venture on some new scheme, just as if God had set up this star in the darkness merely to enlighten them.”  He made no secret of his views on conventional astrology, as to which he claimed to speak with the authority of one fully conversant with its principles, but he nevertheless expressed his sincere conviction that the conjunctions and aspects of the planets certainly did affect things on the earth, maintaining that he was driven to this belief against his will by “most unfailing experiences”.

Meanwhile the projected Rudolphine Tables were continually delayed by the want of money.  Kepler’s nominal salary should have been ample for his expenses, increased though they were by his growing family, but in the depleted state of the treasury there were many who objected to any payment for such “unpractical” purposes.  This particular attitude has not been confined to any special epoch or country, but the obvious result in Kepler’s case was to compel him to apply himself to less expensive matters than the Planetary Tables, and among these must be included not only the horoscopes or nativities, which owing to his reputation were always in demand, but also other writings which probably did not pay so well.  In 1604 he published “A Supplement to Vitellion,” containing the earliest known reasonable theory of optics, and especially of dioptrics or vision through lenses.  He compared the mechanism of the eye with that of Porta’s “Camera Obscura,” but made no attempt to explain how the image formed on the retina is understood by the brain.  He went carefully into the question of refraction, the importance of which Tycho had been the first astronomer to recognise, though he only applied it at low altitudes, and had not arrived at a true theory or accurate values.  Kepler wasted a good deal of time and ingenuity on trial theories.  He would invariably start with some hypothesis, and work out the effect.  He would then test it by experiment, and when it failed would at once recognise that his hypothesis was a priori bound to fail.  He rarely seems to have noticed the fatal objections in time to save himself trouble.  He would then at once start again on a new hypothesis, equally gratuitous and equally unfounded.  It never seems to have occurred to him that there might be a better way of approaching a problem.  Among the lines he followed in this particular investigation were, first, that refraction depends only on the angle of incidence, which, he says, cannot be correct as it would thus be the same for all refracting substances; next, that it depended also on the density of the medium.  This was a good shot, but he unfortunately assumed that all rays passing into a denser medium would apparently penetrate it to a depth depending only on the medium, which means that there is a constant ratio between the tangents, instead of the sines, of the inclination of the incident and refracted rays to the normal.  Experiment proved that this gave too high values for refraction near the vertical compared