
formulate the conditions of equilibrium in the interior of an earth 
mass generally, and in terms of certain data for particular cases 
occurring in practice. 
When he comes to deal with the action of the earth on a wall, 
Rankine refers to his second principle, which was first distinctly 
laid down by the late Canon Moseley. Briefly it is merely this : — 
When a system is in equilibrium under a set of forces, those which 
are called into existence by the action of the others are the least 
possible consistent with the given conditions ; or, among a set of 
forces, active and passive, in equilibrium, the passive forces are the 
least possible. 
