384 



most advantageously communicated. Equability of velocity is ob- 

 tained, though at the expense of some degree of sliding friction, 

 when the outline of the teeth of the wheels are involutes of circles. 

 Friction, on the other hand, is wholly prevented when their form is 

 the logarithmic spiral ; but the angular velocities will then be variable. 

 Hence these two advantages are incompatible with one another ; but 

 on the whole, the author gives the preference to the involute, which 

 produces an equability of angular motion. The most advantageous 

 mode of increasing velocity by a series of wheels is to adjust them 

 so that the multiplication of velocity shall proceed in. a geometrical 

 progression. 



On the Laws of the Polarization of Light by Refraction. By David 

 Brewster, LL.D. F.R.S. L. 4 E. Head February 25, 1830. [Phil. 

 Trans. 1830, p. 133.] 



M. Arago had deduced from some experiments which he made on 

 the polarization of light with plates of glass, that the quantity of 

 light polarized by reflexion is equal to the quantity polarized by trans- 

 mission, whatever be the angle of incidence. The author of the pre- 

 sent paper shows that the views from which this deduction was made, 

 and the observations on which they are founded, are incorrect. By 

 applying to the subject the same principles which he has already de- 

 veloped in the paper lately read to the Society, on the Polarization of 

 Light by Reflexion, he establishes, on the basis of actual experiment, 

 what he conceives to be the true laws of the phenomena. The first 

 step in his inquiry is the determination of the law according to which 

 the polarizing force of the refracting surface changes the position of 

 the planes of polarized light. He shows that when a compound 

 pencil, of which the constituent rays are polarized in planes inclined 

 at angles of 45, the one being to the right and the other to the left 

 of the plane of refraction, is refracted, the planes of polarization of 

 the refracted rays are turned so as to approach to coincidence, not 

 in a plane parallel to the plane of reflexion, as happens in the reflected 

 rays, but in a plane at right angles to it. This contrariety of effect, 

 he observes, is exactly what might have been expected from the op- 

 posite character of the resulting polarization, the poles of the par- 

 ticles of light, which were formerly repelled by the force of reflexion, 

 being now attracted by the refracting force. The author next en- 

 deavoured to ascertain the influence of refracting power in effecting 

 polarization, but experienced great difficulty in prosecuting this in- 

 quiry, from the necessity of having plates without any crystalline 

 structure. He tried gold leaf in a variety of ways, but found it almost 

 impossible to obtain correct results, on account of the light which 

 was transmitted unchanged through its pores. From observations 

 with films of soapy water, and thin plates of metalline glass of high 

 refractive power, he concludes that the rotation of the planes of po- 

 larization increases with the refractive power. By an examination 

 of the effects produced at different angles of incidence, he deduces 



