In the theory of Electrostatics, or of the Newtonian potential, there exists between two systems of potentiating matter, a wellknown reciprocal relation, analytically expressed in the proposition known as Green's Theorrn. By applying his theorem to the case when one of the systems is of the simplest possible character, namely, a mass concentrated at a single point, Green deduced a general method of solving the equation for the potential. The idea of a similar general method of dealing with the equations of Elasticity is due to Professor Betti, of Pisa, who has proved a reciprocal relation between two states of strain of an elastic solid, analogous to the relation in Electrostatics referred to.