103 Prof. Challis on the Direction of the 



as successive lengths of line are drawn into the water, the re- 

 sistance is constantly increased ; so that at 2000 or 3000 fathoms 

 depth, the weight will be almost entirely suspended in the sea 

 by the resistance of the water along the sides of the line. 



Some idea of the resistance which opposes the motion of a 

 sounding line may be formed from the fact, that upon 1000 fa- 

 thoms of a hne one-tenth of an inch in diameter, moving with a 

 velocity of three feet per second, the resistance is between twenty- 

 five and thirty pounds. And if the velocity be increased to six 

 feet per second, the resistance upon the line becomes a hundred 

 pounds nearly. Or, if the length of the line be doubled, with 

 the same velocity, the resistance is doubled; and it is also 

 directly proportional to the diameter of the line. 



These are some of the reasons why an improvement in the 

 mode of measuring the depths of the sea is not only desirable, 

 but necessary, before a certain knowledge of those depths can 

 be obtained. 



XIII. On the Direction of the Vibrations of a Polarized Ray. 

 By Professor Challis*. 



THE existing state of the question as to the direction of the 

 vibrations of a polarized ray, so far as that question has 

 been considered on the principles of the theory of light which 

 ascribes the phrenomena to the oscillations of the discrete atoms 

 of the luminiferous medium, cannot perhaps be better stated than 

 by quoting the following passage from Dr. Lloyd^s ' Address ' at 

 the Meeting of the British Association at Dublin in 1857: — 



" The vibrations of a polarized ray are all pai-allel to a fixed 

 direction in the plane of the wave; but that direction may be 

 either parallel ox perpendicular to the plane of polarization. In 

 the original theory of Fresnel the latter was assumed to be the 

 fact; and in this assumption Fresnel has been followed by 

 Cauchy. In the modified theories of MacCullagh and Neumann, 

 on the other hand, the vibrations are supposed to be parallel to 

 the plane of polarization. This opposition of the two theories 

 was compensated, as respects the results, by other diff"erenccs in 

 their hypothetical principles ; and both of them have led to con- 

 clusions which observation has verified. There seemed, therefore, 

 to be no means left to the theorist to decide between these con- 

 flicting hypotheses, until Professor Stokes, recently, in applying 

 the dynamical theory of light to other classes of phsenomena, 

 found one in which the effects should differ on the two assump- 

 tions. When hght is transmitted through a fine grating, it is 



* Communicated by the Author. 



