10 REPORT 1859. 



in front will almost cancel one another. This clears up at once the maintenance of 

 the onward propagation of an undulation. 



The points of the medium, which were in strictly the same phase as the disturbed 

 element when they transmitted their influence, lie in general (on the hypothesis of 

 homogeneity, &c.) on a surface of revolution round the wave-normal, and passing 

 through the disturbed point. This surface of revolution (which, if we make the 

 simplest hypotheses, becomes a right cone) is of importance in the theory of waves. 



If the medium be such that the disturbing influence is but little enfeebled by di- 

 stance, this cone will obviously be of small angle, and therefore nearly coincide with 

 the backward part of the wave-normal. In such a medium waves will therefore 

 spread but little laterally. A constitution of this kind probably contributes materially 

 to the rectilinear propagation of light, and explains a phenomenon which shows that 

 the common account does not universally hold, viz. the known fact that sound 

 in water bends with less facility round obstacles than sound in air, although the 

 waves constituting it are longer. 



It is necessary to form a clear conception of what is to be understood by the in- 

 fluence contributed by an element of the medium. The parts beyond one of the 

 spherical shells produce an effect on the central disturbance. This effect is modified 

 by the particular condition in which that shell was at some time previous to the 

 central disturbance. It is this modification which is to be regarded as the influence 

 of that shell ; and so of the rest. The resultant is therefore to be obtained by inte- 

 grating from without inwards. 



After the conditions which must be attended to when the influence is transmitted 

 from each origin of disturbance with unequal speed in different directions, or is not 

 at a given moment limited to a surface, &c, were referred to, some applications of 

 the method to familiar phenomena which do not admit of easy explanation by the 

 usual methods, were given. 



On the Relations of a Circle inscribed in a Square. By J. Smith. 



On the Angles of Dock- Gales and the Cells of Bees. By C. M. Willich. 



The author showed by trisection of the cube along different planes, the produc- 

 tion of various solids, and the relation of these to natural forms known in cry- 

 stallography, to the bee's cell, and to the theoretical meeting angle of dock-gates 

 (109° 28' 16"). Thus a rhomboidal dodecahedron is composed of four rhombo- 

 hedra. The bee's cell may be imitated by an elongated dodecahedron composed of 

 seven rhombohedra. 



Light, Heat, Electricity, Magnetism. 



On a New Species of Double Refraction. 

 By Sir David Brewster, K.H., LL.D., F.R.S. 



In 1813 Sir David Brewster discovered that when a ray of light is transmitted 

 obliquely through a bundle of glass plates it is completely polarized ; but he at the 

 same time noticed that this beam is accompanied with other rays, sometimes nebulous, 

 and sometimes in separate distinct images (depending on the polish and parallelism 

 of the glass), but polarized in an opposite plane*. This fact was overlooked by 

 Arago and Herschel in their subsequent researches on the same subject, and was 

 not further pursued by Sir David Brewster at the time. 



In recently examining, however, several hundred films of decomposed glass of 

 extreme thinness, on which the polish and parallelism of the surfaces enabled him 

 to resume the study of the compound beam, he obtained the following results : — 



1. When a beam of polarized light is incident obliquely upon a pile of thin and 

 homogeneous uncrystallized films, and subsequently analysed, the transmitted light 

 will exhibit the phenomena of negative uniaxal crystals, that is, it will consist of two 



* See Phil. Trans. 1814, p. 225-230. 





