402 SCIENCE PROGRESS 



observations are at fault, and have not been made with great 

 accuracy. In calculating the value of r corresponding to a 

 given value of i, he uses an interesting method of successive 

 approximation which need not be given here. In his later 

 work, the Dioptrics, which was published in 1611, he describes 

 methods of measuring the refraction of glass, and shows that 

 he fully understands total reflection, giving the limiting angle 

 correctly ; he describes and gives the correct theory of both 

 the astronomical and Galilean telescopes, but does not arrive 

 at the formula for the focal length of a thin lens. 



Meantime, the telescope was discovered, and made in 

 Holland in 1609 almost simultaneously by different workers ; 

 next year Galileo made his first telescope, and began his cele- 

 brated observations on the moon and planets. The construc- 

 tion and use of the telescope thus preceded the discovery of the 

 law of refraction ; thus often does practice precede theory. 

 But it is clear that the discovery of the law could not now long 

 be delayed. Willebrord Snellius, professor of mathematics at 

 Leyden, devoted himself to its investigation, and discovered 

 it about 1 62 1, after many attempts. He died in 1626 at the 

 age of thirty-five, leaving behind an unpublished manuscript 



on the subject. He stated that if a ray 

 DC emitted by a point D in a dense 

 medium were refracted at C into air, and 

 the direction of the ray in air produced 

 back to meet the perpendicular from D 

 to the surface of the medium at E, then 

 CD was always in the same ratio to CE, 

 4 to 3 in the case of water, no matter 

 what angle DC made with the surface. 

 This, it is easily shown, is the law, but in 

 an unfamiliar form. 



Eleven years after the death of Snell, 

 Descartes published his Dioptrics, in 

 which he announced the law of refraction in terms of 

 sines as we have it now, without mentioning Snell's name. 

 It is said that Descartes had access to Snell's manu- 

 script ; Huygens states that he himself had seen the whole 

 manuscript volume of Snell, and that he believed that 

 Descartes had also seen it. Huygens also states that Snell did 

 not thoroughly comprehend his own discovery, and never 

 imagined that the ratio of the two lines was the ratio of the 

 sines. Brewster, however, thinks that it is incredible that 

 Snell was not very familiar with the trigonometrical functions, 

 and that he really preferred his own form of the law ; there is 

 much to be said for this standpoint, for Snell's diagram is much 

 used by teachers at present in showing elementary classes 



