II. On a property of curves which fulfil the condition d 2 φ/ dx 2 + d 2 φ/ dy 2 = 0

Abstract

1. In a paper “On Stream-Lines,” published in the Philosophical Magazine for October 1864, I stated, and, in a Supplement to the same paper, published in the Philosophical Magazine for January 1865, I proved the proposition that “all waves in which molecular rotation is null begin to break when the two slopes of the crest meet at right angles. 2. I have now to state the purely geometrical proposition of which that mechanical proposition is a consequence. If a plane curve which fulfils the condition d 2 φ/ dx 2 + d 2 φ/ dy 2 = 0 cuts itself in a double point, it does so at right angles .