MATHEMATICAL SECTION. 103 
ported to give terms of the second order, was incorrect, and pointed 
out that the error in Riicker’s process consisted in expanding to 
terms of the second order an expression which included only terms 
of the first order. 
This paper was briefly discussed by Messrs. Hatt, ABBE, Kum- 
MELL, and HARKNEsS. 
This and other related papers appeared in Nature.* 
Mr. R. 8. Woopwarp read a paper on 
THE CONDITIONED COOLING OF A HOMOGENEOUS SPHERE. 
The salient features only of this paper were presented. The funda- 
mental assumptions and analytical conditions of the problem were 
indicated, and especial attention was directed to the distinction be- 
tween the case of “conditioned cooling” and that of “free cooling,” 
which latter was discussed by the author, at the 27th meeting of 
the section. It was shown that the solution for the more complex 
case of “conditioned cooling” is derivable by a comparatively simple 
process from the solution for “free cooling.” The probable discrep- 
ancy between the data presented by the earth as a cooling sphere 
and those assumed in the solution of the problem, and the additional 
data requisite for a more complete solution were pointed out. 
The presentation of the paper was followed by an informal dis- 
cussion participated in by nearly all present. This discussion re- 
ferred chiefly to the physical features of the earth as a cooling sphere, 
and served to disclose a diversity of opinion concerning the con- 
ductive and convective properties of such large masses. 
[This paper appeared in full in the Annals of Mathematics. 4°. Char- 
lottesville, Va. 1887, October; vol. 3, no. 5, pp. 129-144.] 
o 
* Nature, a weekly illustrated journal of science. 4°. London, 1887-1888. 
1887, Aug. 18, vol. 36, no. 929, p. 366. Ontheconstant P; by Wm. Harkness. 
Sept. 8, vol. 36, no. 932, p. 436. Same; by Wm. Ellis. 
Sept. 29, vol. 36, no. 935, p. 508. Same; by A. W. Ricker. 
Dec. 8, vol. 37, no. 945, pp. 127-128. Same; by Harkness and re- 
joinder by Ricker. 
1888, Jan. 19, vol. 37, no. 951, pp. 272-273. Same; by Harkness and re- 
joinder by Rucker. 
