1G2 



the same time. The space of about six miles in depth, within which 

 this increase of density could take place according to known laws of 

 barometric pressure, would not subtend to our eye so much as ^^th 

 of a second, a quantity not to be regarded in an estimate where so 

 much latitude has been allowed for errors. 



In concluding this paper, Dr, Wollaston remarks, that although 

 in reference to a solar atmosphere some doubt may be entertained in 

 consequence of peculiar effects of heat, no such error can be suspected 

 in regard to Jupiter ; and as that planet has not its due share of an 

 infinitely divisible atmosphere, there seems no ground upon which 

 the phenomenon of the earth's atmosphere can be maintained, but on 

 the supposition of ultimate atoms of definite magnitude, no longer 

 divisible by repulsion of their parts. 



On the Expansion in a Series of the Attraction of a Spheroid. By 

 James Ivory, M.A, F.R.S. Read January 17, 1822. [Phil. 

 Trans. 1822, p. 99.] 



Mr. Ivory's principal object in this paper appears to be the re- 

 moval of some difficulties in the demonstration of the method of de- 

 veloping the attractions of spheroids in an infinite series, as employed 

 by Laplace in the Mecanique Celeste. It is natural to think, he ob- 

 serves, that the theory of the figure of the planets would be placed 

 on a firmer basis if it were deduced directly from the general prin- 

 ciples of the case, than when it is made to depend on a nice and 

 somewhat uncertain point of analysis ; and he conjectures that the 

 theory will probably be found to hinge on this proposition, that a 

 spheroid, whether homogeneous or heterogeneous, cannot be in equi- 

 librium by means of a rotatory motion about an axis, and the joint 

 effect of the attraction of its own particles and of the other bodies of 

 the system, unless its radius be a function of three rectangular co- 

 ordinates ; for if this proposition were clearly and rigorously demon- 

 strated, the analysis of Laplace, on changing the ground on which it 

 is built, would require little or no alteration in other respects. 



Without, however, attempting to demonstrate this proposition in 

 all its extent, the author has substituted a more direct and simple 

 mode of argument than that of Laplace, which is perfectly conclusive 

 with respect to all the cases to which the theorem in question can 

 possibly require to be applied. He has shown that by immediately 

 transforming a given expression into a function of three rectangular 

 coordinates, we obtain the same development as is deduced in the 

 Mecanique Celeste, by a more general and complicated mode of reason- 

 ing, which seems to be so far objectionable, as it tends to introduce a 

 variety of quantities into the series which do not alter its total value, 

 since they destroy each other, but which may possibly interfere with 

 the accuracy of its application to particular cases, in which it may be 

 employed as a symbolical representation : for example, when any 

 finite number of terms is assumed as affording an approximate value ; 



