206 



servations, in 1 740 ; of Maskelyne's at Schehalien, in 1774 ; General 

 Mudge's, in 1802; and General Lambton's, in 1805 ; as well as of 

 Piazzi's Catalogue. Mr. Pond's observations at Westbury agree too 

 little with the Catalogue of Greenwich, he thinks, to be of any use 

 in the inquiry; and Mechain's are opposed to others made by better 

 instruments. 



Dr. Brinkley does not think it an argument in favour of Bessel's 

 refractions, that they give the obliquity of the ecliptic the same for 

 both solstices ; he rather supposes some particular equation is re- 

 quired for the solar refraction, Bessel's refraction at low altitudes 

 being manifestly too large for the stars. 



The question of parallax Dr. Brinkley still reserves for future dis- 

 cussion. 



On the Figure requisite to maintain the Equilibrium of a Homogeneous 

 Fluid Mass that revolves upon an Axis. By James Ivory, A.M. 

 F.R.S. Read December 18, 1823. [Phil. Trans. 1824, p. 85.] 



The author enumerates the various steps by which Sir Isaac New- 

 ton, M c Laurin, and Laplace have carried the theory of the equili- 

 brium of a revolving fluid very near to perfection, but he observes 

 that they have generally supposed the spheroid to differ but little 

 from a sphere ; and he proceeds in the present paper to investigate 

 the figure " by a direct analysis, in which no arbitrary supposition is 

 admitted." 



Mr. Ivory thinks it necessary to distinguish carefully two separate 

 cases ; the first is when the particles of the fluid do not attract one 

 another, and the second when the particles are endued with attrac- 

 tive powers. These, he says, are plainly two cases that are essentially 

 different from one another ; for in the first, a stratum added induces 

 no other change than an increase of pressure caused by the action 

 of the accelerating forces at the surface ; but in the second, besides 

 the pressure, a new force is introduced, arising from the mutual at- 

 traction between the matter of the stratum and the fluid mass to 

 which it is added. 



Mr. Ivory gives two different methods of investigating the funda- 

 mental laws of this equilibrium, the one which is the newest and 

 most simple being contained in two propositions. 



First, If a homogeneous fluid body revolving about an axis be in 

 equilibrio by the attraction of its particles, any other mass of the 

 same fluid having a similar figure, and revolving in the same time 

 about an axis similarly placed, will likewise be in equilibrio by the 

 attraction of its particles. 



The proof is easily deduced from the well known properties of an 

 attraction inversely proportioned to the square of the distance. 



Secondly, If a homogeneous fluid mass revolve about an axis, and 

 be in equilibrio by the attraction of its particles, all the level sur- 

 faces will be similar to the outer surface ; and any stratum of the fluid 

 contained between two level surfaces will attract particles in the in- 



