78 Intelligence and Miscellaneous Articles. 



attention of the Academy to some effects of calorific reflection which 

 are connected with the phenomena of anomalous dispersion ; and, 

 on this subject, I was led to say that, on resuming the study of the 

 reflection of polarized heat, I ascertained that when the rays are po- 

 larized parallel to the plane of incidence the intensity of the re- 

 sin" (i — 7'^ 



flection is always ^iven by Fresnel's formula v-= . .. ; . x, as well 



^ ^ ^ sm- {i + r) 



when the rays are partially transmissible through the mirrors as 

 when the portion which escapes reflection is completely absorbed by 

 the mirrors. I said also that in the case of the rays being polarized 

 perpendicularly to the plane of incidence a very little modification 

 of Fresnel's hypotheses or equations is sufficient for arriving at a 

 formula very well representing the phenomena. In fact, if we 

 admit that at the most superficial part of an opaque medium trans- 

 mission commences as Fresnel conceives it to do in transparent 

 media, but under the condition that the vis viva of the incident ray 

 does not all reappear in the reflected and in the refracted ray pro- 

 perly so called, the equation of the vires vivcB may be written in the 

 ordinary notation 



, sirWcos^;^. (1) 



^ ^ sinrcos* ^ ^' ^ ^ 



3 being a quantity of which the sign is at first indeterminate. If to 

 this equation be added that which expresses the continuity of the 

 motion in a direction parallel with the surface of the mirror a, viz. 



(1 4-i') cos i=u cos r, ........ , (2) 



we hence readily deduce that the coefficient of vibration v in the re- 

 flected ray is given by the formula 



tang ^ + r 



— __./*!__ sin z cos i \ 



\ sin i cos i + sin r cos rj 



c sm I cos z 



+ -^—. — ^ (3) 



sm 2 cos i + sm?*cos r ^ ^ 



So far ^ is still indeterminate ; but I have ascertained empirically 

 that all the determinations I have made are well represented by 

 putting c = K tang' (z — r), and giving to K the follovring negative 

 values for the extreme red rays: K= — 0*19 for platinum, and 

 — 0*22 for speculum-metal; for glass and the same rays, K = 0. 

 For glass and the extreme dark rays, K=— 0*8; for speculum- 

 metal and the same rays, K= — 1*9. Lastly, for the total solar 

 heat, but transmitted through a sufficiently considerable thickness 

 of glass and Iceland spar, K=— 0"11 in the case of steel; and in 

 that of silver, K = — 0"3. For rock-salt, K is always =0. 



In each of these cases it is understood that the constant ?i pre- 

 serves the value found for it in the corresponding case when opera- 

 ting with rays polarized parallel to the plane of incidence. All 

 these assertions are verified by the following Tables : — 



