1871. ] Proceedings of the Asiatic Society. 1638 
also in canals of comparatively short length; and in various cases 
in canals where the wave is derived from a tide wave in the sea. 
The last case does not concern this problem greatly, andas regards 
the former cases the conditions imposed by the necessities of analysis 
make the results rather representations of the kind of phenomenon, 
than capable of giving accurate values by calculation. Of course 
when on any such hypothesis a theoretical result has been obtained, 
which shows that aretardation would take place in the earth’s ve- 
locity of rotation, it is easy to assign values to the constants and to 
deduce a numerical result, but such results should be considered as 
arithmetical exercises, and not as real deductions proved. It was 
very much to be regretted, Col. Tennant thought, that mathematicians 
who calculate such things occasionally give the results without those 
words of caution which would prevent their being misunderstood. 
This matter has of late received a great importance from the 
strong suspicion that there is a true retardation of sensible amount, 
and the evidence is quite unconnected with any investigations into 
the tides. It was found very soon after accurate observations of 
the Moon were taken, that the time of describing its orbit was 
less than formerly, it being quite impossibie to represent old Eclip- 
ses by calculating from the known elements. For long it was 
found impossible to account for this phenomenon from gravity: 
at last Laplace deduced a result from this cause which so com- 
pletely coincided with that necessary to explain the old Eclipses, 
that he thought himself justified in asserting that the sidereal 
day had not varied by 53, of a second between the time of 
Hipparchus and his day. His results were confirmed almost iden- 
tically by Lagrange, and till very recently were accepted, with their 
consequence that any action of the tides wasrejectaneous. Lately, 
however, Mr. J. C. Adams in the course of a re-examination of the 
Lunar Theory was led to a different result. He found that the true 
theoretical value of the Moon’s acceleration only served to explain 
about half ofthe observed change in its motion of which the rest had 
to be explained. This conclusion was hotly disputed. French mathe- 
maticians, jealous of the honor of their countryman, upheld his re- 
sults, but Mr. Adams’ reasoning was unanswerable and has prevailed ; 
it is acknowledged now that gravity alone does not produce the 
