It is an established conviction of the mathematical scientist that, once an observed regularity in nature has been expressed as a mathematical equation, this equation may be transformed in any mathematically valid way, and the resulting formula will still apply to some existing fact in the world. On innumerable occasions this principle has been used in the expectation of providing further insight into the secrets of nature. We came across a typical instance of this in discussing the basic theorem of kinematics and dynamics (Chapter VIII). Another example is Newton's treatment of Kepler's third law, or - more precisely - the way in which Newton's law of gravitation has been held to confirm Kepler's observations, and vice versa,