CONTRIBUTIONS TO THE THEORY OF THE MOTION OF THE MOON. 239 
secular acceleration of 12*2", or nearly double that which has 
received a theoretical explanation. This leaves a difference of 
6" per century in the secular acceleration whose origin had to 
be found. Newcomb and Delaunay both suggested that perhaps 
this difference between the observed and theoretical values of 
the secular acceleration might be only apparent, and that the 
difference might be due to a gradual increase in the length of 
the day. It was pointed out that if the earth be supposed to 
be slowly retarded in its axial rotation, the day will be longer, 
and as the moon will advance further in its orbit in the space of 
one day, it will appear to have a secular acceleration. An in- 
crease in the length of the day of only one thousandth part of a 
second in a century would amply account for the difference 
between the theoretical and observed secular acceleration. It 
remained to be shown what would produce this retardation of 
the earth’s' axial rotation. Both Newcomb and Delaunay sug- 
gested that it might arise from the action of the tides, which, 
by their friction on the solid crust, might prove to be the origin 
of this decrease in the velocity of the rotation of the earth. 
Delaunay attempts to show, mathematically, that it was possible 
for the tides to produce this effect. It cannot, however, be said 
that this attempt was successful. 
This assumed retardation of the axial rotation of the earth 
and its hypothetical origin in the friction of the tides of the 
ocean against the earth, have been very generally accepted, and 
are very commonly employed for purposes of scientific argument, 
as if their truth had been rendered highly probable. It is, 
however, important to remember that it has never yet been 
shown in a satisfactory manner that it is even possible for the 
tides to retard the rotation of the earth to a sensible extent. 
Moreover, as will now be shown, it is still most uncertain that 
there is really any retardation to be accounted for in this way. 
It must not be forgotten that the value found by Hansen pre- 
supposes that his tables are correct, but it has been seen already 
that this is not the case. The late investigations of Professor 
Newcomb afford much valuable information on this subject. 
It has been already mentioned that Professor Newcomb, 
when correcting the data employed in Hansen’s tables, found that 
the value of the secular acceleration which had been employed 
ought to be diminished by one-third. According to him the 
value 8*4" is that which best represents the observations, and 
these observations are more trustworthy than any previously 
made use of. Thus it is evident that the greater part of the 
supposed difference between the values of the theoretical and 
observed secular inequality arises from the imperfect nature of 
the observations which hitherto have been made use of, together 
with the effect of the empirical term employed by Hansen to 
