380 Royal Astronomical Society. 



where Aj A^ A3 are the three coefficients of direct elasticity with 

 reference to the three axes of symmetry, and B, B/ B^ B2' B3 MJ the 

 six coefficients of lateral elasticity with reference to the same axes. 

 If the vibrations be transverse, this equation is reducible to the 

 form 



^ = -(DID.) V?a+&^oj/3 + c^?7) 



= — (DlD.)^(a -aAa + i^jS A/3 + c^^y)v, 



assuming the vibrations of a polarized ray to be perpendicular to 

 the plane of polarization. 



The well-known condition that a plane polarized ray may be 

 transmissible without subdivision, and the velocity of propagation 

 may be immediately deduced from this equation. 



If we assume the vibrations of a polarized ray to be in the plane 

 of polarization, the equation becomes 



1!H = _DlD.(a^aAa+62/3A/3 + c2yA7)D5D.u. 



This includes Professor MacCullagh's three equations. 



ROYAL ASTRONOMICAL SOCIETY. 

 [Continued from p. 146.] 



May 14, 1847. — Extract of a letter from Mr. Adams, with new 

 Elements of Neptune. 



" The following elements of Neptune have been obtained by taking 

 into account Prof. Challis's observations made since the reappear- 

 ance. * * * The elements are now sufficiently correct to enable me 

 to approximate to the perturbations of Neptune by the action of 

 Uranus, in order to compare more accurately the ancient observa- 

 tions of 1795 with those .... made recently. I have used the old 

 observations, supposing the elements not to have changed. I hope 

 immediately to set about a new solution of the perturbations of 

 Uranus, starting with a very approximate value of the mean distance. 

 * * * I do not think, with Professor Pierce, that the near commen- 

 surability of the mean motions will interfere seriously with the re- 

 sults obtained by the treatment of perturbations ; but it will be in- 

 teresting to see how nearly the real elements can be obtained by 

 means of the perturbations." 



Elements of the Orbit of Neptune. 



Mean longitude, Jan. 1, 1847, G. M. T... 328 13 54-5 T 



Longitude of perihelion (on the orbit)... 11 13 41-5 LM. Eq. 1847-0 



Longitude of ascending node 130 5 39-0 J 



Inclination to ecliptic 1 47 I'S 



Mean daily motion 213774 



Semi-axis major 302026 



Eccentricity of orbit 0-0083835 



On the communication of Mr. Adams's paper, the Astronomer 



