356 
POPULAR SCIENCE REVIEW. 
This has been the salient discovery of the quarter. We must now call 
attention to a subject on which we remarked in our last Summary — the 
the action of the moon on the tides, and indirectly through them on the rota- 
tion-time of our earth. It has recently been shown, not only that M. 
Delauney was anticipated by Ferrel in 1853 {Astronomical Journal, iii. pp. 
138 — 141), but that the connection is most probably a real one, an extension of 
the Astronomer Royal’s mathematical investigation having lead him to support 
the theory. Professor Adams is of the same opinion. Professor William 
Thomson has pointed out that an equal retardation (10" in a century) would 
result in a rise of the sea-level f of an inch, or, were meteoric dust to fall at 
the rate of -gVth of a foot in a century. The Astronomer Royal has also given 
us a very beautiful geometrical proof that, contrary to generally received 
notion, were the tides to move without friction, there would always be low 
water under the moon. 
The method of proof is as follows ; we give it in the Astronomer Royal’s 
own words : — “ To assume that the ring of water has an elliptic form, the 
elliptic shape (not the water) travelling round with the same angular velocity 
as the hour-angle velocity of the moon, and that the motion of every particle 
of the water is oscillatory ; to examine more precisely the laws of the oscillatory 
motions of the waters in different parts of the elliptic ring ; to investigate the 
forces which are required for maintenance of those oscillatory motions ; and 
to show that those forces are such as to correspond to low water under the 
moon, and to no other relative position of the tide and the moon. 
“ First, it is to be carefully remarked that the rising of the water at any 
place does not depend on the horizontal movement of the water at that place, 
but on the relative values of the horizontal movement of the two sides of 
the place. If the water on both sides of that place is flowing towards that 
place, the water rises there. If the water on one side is flowing rapidly 
towards it, and the water on the other side is receding slowly from it, the 
water rises there. When the surface at any one place is stationary as to 
height, there may nevertheless be considerable horizontal velocity ; only it is 
certain that the water is flowing towards it on one side exactly as fast as it is 
receding from it on the other side.” 
In the first diagram the strong elliptic outline represents the form of the 
surface of the water at the present instant, and the dotted line the form 
which it will take in a short time ; the form of — 
the dotted curve being the same as that of the 
strong-line curve, but having turned round with 
the same angular velocity as the moon. 
“At A, C, E, and G, the height of the water 
has scarcely altered from the state of things with 
the strong outline to the state of things with the 
dotted outline. Therefore, the spread of the water 
is equal on both sides of each of these four points. 
And therefore it will readily be understood from 
the ordinary theory of maxima and minima, that 
at these four points the horizontal motion of the 
water is most rapid ; its direction at each being 
at present undecided. At B and F the water is rising most rapidly ; there- 
