CRITICAL AND SUPPLEMENTARY. 203 



The masses of the asteroids are purely conjectural, while that of Mer- 

 cury is too uncertain to be used. For Venus the computed mass exceeds 

 the observed; but at least part of the difference may be ascribed to the 

 influence of atmosphere and irradiation in bringing about an overestimate ■ 

 of the planet's true diameter; for example, if the observed radius were 

 corrected by — 2 per cent of its value, the computed and observed masses 

 would agree. For the moon and Mars, the computed masses fall below 

 the observed by 15 per cent and 20 per cent, respectively. 



From this, as before, the suggestion is that the assumed law of com- 

 pression should be modified in the direction of allowing greater compressi- 

 bility at the lower densities, and less at the higher, which would have the 

 effect of assigning greater mass to the nucleus at intermediate sizes, and to 

 the present earth a steeper density-gradient near the surface, together with 

 a relatively more nearly homogeneous central portion. This agrees with 

 conclusions which have been drawn from observations of precession and the 

 transmission of seismic disturbances. 



In view of this comparison it seems quite conceivable that a law of com- 

 pressibility might be constructed, agreeing with the data furnished by the 

 earth in its present condition, and such that the observed masses of the 

 planets now existing in its neighborhood would prove to be the same as 

 those computed for the nucleus at epochs when the dimensions correspond. 

 It will accordingly be of interest to review the previous theory, with the 

 substitution of a density-formula whose variations from that of Laplace 

 have the general trend indicated. 



A formula of this character for the density is the simple one proposed 



byRoche:^ ^=^„ (l-ca;==) c=const. (74) 



From this, according to the general equations previously used, are derived: 



w=^7:/>or3M— — cxM (75) 



whence H is determined by (15) ; also: 



• p=^|(22_;3-^2) + (,3_^^3)| (77) 



^ (,_,j3 . ^_±2^^ (78) 



2p^c z 



3 



=<Oo(l-|c) p,^p,{\-c) (79) 



E=%7:Ar^ • ^c(l-^c) (80) 



0=%TzAr^{\-^c^^c^ (81) 



Roche, Acad^mie des Sciences et Lettres de Montpellier, v. 8, 1848, p. 235. 



