Cambridge Philosophical Society. 521 



1. Diameter of cylinder of water = 0-0206 inch ; index of re- 

 fraction = r3318. 



(Radius of geometric primary bow = 42° 15'.) 



Observation. Tlieory. 

 Radius of brightest part of primary 41" 51'-4 41" 45'-4 



Radius of first dark ring 41 7 



Radius of second dark ring 40 16 40 14'4 



(Radius of geometric secondary bow = 50° 34'.) 

 Radius of brightest part of secondary 51°25' 51° 27 '"5 



Radius of first dark ring 52 37 



Radius of second dark ring 54 7 54 12, 



2. Diameter of cylinder of water = 0*02105 inch; index of re- 

 fraction = 1-33464. 



(Radius of geometric primary bow = 41° 50'-4.) 



Observation. Theory. 

 Radius of brightest part of primary. . 41° 27'-7 41°24'-7 



Radius of first dark ring 40 51 "4 



Radius of second dark ring 40 4-4 40 5'- 7 



(Radius of geometric secondary bow = 51° 19'). 



Radius of brightest part of secondary 51° 57' 52° 5'-3 



Radius of first dark ring 53 5 



Radius of second dark ring 54 27"6 54 27 



3. Diameter of cylinder of water = 0-0135 inch; index of re- 

 fraction = 1-33453. In this series of ol)scrvations the values of 

 the diameter of the cylinder and of the index of refraction are rather 

 doubtful. 



(Radius of geometric primary bow = 41° 52'.) 



Observation. Theory. 

 Radius of brightest part of primary 41° 20' 41° 18' 



Radius of first dark ring 40 33 



Radius of second dark ring 39 29 39 32 



(Radius of geometric secondary bow = 51° 17'"5.) 

 Radius of brightest part of secondary 52° 16' 52° 18'-5 



Radius of first dark ring 53 37 



Radius of second dark ring 55. 31 55 26. 



April 26, 1841. — Prof. ChalUs read a communication on the motion 

 of a small .«phere submitted to the dynamical action of the vibrations of 

 an clastic medium. The mathematical reasoning embraced terms in- 

 volving the aqnare of the velocity of tlie vibrating medium, and the 

 principal conclusion arrived at was, tliat the motion of the sphere 

 consists jjartly of a vibratory motion, and jiartly of a permanent mo- 

 tion of translation, the latter depending on the terms which contain 

 the square of the velocity. It \va.~ thouglit that tliis result may have 

 imj)ortant applications in the jjhysical theories of light and heat. 



The solution of the above problem involves that of another of more 

 immediate interest, viz. the determination of the resistance to the 

 motion of a ball-pendulum vibrating in the air. Professor Challis 

 obtains the same coefficient of resistance as in several previous solu- 



