Thirty-five years ago it was my privilege to read before this Society a paper communicated by Rutherford. I was invited to the meeting the week before. Rutherford spotted me among the guests and he said: ‘Er, you’re the young man who is coming to give us a short talk next week, are you not?’, I admitted it. ‘Make it short, young man—make it short! If you don’t make it short they won’t stay! They’ll vanish! Make it short, young man—make it short! ’ I cannot do better than follow Rutherford’s advice this afternoon, in respect of each piece of physics that I shall describe. Thirty-two years ago I went as Leverhulme Fellow to the Imperial College, to study the optics of non-spherical surfaces. Within a month, I had evolved a technique for applying the principle of phase contrast, newly discovered by our Foreign Member, Fritz Zernike, to the testing of ellipsoidal and spherical mirrors, using squashed resin globules as phase retarding disks. I used this method, and knife-edge testing, and extra-focal image observation, as well as interferometry, for optical testing, and it occurred to me to subsume all these methods under one generalization—they are all interference methods. In the first case the comparison wave is a delayed and relatively error-free version of the job wave; in the second it is a Laplace transform, and in the third a convolution of the job wave. This raises the question—Is there some special transform of the job wave, peculiarly well suited to testing?—and the obvious answer is—A displaced, or ‘sheared’ alter ego of the job wave.