334 



You will notice that the two elements left indeterminate in my former 

 direct solution II. are now completed. They confirm my former 

 conclusions respecting the smallness of the eccentricity. 



They exhibit, moreover, an unexpected coincidence between the 

 perihelion points of Elements III. and V. — thus: 



Elements III. 5r = 0' 12' 25".51 hypothesis of identity with Lalande star. 

 „ V". 5r = 1 45 32 .90 deduced from direct observation. 



When we consider the difficulty of deducing the perihelion point of 

 an orbit so nearly circular, from an apparent arc of less than two de- 

 grees, it must be admitted that the close agreement is accidental. 

 Yet we cannot with propriety refuse it some weight in favour of the 

 affirmative of the hypothesis. 



You will, doubtless, wish to know what modification the present 

 disturbed elements V. require in order to represent the present path 

 of the planet, and locate it. May 10th, 1795, where the Lalande star 

 (now missing) was observed. I would answer that the node should 

 be increased about 927", and the inclination one tenth of that amount 

 (92.7"), and the planet should be supposed to have had its average daily 

 orbital motion increased, by the perturbations of the other planets, 

 0". 02061, during the last fifty-two years. In other words, the actual 

 period must have been oscillating from a value, 165.668, nearer the 

 double of that of Uranus, towards one more remote, viz: 165.513. 



Such is the residual quantity to be explained, before pronouncing 

 conclusively on the question of identity. It is probable that it might 

 be reduced in amount, by using intermediate values of the elements 

 modified so as to represent the planet's recent path: but in my exa- 

 mination of the question, I was disposed to borrow nothing from the 

 hypothesis itself towards its confirmation. 



The members of the American Philosophical Society must be gra- 

 tified to learn that one of their number. Prof. Peirce, has, so far as 

 we are informed, anticipated the Europeans in applying Laplace's 

 analysis to the remarkable inequality of (2 [^ — m,) between the mo- 

 tions of Uranus and Neptune. Prof. Peirce has shown under what 

 conditions we must have for the permanent value of (2 ft' — ^), by 

 the same course of reasoning as that by which Laplace demonstrated 

 that we must have the same value for the expression (2 ,« — 3 j«.' 

 + 2 /M,) for the three innermost satellites of Uranus. 



The researches of Prof Peirce generally, on the problem of finding 

 the mathematical planet or planets, that satisfy the residual perturba- 



