Chase.] 124 (June 16th, 1871. 
friction, it should be low water under the moon, rest on the assumption 
that Or is so slight (see Mec. Celeste 327 iv, 887 iv, 342, 2177, Ge., ) that 
it may be neglected, in order to satisfy equations which would otherwise 
be impossible of integration. Itis true that the radial codrdinate of 
the tide wave, is insignificant in comparison with the coédrdinates in lati- 
tude and longitude, but the cause of that insignificance is not immediate- 
ly evident, and I can see-no reason for omitting, in tidal discussions, any 
term which would be important in the discussion of planetary motions. 
I presume the following postulates will be readily granted. 
I. If the earth had no axial rotation, the tide would be one of equilib- 
rium, with high water under the moon. 
II. If rotation were to commence after the establishment of the equi- 
librium tide, the tidal ellipsoid would be thrown forward in the direction 
of rotation. 
Ill. If the water flowed with such velocity as to be self-sustaimed, the 
centrifugal balancing the centripetal force, it would be low water under 
the moon. 
As neither the first nor the third of these conditions is true, it would 
seem reasonable to infer that the tidal crest should be at some point inter- 
mediate between the lunar meridian and the lunar astronomical horizon. 
The second postulate favors this inference, provided there is any force, 
other than friction, which would tend to set back the crest of the third 
postulate. 
Such forces, itseems to me, exist in the cohesive attraction and incom- 
pressibility of the water, and the rigidity of the earth, all of which tend 
to shorten the radius vector and increase the velocity of every particle 
dm, in two of the quadrants, and to lengthen the radius and diminish the 
velocity, in the alternate quadrants. These successive increments and de- 
crements of velocity terminate at the octants, thus tending to produce 
low water three hours before, and high water three hours after, the moon 
passes the meridian. 
Airy (Mo. Notices, R. A. S., April 18, 1866), gives a diagram to show, 
from the position of the points at which zero horizontal currents become 
plus or minus currents, that it must be low water under the moon. Tam 
unable to reconcile his hypotheses, respecting the direction and velocity 
of the currents, with actual tidal observations, but even if they are cor- 
rect, I think we should look to the total action of the moon, rather than 
to the flow of water at particular points. The water falls in the entire 
quadrants immediately following, and rises throughout the quadrants im- 
mediately preceding the meridian of high water. Would not this contin- 
uous action be best sustained if the moon were on the great circle 45°W. 
of the crest and 45°. of the trough of the tidal wave, as Newton sug- 
gested in his Principia, B. I., Prop. 66, Cor. 20? 
