394 Chronicles of Science. [ July, 
plicated circumstances of unsymmetrical boundaries, varying depths, 
and unknown laws of friction. Still attempts have been made upon 
different hypotheses admitting of mathematical treatment, by which 
the different pomts of M. Delaunay’s theory may be tested. 
Newton, Laplace, and Airy agree in this, that there will be low 
water under the Moon. In a subsequent part of the ‘ Principia,’ 
Newton thinks that the high water would in some measure follow 
the Moon’s place. 
Airy shows that the effect of friction is to accelerate the time of 
each individual tide. 
It is a result of this friction that the velocity of the earth’s rota- 
tion is not affected. 
It is a further result of this friction, and the consequent 
disturbance of the form of the waters, that the Moon’s motion 
is affected ; her orbit is made to become large, and her motion in 
longitude is retarded. The phase of low water (and consequently 
of the tide) is accelerated by the friction. Amongst the conclusions 
arrived at in this elaborate memoir are the following :—The friction 
of the tides does not tend at any instant either to accelerate or to 
retard the rotation of the solid globe. The friction of the tides 
produces a retardation of the Moon’s mean longitude. 
It would seem probable that the reaction of these forces will in 
some way produce a retarding effect on the earth’s rotation. There 
are other instances in the lunar theory in which the Moon’s action 
on the equatorial protuberance of the earth is accompanied by 
action of that protuberance on the Moon, both producing well- 
recognized effects. But in a case like this before us, where the very 
existence of the force depends on friction, and consequent disturb- 
ance of the law of vis viva, the author does not profess himself able 
to follow out all the consequences. It will probably be difficult to say 
what is the effect of friction in more complicated cases. Conceive, 
for instance (as a specimen of a large class), a tide-mill for grinding 
corn. The water which has been allowed to rise with the rising 
tide is not allowed to fall with the falling tide, but, after a time, 
is allowed to fall, thereby doing work and producing heat in the 
meal formed by grinding the corn. It is not doubted that this heat 
is the representative of vis viva, lost somewhere, but whether it is 
lost in the rotation of the earth, or in the revolution of the Moon, 
Prof. Airy is quite unable to say. 
In an addendum, dated April 5, the Astronomer Royal says he 
has at length discovered two terms which appear to exercise a real 
effect on the rotation of the earth. By a process of mathematical 
reasoning, he proves that there is a constant acceleration of the waters 
as following the Moon’s apparent diurnal course. As this is opposite 
to the direction of the earth’s rotation, it follows that from the 
action of the Moon there is a constant retarding force on the 
rotation of the water, and therefore (by virtue of the friction between 
