43] ROYAL ASTRONOMICAL SOCIETY TO MR HIND. 325 



To the physical astronomer these bodies offer problems of great interest 

 and difficulty. On account of the large eccentricities and inclinations of 

 some of the orbits, methods of approximation which succeed in determining 

 the perturbations of the older planets become quite inadequate to deal 

 with these, and, consequently, astronomers have hitherto been compelled to 

 have recourse to the method of mechanical quadratures in order to calculate 

 their motions. But although this method may be employed in all cases, 

 and the use of it becomes much simplified by applying it directly to the 

 differential equations of motion, in the elegant manner which has been recently 

 devised by Mr Bond and Professor Encke, yet it only enables us to follow 

 the disturbed planet, as it were, step by step, and it is, therefore, very 

 desirable to have a method by which the course of the planet might be 

 traced through an indefinite number of revolutions, and the results of which 

 might be embodied in tables. 



Professor Hansen has attacked this very difficult problem with his 

 characteristic originality and skill, and Sir J. Lubbock has also treated the 

 same subject very ably in his tracts on the perturbations of the planets. 

 Much, however, remains to be done before the application of the method 

 of quadratures to these cases can be superseded. It will be quite indis- 

 pensable to take into account the square and higher powers of the disturbing 

 force. 



It may be remarked, however, that the eccentricities and inclinations of 

 the orbits of several of these new planets are so moderate, that there will 

 be little difficulty in calculating their perturbations by the ordinary methods. 



The disturbances which these bodies suffer from the action of Jupiter 

 are so large as to afford an excellent means of determining the mass of 

 that planet. It was thus that Nicolai found that the value of this mass 

 which had been employed by Laplace and Bouvard was considerably too 

 small, a result which Mr Airy afterwards confirmed by direct measures of 

 the elongations of the satellites. Considering the great degree of proximity 

 to each other, to which these bodies sometimes attain, it does not seem 

 improbable, notwithstanding their minuteness, that they may occasionally 

 produce a sensible effect on each other's motions ; in which case the astro- 

 nomer would be able to weigh these minute atoms in the same balance 

 which he has already applied to the larger bodies of our system. 



In examining the heavens in search of small planets, Mr Hind has 

 naturally been led to pay great attention to the variable stars, and he 



