416 
PROFESSOR G. H. DARWIN ON FIGURES OF 
Thus, as far as this investigation goes, it appears that when the fluid Moon is on the 
point of breaking up from stress of tidal and centrifugal forces the distance between 
the centres of Moon and Earth is 6500 miles, and the shortest distance between the 
two surfaces is 380 miles. 
This result must, however, from the nature of the approximation, be an under¬ 
estimate of the distances. 
The whole of the present section has been suggested by a pamphlet by Mr. James 
Nolan # in which he criticises some of my previous papers. I have commented 
elsewhere on his criticisms.t 
§ 12. On the Case where the two Masses are unequal. 
The results of the previous section point to a very remarkable limitation to the 
possibility of approach of two masses of unequal size. It has, therefore, seemed worth 
while to consider this case numerically, and a case is therefore chosen which shall 
approach near to that which we know is the limit of possibility. I choose, therefore, 
a = 1, A = 3, which makes the ratio of the masses 1 to 27, and c — 5'3, which brings 
the protuberances into close proximity. 
The numerical details are omitted, but figs. 5 and 6 (Plate 23) give the results, the 
numerical values of the radius-vectors being, as before, entered on the figure. 
The elongation of the smaller mass is so extreme that it is obvious that, rigorously 
speaking, the spherical harmonic approximation must be considered to break down. 
Nevertheless, I conceive that these curious figures may be held to indicate the general 
nature of the true result. 
It is remarkable that the smaller mass exhibits a marked furrowing round the 
middle. This seems to indicate that such a system tends to break up by the separa¬ 
tion of the smaller mass into two parts. 
§13. Summary. 
The intention of this paper is, first, to investigate the forms which two masses of 
fluid assume when they revolve in close proximity about one another, without relative 
motion of their parts ; and, secondly, to obtain a representation of the single form of 
equilibrium which must exist when the two masses approach so near to one another as 
just to coalesce into a single mass. 
When the two masses are far apart the solution of the problem is simply that of the 
equilibrium theory of the tides. Each mass may, as far as its action on the other is 
* ‘ Darwin’s Theory of the Genesis of the Moon.’ Robertson, Melbourne, Sydney, Adelaide, and 
Brisbane, 1885. 
f ‘Nature,’ February 18 and July 29, 1886. 
