392 Notices respecting Neio Books. 



these ray-surfaces, there are also to be considered those which are 

 due to all the rays reflected from the lateral surface of the interior 

 ring ; consisting, in certain positions, of light incident directly from 

 the sun, but principally of rays which are incident after a first re- 

 flexion at the surface of the planet. In the former case, the direct 

 solar rays will pass off in ray-surfaces defined by the equation 



assuming the origin at the centre of the planet, and the plane of l'(, 

 at any moment to pass through the centre of the sun. The rays 

 which are incident after reflexion from the planet, will be situated 

 in surfaces of a similar character given by the general equation. 

 The surfaces which are thus generated from the interior parts of the 

 ring, all pass into the less enlightened atmosphere, and must contri- 

 bute in some degree to its illumination. In virtue of these ray- 

 surfaces, we may conceive the darkness of those regions to be relieved 

 by a thin luminous equatorial cincture reposing on the bosom of the 

 sk)', which, while it may bear a faint and shadowy resemblance to 

 the bright arch which sheds its lustre over the more favoured hemi- 

 sphere, shines with a chastened light, subdued to a character of far 

 less resplendent magnificence and beauty. 



" From the preceding investigations it appears that the nature of 

 the envelope is intrinsically the same, whether the luminous surface 

 is supposed to be a sphere or a spheroid. In order to illustrate the 

 formulse, the planet may be assumed to be spherical ; and, using the 

 elements given by Sir J. Herschel in the ' Outlines of Astronomy,' 

 page 315, we find, for the interior limiting circle of the inner ring, 



Vr^ — ^'^ =43308 miles, '~ ^ = 1-0942; and for the exterior 

 k 



limiting circle of the outer ring, Vr2—A'2= 78831 miles, 

 J- 11 = 1-9917; 



from these data the limiting envelope cones may be readily delineated. 



•' The fainter illumination which belongs to the external ring has 

 been attributed to the presence of a dense atmosphere ; it is possible 

 that this eff"ect may be also due, in part, to the greater distance of 

 this ring from the planet, in consequence of which, light of dimi- 

 nished intensity is reflected in the ray-surfaces ; although it is to be 

 remembered, that the same cause will slightly augment the illumi- 

 nation arising from the direct rays of the sun." — Pp. 75-77. 



We trust that the important question of refracted ray-surfaces and 

 caustics will not escape Mr. Childe's attention. It would form an 

 admirable subject for another volume. 



