which a ray of light assumes in passing from one medium to another。 Kepler measured the angle of refraction by means of a simple yet ingenious trough…like apparatus which enabled him to compare readily the direct and refracted rays。 He discovered that when a ray of light passes through a glass plate； if it strikes the farther surface of the glass at an angle greater than 45 degrees it will be totally refracted instead of passing through into the air。 He could not well fail to know that different mediums refract light differently； and that for the same medium the amount of light valies with the change in the angle of incidence。 He was not able； however； to generalize his observations as he desired； and to the last the law that governs refraction escaped him。 It remained for Willebrord Snell； a Dutchman； about the year 1621； to discover the law in question； and for Descartes； a little later； to formulate it。 Descartes； indeed； has sometimes been supposed to be the discoverer of the law。 There is reason to believe that he based his generalizations on the experiment of Snell； though he did not openly acknowledge his indebtedness。 The law； as Descartes expressed it； states that the sine of the angle of incidence bears a fixed ratio to the sine of the angle of refraction for any given medium。 Here； then； was another illustration of the fact that almost infinitely varied phenomena may be brought within the scope of a simple law。 Once the law had been expressed； it could be tested and verified with the greatest ease； and； as usual； the discovery being made； it seems surprising that earlier investigatorsin particular so sagacious a guesser as Keplershould have missed it。 Galileo himself must have been to some extent a student of light； since； as we have seen； he made such notable contributions to practical optics through perfecting the telescope； but he seems not to have added anything to the theory of light。 The subject of heat； however； attracted his attention in a somewhat different way； and he was led to the invention of the first contrivance for measuring temperatures。 His thermometer was based on the afterwards familiar principle of the expansion of a liquid under the influence of heat； but as a practical means of measuring temperature it was a very crude affair； because the tube that contained the measuring liquid was exposed to the air； hence barometric changes of pressure vitiated the experiment。 It remained for Galileo's Italian successors of the Accademia del Cimento of Florence to improve upon the apparatus； after the experiments of Torricellito which we shall refer in a momenthad thrown new light on the question of atmospheric pressure。 Still later the celebrated Huygens hit upon the idea of using the melting and the boiling point of water as fixed points in a scale of measurements； which first gave definiteness to thermometric tests。
TORRICELLI In the closing years of his life Galileo took into his family； as his adopted disciple in science； a young man； Evangelista Torricelli （1608…1647）； who proved himself； during his short lifetime； to be a worthy follower of his great master。 Not only worthy on account of his great scientific discoveries； but grateful as well； for when he had made the great discovery that the 〃suction〃 made by a vacuum was really nothing but air pressure； and not suction at all； he regretted that so important a step in science might not have been made by his great teacher； Galileo； instead of by himself。 〃This generosity of Torricelli；〃 says Playfair； 〃was； perhaps； rarer than his genius： there are more who might have discovered the suspension of mercury in the barometer than who would have been willing to part with the honor of the discovery to a master or a friend。〃 Torricelli's discovery was made in 1643； less than two years after the death of his master。 Galileo had observed that water will not rise in an exhausted tube； such as a pump； to a height greater than thirty…three feet； but he was never able to offer a satisfactory explanation of the principle。 Torricelli was able to demonstrate that the height at which the water stood depended upon nothing but its weight as compared with the weight of air。 If this be true； it is evident that any fluid will be supported at a definite height； according to its relative weight as compared with air。 Thus mercury； which is about thirteen times more dense than water； should only rise to one…thirteenth the height of a column of waterthat is； about thirty inches。 Reasoning in this way； Torricelli proceeded to prove that his theory was correct。 Filling a long tube； closed at one end； with mercury； he inverted the tube with its open orifice in a vessel of mercury。 The column of mercury fell at once； but at a height of about thirty inches it stopped and remained stationary； the pressure of the air on the mercury in the vessel maintaining it at that height。 This discovery was a shattering blow to the old theory that had dominated that field of physics for so many centuries。 It was completely revolutionary to prove that； instead of a mysterious something within the tube being responsible for the suspension of liquids at certain heights； it was simply the ordinary atmospheric pressure mysterious enough； it is truepushing upon them from without。 The pressure exerted by the atmosphere was but little understood at that time； but Torricelli's discovery aided materially in solving the mystery。 The whole class of similar phenomena of air pressure； which had been held in the trammel of long…established but false doctrines； was now reduced to one simple law； and the door to a solution of a host of unsolved problems thrown open。 It had long been suspected and believed that the density of the atmosphere varies at certain times。 That the air is sometimes 〃heavy〃 and at other times 〃light〃 is apparent to the senses without scientific apparatus for demonstration。 It is evident； then； that Torricelli's column of mercury should rise and fall just in proportion to the lightness or heaviness of the air。 A short series of observations proved that it did so； and with those observations went naturally the observations as to changes in the weather。 It was only necessary； therefore； to scratch a scale on the glass tube； indicating relative atmospheric pressures； and the Torricellian barometer was complete。 Such a revolutionary theory and such an important discovery were； of course； not to be accepted without controversy； but the feeble arguments of the opponents showed how untenable the old theory had become。 In 1648 Pascal suggested that if the theory of the pressure of air upon the mercury was correct； it could be demonstrated by ascending a mountain with the mercury tube。 As the air was known to get progressively lighter from base to summit； the height of the column should be progressively lessened as the ascent was made； and increase again on the descent into the denser air。 The experiment was made on the mountain called the Puy…de…Dome； in Auvergne； and the column of mercury fell and rose progressively through a space of about three inches as the ascent and descent were made。 This experiment practically sealed the verdict on the new theory； but it also suggested something more。 If the mercury descended to a certain mark on the scale on a mountain…top whose height was known； why was not this a means of measuring the heights of all other elevations？ And so the beginning was made which； with certain modifications and corrections in details； is now the basis of barometrical measurements of heights。 In hydraulics； also； Torricelli seems to have taken one of the first steps。 He did this by showing that the water which issues from a hole in the side or bottom of a vessel does so at the same velocity as that which a body would acquire by falling from the level of the surface of the water to that of the orifice。 This discovery was of the greatest importance to a correct understanding of the science of the motions of fluids。 He also discovered the valuable mechanical principle that if any number of bodies be connected so that by their motion there is neither ascent nor descent of their centre of gravity； these bodies are in equilibrium。 Besides making these discoveries； he greatly improved the microscope and the telescope； and invented a simple microscope made of a globule of glass。 In 1644 he published a tract on the properties of the cycloid in which he suggested a solution of the problem of its quadrature。 As soon as this pamphlet appeared its author was accused by Gilles Roberval （1602…1675） of having appropriated a solution already offered by him。 This led to a long debate； during which Torricelli was seized with a fever； from the effects of which he died； in Florence； October 25； 1647。 There is reason to believe； however； that while Roberval's discovery was made before Torricelli's； the latter reached his conclusions independently。
VI。 TWO PSEUDO…SCIENCESALCHEMY AND ASTROLOGY In recent chapters we have seen science come forward with tremendous strides。 A new era is obviously at hand。 But we shall misconceive the spirit of the times if we fail to understand that in the midst of all this progress there was still room for mediaeval superstition and for the pursuit of fallacious ideals。 Two forms o