In a paper “On the Theory of Long Waves” recently published, I drew attention to a point of some interest in the theory of the solution of partial differential equations by what is usually termed the method of reciprocation. As the subject was apart from the main object of the paper, however, I there noticed the peculiarity but briefly, and so I have thought that it might be of some use to enter into the matter here somewhat more fully. On first adverting to the point, it was my opinion that it could hardly have escaped the notice of those who had made much application of the method of solution by reciprocation, though I had not myself seen any reference made to it; but as I have not had my attention drawn to any such notice since the publication of the paper last March, it seems probable that it has not previously been discussed.