May 18, 1871] 
NATURE 
45 - 

valuable memoirs by Baeyer, on the progress lately made 
in the measurement of the degree; by Griesbach, on the 
Geography of Plants ; by Schmarda, on the progress of our 
Knowledge of the Distribution of Animals ; by Seligmann, 
on the Progress of Ethnology ; by Miiller, on Linguistic 
Ethnography in Relation to Anthropology ; by Fabricius, 
on the Progress of our Knowledge of National Statistics ; 
by Spdrer, on the History of Geography ; by Neumann, on 
the Products, Merchandise, and Currency of Different 
Nations ; and byBehm, on the most important Geographical 
Travels during the years 1868-69. Behm’s memoir, which 
extends over more than a hundred pages, is unquestion- 
ably the most valuable portion of the book, and next in 
order of interest, at all events to the naturalist, we should 
place the essays of Schmarda and Griesbach. The last 
part of the volume is purely numerical, and requires no 
comment. Everyone desirous of keeping himself up to 
the existing level of geographical knowledge should pur- 
chase both the German and French annuals. For those 
who must content themselves with a single volume, we 
should say the French one was the better. 
Gre, DD? 
The Romance of Motion. (Longmans : 
1871.) 
THis is another of those books in which the author does 
not understand the first principles of the science with 
which he deals. The laws of motion seem to be affording 
more than usual trouble to c2rtain people just now, and 
most unfortunately they write books about it couched in 
the longest scientific terms and the most formidably 
accurate-looking phraseology. The author alleges, as 
one of the extraordinary paradoxes among the opinions 
of the nineteenth century, “ how all bodies are supposed 
to persevere in their state of rest or of motion, in a 
straight line, unless compelled to change that state of rest 
or motion by the impression of some force on them; and 
how, in opposition to this law, the planets become ac- 
celerated and retarded in their orbits without such adequate 
impression of force ; also how bodies initially projected 
at the surface of the earth, fall by the force of gravitation 
with velocities uniformly accelerated, and how the planets 
similarly projected descend towards the sun with velocities 
comparatively equal throughout the entire duration of their 
revolutions.” We need hardly remind the rea:ler that these 
conclusions, so far from being in any way inoffosition to 
the law of motion stated by the author, are in complete 
harmony with that law, and, as was demonstrated by 
Newton, follow from it on the hypothesis (to give it no 
higher name) of gravitation. The author at least might 
have observed, in comparing the case of the stone and of 
the planet, that the direction of the force on the former 
is unaltered, while that of the force on the latter is con- 
tinually changing. 
By Alec Lee. 


LETTERS TO THE EDITOR 
[The Editcr does not hold himself responsible for opinions expressed 
by his Correspondents. No notice is taken of anonymous 
communications. | 
Thickness of the Earth’s Crust 
ARCHDEACON PRATT’S explanation in NATURE of May 11 
seems to assume that a rigid body moving in contact with a fluid 
body can never communicate its own rate of motion to the latter 
as quickly as it would doifthis were also a rigid body attached to 
itself. Supposing the earth to consist of a rigid crust inclosing 
a fluid interior, and the crust to be moved by the forces producing 
precession, it would, he says, ‘‘slip over the surface of the re- 
volving fluid through a small space proportionate to the push 
given to the poles. The fluid could not possibly acquire in an 
instant this new motion, however smull it might be, because the 
fluid is not rigidly connected with the crust.” 
I venture to suggest that if in the last sentence Mr. Pratt would 
substitute the word ‘‘slow” for ‘‘small,” the question would 
it 


have a different aspect, notwithstanding his subsequent state- 
ment to the contrary. 
Strictly speaking, when a body, however rigid, is moved, the 
whole of it never movesinstantaneously. The particles on which 
the moving force immediately acts move first, and the rest move 
in succession afterwards. The smallness of the interval is 
the measure of the rigidity, but some interval must 
always be assumed. Bodies move as a whole through the 
attractive or repulsive forces of their particles; and every 
such force resolves itself into a power of moving something 
through a certain space in a certain time. The reason 
why a moving solid will ‘‘slip over” the surface of a fluid 
instead of carrying it with it, is that the rate at which it can 
carry it with it by reason of its attractive force is commonly less 
than the rate at which the solid is moving. But if the motion is 
slow enough to exceed that which the attractive force will cause 
in the fluid, it will slip over no longer; and if it be so slow that 
not only the power of the solid over the fluid, but of the fluid par- 
ticles over each other, is able to produce an equal rate of motion, 
the whole mass will move together as if it were a rigid body. 
This rate will depend chiefly on the nature of the fluid. Ifa 
metal plate four inches in diameter is filled with lamp oil, and 
made to rotate at about one revolution in three minutes, the oil 
will move with the plate without appreciable retardation, though 
if the speed be doubled, the oil is seen to be “slipped over.” 
If water is used, or the size increased, the rotation must of course 
be very much slower. It would appear on these grounds, I 
think, that the extremely slow movement of precession might 
practically affect the whole body of the earth as if it were rigid, 
notwithstanding the granting of a fluid interior. 
May 14 TS Mn Wile 
Ir requires no little courage to attack so eminent a mathemati- 
cian as Archdeacon Pratt on his own ground, and it is, therefore, 
with the utmost diffidence that I venture to suggest that in his 
defence of Hopkins against Delaunay in your last number, he 
has mistaken a mathematical fiction for a fact. 
In calculations involving quantities which vary in magnitude, 
the imperfection of our methods oblige us to have recourse to an 
artifice, and for the benefit of the non-mathematical reader, I 
will try to explain what this artifice is, taking the case of nuta- 
tion as an example :— 
The motion of the earth’s axis which is known by this name, 
is caused mainly by the attraction of the moon on that part of 
the earth which lies outside a sphere, whose centre is the earth’s 
centre, and its radius the polar radius of the earth. Now this force 
of the moon’s attraction is never the same in magnitude ; and, 
however small be the interval of time we consider, it is not the 
same at the end as the beginning of that interval; it is incessantly 
changing. Everyone will realise the difficulty of estimating the 
effect of sucha force. This difficulty is got over by the artifice 
I mentioned, which is as follows :—The time is divided into a 
number of small intervals, and the attraction is supposed to keep 
during anyone of these intervals the magnitude which it has at 
the beginning of that interval, and at the end of that interval 
suddenly to assume the magnitude which it has at the beginning 
of the interval next following, and so on; the force, in short, in- 
stead of varying by insensible changes, is supposed to act bya 
series of fits and starts. This must be what Archdeacon Pratt 
means when he talks of ‘‘a succession of slight horizontal 
pushes being given to the poles.” The amount of motion pro- 
duced during each interval on the above supposition is then de- 
termined, and these amounts are added together to obtain the 
displacement produced. 
It is clear enough that such a method can only be approxi- 
mately correct ; but it is also clear that the smaller each interval 
is, the nearer will the hypothetical be to the real state of the 
case, and the nearer will the calculated be to the actual result. As 
long as the intervals are finite there must be some error, but the 
smaller the intervals are made the less will this error be. Ineed 
not go into the methods of mathematical analysis which enable 
us to get rid of this error, and which, when we have found out 
what will be the effects of a force acting with variable intensity 
by fits and starts separated by small finite intervals, enables us to 
deduce the effect of the same force when it comes to vary inces- 
santly ; for [ hope I have made clear the nature of the mathe- 
matical artifice on which this analysis is founded. 
Now it seems to me that Archdeacon Pratt all along reasons 
on the supposition that the moon’s attraction acts after the 
manner the mathematical artifice I have described supposes it 
