398. Intelligence and Miscellaneous Articles. 
whence we have’ 
ba 7 _ ay SN =w'ay (a . b°), tae —a°z = ware. 
Each of these partial differential equations can be easily integrated ; 
and the value of V, finally obtained, is equivalent to the equation 
of fluid equilibrium, or 
VtS@+y)=c. 
Let 6 represent the complement of the latitude, and ¢ the longitude, 
, counted from the meridian of the greatest axis, then 
z=r cos 0, =r sin 6 cos ¢, y=r sin 6 sin g, 
and 
- rw" . 
V+ = sin? @6=C. 
In the case of an ellipsoid having the ellipticity e, we have, neglect- 
ing small terms, 
r=a (1—e cos’). 
From these equations, and from the properties of Laplace’s functions 
into which V can be expanded, an expression can be obtained of the 
same kind as that deduced by Professor Stokes from his own and 
Gauss’s theorems relative to attractions.—Proceedings of the Royal. 
Irish Academy, Feb, 25, 1861. 
ON A METHOD OF TAKING VAPOUR-DENSITIES AT LOW TEMPERA- 
TURES. BY DR. LYON PLAYFAIR,:C.B., F.R.S.. AND J. A. WANK- = 
LYN, F.R.S.E. 
The authors refer to Regnault’s experiments, which have shown 
that aqueous vapour in the atmosphere has the same vapour-density 
at ordinary temperatures as aqueous vapour above 100° C.; and 
they bring forward fresh experiments upon alcohol and ether to show 
that when mixed with hydrogen these vapours preserve their normal 
density at 20° or 30°C. below the boiling-points of the liquids, and 
infer generally that vapours, when partially saturating a permanent 
gas, retain their normal densities at low temperatures. 
From their researches the authors deduce the consequence—re- 
markable, but quite in harmony with theory—that permanent gases 
have the property of rendering vapour truly gasecus. Stated in 
more precise terms, the proposition maintained by the authors is, 
«The presence of a permanent gas affects a vapour, so that its ex- 
pansion-coefiicient at temperatures near its point of liquefaction 
tends to approximate to its expansion-coefficient at the highest tem- 
peratures.” 
