"14th. The principles which have served to establish for us the analytical theory of heat, apply directly to the investigation of the movement of waves in s, a part of which has been agitated. They aid also the investigation of the s of elastic laminae, of stretched flexible surfaces, of plane elastic surfaces of very great dimensions, and apply in general to problems which depend upon the theory of elasticity. The property of the solutions which we derive from these principles is to render the numerical applications easy, and to offer distinct and intelligible results, which really determine the object of the problem, without making that knowledge depend upon integrations or eliminations which cannot be effected. We regard as superfluous every transformation of the results of analysis which does not satisfy this primary condition."