While tracing the lines of motion and the meridian sections of their orthogonal surfaces for an infinite mass of perfect fluid disturbed by a moving sphere :—the question occurred to me “When are such systems similar?” In the problem alluded to, the equations of the curves are, respectively,

It was at once obvious that any sets of curves such as

are orthogonals. But they form similar systems only when

Hence the only sets of similar orthogonal curves, having equations of the above form, are (a) groups of parallel lines and (b) their electric images (circles touching each other at one point).