Proceedings of the British Association. 171 



where the forces are any functions whatsoever of the coordinates. 

 When the time enters explicitly into the analytical expressions 

 for the forces, and into the equations of condition of the system, 

 the principle of the final multiplier found by a general rule, is 

 applicable also to this class of dynamical problems. There are 

 also some particular problems into which enters the resistance of 

 a medium, which give rise to similar theorems. It is the case of 

 a planet revolving round the sun in a medium whose resistance 

 is proportional to any power of the velocity of the planet. " The 

 analysis," observed M. Jacobi, " which has conducted me to the 

 new general principle of analytical mechanics, which I have the 

 honor to communicate to the Association, may be applied to a 

 great number of questions in the integral calculus. I have col- 

 lected these different applications in a very extensive memoir, 

 which I hope to publish on my return to Konigsberg, and which 

 I shall have the honor of presenting to the Association as soon as 

 it shall be printed." 



On certain cases of Elliptically Polarized Light, by Prof. 

 Powell. — At the last meeting of the Association, Prof. Lloyd 

 gave a theoretical investigation of certain results obtained by Sir 

 D. Brewster relative to thin films from which polarized light is 

 reflected. Besides completely explaining those results, Prof. L. 

 infers that such films ought to give the portions of light reflected 

 at their two surfaces differing in phase, and that the light should 

 be consequently in general, elliptically polarized. The author 

 of the present paper, before he was aware of the investigation of 

 Prof. Lloyd, had made many observations on the elliptical polari- 

 zation of light by reflection from metallic and other surfaces, 

 the method of observation being by the well known dislocation 

 of the polarized rings. Some of these experiments went merely 

 to prove the existence of elliptic polarization in cases where it 

 had not previously been detected, as in certain minerals and other 

 bodies in which it is seen, though of small amount. In other 

 cases, the reflecting surface consisted of the thin films formed on 

 polished metal by tarnish, by heat, or by the galvanic process of 

 Nobili. In these instances, a verification of Prof. L.'s theory 

 was afforded by direct observation. But, further, — these films 

 give periodic colors, and in passing from one tint to another, the 

 ellipticity, as disclosed by the form of the rings, underwent reg- 

 ular changes, passing from a dislocation in one direction to the 

 opposite, through points of no dislocation or of plane polarization, 



