TRANSACTIONS OF SECTION A. 915 
hand, a very warm and very dry August is prone to be succeeded by a wet 
September, 4 to none out of 7. In each of these cases the actual probability is four- 
sevenths, but the value of this fact is much strengthened by there being no case of 
the opposite. 
14. Cold and Wet.—If July have this character the next month will generally 
‘be a cold one, 3 to none out of 5. So, likewise, a very cold and yery wet August 
tends to be followed by a cold September, 3 to none out of 5. 
15. With regard to the meteorological seasons, there is only one case in which 
the combination of extremes of temperature and moisture in one season seems to 
definitely influence the following one. A very cold and very wet summer is usually 
succeeded by a cold autumn. The facts in this case, although few in number, give 
evidence of a remarkably strong probability, being 5 to none out of 4. 
In conclusion, I beg to offer these results, so far as they go, with some confi- 
dence, obtained as they are from the purely numerical treatment of a long course 
of carefully recorded facts, whilst they are utterly free from any bias derived from 
theory. Let it be freely acknowledged that they take the rank only of empirical 
laws, which may some day be knit together by cautious induction to form a part 
of the future science of meteorology. 
8. Notes upon the Rotational Period of the Earth and Revolution Period of 
the Moon deduced from the Nebular Hypothesis of Laplace. By W. F¥. 
Stanzey, £.G.S., F.R.MS. 
This paper was in part a defence of the nebular hypothesis of Laplace (last note 
<Systéme du Monde’) in opposition to a modification of it proposed by Mr. G. H. 
Darwin (‘ Phil. Trans.’ 1879, p. 536) as regards the present and former velocities of 
motions of the earth and moon, The author proposed a theory by which the rela- 
tive velocities of an earth and moon might be deduced from consideration of the 
early nebulous conditions. Thus where the nebulous system of the earth was con- 
tracting by loss of heat, and the tangential velocity of the exterior parts of it ex- 
ceeded the centralising action of gravitation, so that it was possible for a sateliite 
system to become detached, there must necessarily be a plane of equilibrium of the 
particles surrounding the earth where they would he equally solicited by the earth 
and by its satellite, and this would be the plane of separation of the system. After 
the separation, the tangential velocities of the separate parts would give the final 
velocity of the central mass when these parts had condensed to form it. Thus 
taking the earth and the moon, or their original nebular systems by the simple 
formula e : m :: d*:d,?, where e and m are earth and moon, and d and d, the respec- 
tive masses. The attraction being directly proportional to the mass, and inversely 
as the square of the distance, we find by this formula in taking the separate den- 
sities and distances of the earth and moon, that the earth at its point of separation 
where a particle would be in equilibrium would form at first a nebulous globe of 
212,347 miles radius. The tangential velocity of the equatorial surface of this 
globe, assuming it moved at the present rate of the moon, of one revolution in about 
27% of our days, would be a sidereal tangential velocity of 1,534,215 miles in this 
period. The present velocity of the earth’s equator taken for the same period is 
679,305 miles, or only about half this. If we assume the density of matter of the 
nebulous system which formed the earth diminished directly as the square of the 
distance from the centre, then upon condensation the equatorial surface of the 
present globe should have the final velocity of its original nebulous equator imme- 
diately after its separation from the moon, supposing the system acting entirely 
without friction. But during the formation of the present globe, the matter con- 
densed upon the central mass impressing its momentum of higher tangential velocity 
upon this mass would cause the centre of the system to have higher radial 
velocity than the exterior parts, and as the exterior of the system would still be 
nebulous matter offering considerable resistance to the central mass moving at 
higher radial velocity, this motion would be necessarily frictional, causing a relative 
loss of velocity in the central mass which would be developed into heat. It is also 
3N 2 
