344 
NATURE 
[ Aug. 31, 1871 

not directly comparable: that the mercury in Gay- 
Lussac’s tube is hot, while a barometer is generally cool ? 
A student of Nature will scarcely be taught much that is 
satisfactory concerning Gay-Lussac’s beautiful method of 
determining vapour densities, by being led away at once 
into intricate formule “ which burden the memory, with- 
out cultivating the understanding.” This one example 
will sufficiently indicate the fault which runs through 
the whole volume before us. Much new and valuable 
matter, albeit besprinkled with formulz, has been added 
by the translator; and various passages in the original 
have been modified or otherwise corrected. But, though 
we have no hesitation in saying that the original has been 
thereby improved, yet the final result is neither remarkable 
for its novelty, nor edifying from its simplicity. 


LETTERS TO THE EDITOR 
[Zhe Editor does not hold himself responsible for opinions expressed 
by his Correspondents. No notice is taken of anonymous 
communications. | 
Thickness of the Earth’s Crust 
I TAKE in NaTURE in parts. Your part for May last has just 
reached me in Calcutta, and is somewhat rich on the question of 
the thickness of the earth’s crust ; for three of its four numbers 
contain letters on that subject. First, my letter to you, p. 28 ; 
two critiques upon it from ‘‘A. J. M.” and Mr. Green, p. 45 ; 
and a third from Mr. David Forbes, p. 65. 
Reply to ‘‘A. J. M.” Ido not think it safe to draw inferences 
from a comparison the members of which differ so materially ; 
a plate of lamp oil, probably a quarter of an inch deep, and the 
solid crust of the earth resting on a fluid mass 3,856 miles deep, 
supposing the crust, according to the thin-crust theory, to be 100 
miles thick. To be sure, the motion in the experiment is very 
much greater than precession ; but the depth of fluid is also very 
different, and the cases are not parallel. Moreover, in the one 
case, the oil rests on the plate, weighed down by gravity, and is 
easily carried round bodily with the plate. This is different to 
the hard crust rubbing over a depth of fluid. I see the writer, 
like M. Delaunay, relies much on the extreme slowness of the 
motion. More on this soon. Weshall have to beware how we 
adopt the phrase ‘‘a rope of sand,” for if we use the rope s/ow/y 
enough, it may become in our hands a ‘‘rod of iron.” 
Reply to Mr. Green. By ‘‘ pushes” I did not mean mechanical 
knocks, but merely geometrical movements. The pole of the 
earth goes round the pole of the ecliptic in a circle in about 
26,000 years. I divided this circle into a multitude of little 
pieces. Nor was my description meant to represent this motion 
as being by fits and starts, but only in portions, to assist the mind 
in a popular explanation, not of precession, but of the thing I 
wanted to be understood, the slipping of the hard crust over the 
fluid. I think it is very likely my own fault that my description 
has been misunderstood. 
Reply to Mr. David Forbes. Mr. David Forbes glides out of 
the discussion on the plea, that after all I make out that Mr. 
Hopkins’ calculations were based only on “an idea.” But so is 
M. Delaunay’s opinion based on anidea, We must start with 
an idea. Ideas are of two kinds, sound and unsound ; and if 
the idea we rest upon is sound, we cannot possibly do better than 
build upon it. M. Delaunay thinks his ideais supported by an 
experiment. I have tried to find a description of the experiment, 
but without success. I altogether doubt whether any experiment 
with models can be devised to lead to trustworthy results, regard- 
ing such a huge mass as the earth affected by such slight motions 
as precession. Mr. David Forbes says he went to the Royal 
Society to hear a paper of mine read on the constitution of the 
solid crust of the earth. It was natural that he should suppose 
from the title, that it might bear upon this question of the thick- 
ness of the crust. But this is not the case at all, as he would 
find, M. Delaunay’s strictures on Mr. Hopkins’ investigation 
seemed to me so important, that I did dvag in, I may say, an 
allusion to them in anote. It is very likely that, as my paper 
was almost entirely a calculation of mathematical formule and 
their numerical application to the pendulum observations lately 
made in India, the paper itself was not read aloud, and that 
conversation turned on the incidental note. 

