PHYSICAL AND LITERARY. ' 43 



40. Hence their velocities in any other 

 medimiy may be found; for, they are, to 



thefe. 



From what follows, perhaps, an exafter computation might 

 J>e made, if a proper mean angle of incidence were n-ade 

 ufe of, akho' the quantities in the canon are really not in a 

 conftant ratio. 



Tab. iii. fig. i. Let two rays, falling in the fame line of 

 incidence IC, with different velocities, upon AB the furface 

 of a denfer medium, be refraded into different lines CR, CV. 

 Taking any line CD in the perpendicular to reprefent the to- 

 tal aaion of the refrafling power on the lefs refrangible 

 ray, and CE on the more refrangible : If, thro' D and E, 

 parallels to IC be drawn, meeting the refraaed rays in 

 V, R and G ; it is plain, that CR, CV will be, as their 

 refpeftive velocities after refradlion ; and DR, EV, as their 

 velocities before incidence. Since the whole acceleration 

 which a given power produces in a body, is, cateris paribus, 

 as the time in which it operates ; CD muft be to CE near- 

 ly as the time which the fwifter ray takes to pafs thro' the 

 refrafling fpace, to that which the flower ray takes in paf- 

 fing thro' the fame, inverfely , as their velocities before inci- 

 dence; that is, as EV to DR : but CD is likeways to CE as 

 DG to EV ; therefore DR, EV and DG, are continued 

 proportionals; therefore DR' is to EV in the fubduplicate 

 r(itio of DR to DG : but DR is to DG in a tatia compound- 

 ed of DR to pC, and DC to DG, that is, in the com- 

 pounded ratio of S, DCR to S, DRC and of S, DGC to 

 S, DCG ; wherefore DR is tb EV in the fubduplicate ra- 

 tio of S, DCR X S, DGC to S, DCG X S, DRC; that 

 is, " The velocities before incidence are nearly in the direft 

 •" fubduplicate ratio of thefe fines and the reciprocal fub- 

 f duplicate ratio of the fines of the exctiTes of the commoa 

 " anole of incidence above the fcveial angles of retra(fijon." 



