Controversy between Archdeacon Pratt and Prof. Haughton. 348 
surface. This is quite consistent with its assumed temperature, 
which is much less than any probable estimate we can make of 
the temperature of the conversion of the force of a body striking 
the sun’s atmosphere with a velocity of from 400 to 500 miles 
per second, The existence of a transparent atmosphere seems 
also to be positively demonstrated by the blaze occurring above 
the spots. 
Edinburgh, February 15, 1860. 
XLVIII. Controversy between Archdeacon Pratt and Professor 
Haughton. 
To the Editors of the Philosophical Magazine and Journal. 
GENTLEMEN, 
N Archdeacon Pratt’s last paper, published in your Number 
for the present month, he states that the question at issue 
between him and Professor Haughton is not what I have repre- 
sented it to be, namely, by what rule the equation 
ee il a d.a'e! az a de! maz a : 
eh ee — as Rae "eal P aa — Bax Pa2=0 alre) 
is to be differentiated when the continuity of the laws of the 
density and the ellipticity throughout the entire mass is not 
assumed. Professor Haughton asserts that, by the process of 
differentiation, and without the assumption, he can deduce the 
equation 
d?e  2pa? de =F pe \ 
da? al da a? 3 “ pla? EHS ead aL) 
from that just given. Archdeacon Pratt asserts that, without 
this assumption, the second of these equations does not follow 
from the first. If this be not a eontroversy as to the proper 
mode of differentiating equation (12), I confess myself quite 
unable to understand what it is. But to obviate all possibility 
of misconception, I assert, and shall proceed to prove, that 
equation (13) does follow from equation (12), without any 
assumption as to the law of density or ellipticity for the solid 
part of the earth. 
I will suppose that, for all values of a! from a! =0 to a!=a (in 
other words, for the whole of the fluid nucleus), we have e’=¢(a’), 
p'=y(a'), and that, for values beyond a, we have ¢ =/(a'), 
p'=F(a'), f and F denoting any functions, continuous or dis- 
continuous. 
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