I 5 6 



HISTORY OF SCIENCE. 



angle of incidence, is represented by i, and that the angle b c , simi- 

 larly denominated the angle of refraction, is represented by R, we may 

 use the language of trigonometry (page 61) and say that |^=|-=: 1*33. 

 The number 1-33 is called the Refractive Index for air and water, and 

 the refractive index is, of course, always the same for the same pair 

 of media. The general law of refraction is therefore summed Up by 

 saying that for the same media the ratio of the sines of the angles of in- 

 cidence and of refraction is constant. It is characteristic of Descartes 

 that this law of refraction was not arrived at by comparing the results 

 of a number of experiments, but was deduced from certain assumed 

 hypothetical principles concerning moving bodies. It may serve to 

 show the danger of thinking that hypotheses are true merely because 

 correct conclusions can be deduced from them, to mention that while 

 Descartes assumed that light moves more rapidly in the denser medium, 

 Fermat, another French mathematician, deduced the law of the sines 

 from the opposite assumption, and a very long discussion was raised upon 

 these so-called demonstrations. Amid the din raised by the conten- 

 tions of the a priori philosophers, a physicist named Petit bethought 

 himself of putting the law of the sines to the test of experiment, and 

 he announced that his results completely verified the law. 



FIG. 59. 



FIG. 60. 



In the treatise on dioptrics Descartes also investigates many pro- 

 blems relating to refraction by lenses, and he gives some elegant de- 

 monstrations of the shapes which lenses should have, in order that 

 rays falling upon them parallel to their axes should meet in one point. 

 The inventions of the telescope and microscope, which both date from 

 the beginning of the seventeenth century, have in the highest degree 

 aided the progress of scientific research. We have already seen what 

 the telescope could effect in the hands of Galileo, and the microscope 

 was soon afterwards to reveal another world of wonders. Considering 

 the importance of the refracting telescope and microscope in the history 

 of scientific discovery, a brief explanation of the principle of the lens, 

 and of the effect of a combination of lenses, may not here be out of 

 place, and will give us an opportunity of indicating the nature of 

 Descartes' proposed improvement in the leases of such instruments. 

 Assuming that the reader is familiar with trie refractions of a ray of 