I propose now to view the subject ina new light, and to 
begin de ovo ; and I feel confident that your readers will see 
that there is more to be said for Mr, Hopkins’ method than they 
have by this time been led to think. 
The precessional motion is no doubt extremely slow : and that 
because the precessional force is extremely small. But the par- 
ticles of the earth’s mass have a good deal more to do in the 
matter than to partake of this small motion. Every twenty-four 
hours they have to undergo a strain, first this way and then that, 
such that I believe no fluid, however viscous, could sustain. 
Though the precessional force is so minute, it is the resultant or 
residuum of an almost infinite number of other disturbing forces 
nearly balanced ; as I proceed to show. 
Let G be any point in the earth’s mass ; 4 its distance from 
the centre ; @ the radius of the earth ; ¢ the distance of the sun ; 
@ the angle between 6 and c; S thesun’s mass. ‘Then, consider- 
ing the sun’s action by itself, its attraction on G I resolve 
parallel and at right angles to c, and from the former position 
subtract the sun’s attraction on the disturbing forces on G which 
are wanted, These are, neglecting the smallest quantities, 
Sé 
454 & 
se Cos 8 and ae 
sin 6, 
For the sake of a name I will call the plane through the earth’s 
centre, at right angles to the line joining it and the sun, the 
Boundary Plane, as it intersects the surface almost exactly in the 
boundary line between sunlight and darkness. It will be observed 
that at this plane the first of these disturbing forces equals zero, 
and is positive on the sun side of the plane, and negative on the 
opposite side. The amount of this force is the same at all points 
lying in any plane parallel to the boundary plane, and the aggre- 
gate of the positive forces on the one side, and of the negative on 
the other, would be in each case a force acting through the 
earth’s and sun’s centres, but for the slight deviation of the 
earth’s figure from a sphere, and the consequent arrangement of 
its mass. Suppose, for argument’s sake, that the particles of the 
earth’s mass are held invariably together as a rigid body ; then 
the disturbing forces parallel to ¢ will amount to an aggregate 
positive force, and an aggregate negative force, tending to 
separate the two parts of the earth formed by the boundary plane. 
These forces are equal to each other, and pass nearly through the 
earth’s centre, at opposite and equal distances from it. They 
form, in fact, a mechanical ‘‘ couple,” and twist the earth round 
some diameter lying in the boundary plane. The arm of this 
couple is a minute quantity depending upon the ellipticity of the 
earth’s figure. Hence the movement of the couple, from which 
precession and nutation arises, is a minute quantity, while the 
Jorce of the couple (which is the tension of the earth’s mass per- 
pendicular to the boundary plane) is not of that minuteness. The 
other disturbing forces, represented by the second formula, all 
tend towards c, and compress the mass. They would all balance 
each other, were the earth spherical. The resultant of these 
forces on the sun side will be a minute quantity of the order of 
the ellipticity, and will act at a certain distance from the centre ; 
and the resultant on the opposite side will be an equal force, act- 
ing at an equal distance from the centre, but in an opposite di- 
rection ; so that again there will be a couple of minute power, 
assisting with the other couple to produce the combined motion 
of precession and nutation. In this case, although the forces 
nearly balance each other on each side the boundary plane, 
parallel to it, and but a small resultant follows, yet the particles 
of the mass have to undergo the compression from opposite sides, 
as in the other case they have to sustain the tension caused by 
the opposing forces tending to separate the two halves of the 
earth. 
The moon will produce forces precisely similar to these, and a 
little more than twice their amount. The forces of the sun and 
moon do not come to their maxima and minima at the same time, 
except at new and full moon, At other times they partly con- 
spire or counteract each other according to their position. Sun 
and moon together will produce most irregular cross-strains 
through the mass, if the particles are held together by any degree 
of rigidity. 
It will be seen, then, that as within twenty-four hours every 
particle of the mass in its rotation is carried through the bound- 
ary plane some days in the year, and most of the particles every 
day, every part of the mass will be periodically subject to the 
maximum strain I have described as taking place at that strain, 
and most parts twice a day, as well as the compressing force at 
right angles to ¢, 
The same will be the case, and at different times, except at new 

