148 



Mr potter, on THE PROBLEM OF THE RAINBOW, 



these osculating circles. Returning thence to polar co-ordinates for the 

 branches eg and ^g to the same pole O, we find the space {pp) between 

 the branches at the required point. The caustic in any observation 

 of the rainbow may be considered at the eye as coinciding with its 

 asymptote, as a spherule of water of i inch diameter subtends no sen- 

 sible angle at 1000 yards distance. 



Let A be centre of circle osculating at p, 

 A V'' 



a, b rectangular co-ordinates of A, 



a',b' A', 



Oj9 = radius vector = ?/, 

 Op' = =m'. 



Also Z xOp = a. 



Now \i {x —ay + {y—by = R!' be equation of circle whose centre is A, 

 {x'-aJ + iiZ-by^R' A\ 



