36 THE HAMILTON ASSOCIATION. 
are therefore displaced eastwards, and occur /a/er than they would 
if the sun were absent. The tides are then said to /ag. 
Between full Moon and last quarter the Sun is over some point 
S, between B and A’, but the antipodal point S, is between 4 and 
B'; hence the przmes. 
Between last quarter and new Moon, when the Sun is at a point 
S, between B and A, it is evident in like manner that the tide /ags. 
Hence spring tides occur at the Syzygies (conjunction and oppo- 
sition). Neap tides occur at the quadratures. 
From Syzygy to Quadrature the tide primes. 
From Quadrature to Syzygy the tide lags. 
All mathematicians know the difficulty of working out the prob- 
lem of the three bodies. So complicated is it that it defies the 
instruments of analysis. The problem of two bodies is capable of 
exact demonstration. This is somewhat analogous to the difficulty 
of predicting tides by calculation. Ifthe globe were covered with 
water to a uniform depth and the friction of continents and configur- 
ation of land and the complications cccasioned by estuaries and 
bays and inlets and varying depth of ocean were eliminated, then 
the tidal problem would be an exact one, but that would be a con- 
dition of matters where the solution of this problem would be use- 
less as the Earth’s inhabitants would be aquatic creatures whose 
calm content would not be disturbed by any perplexing inquiries 
from the ‘‘ crossgrained muses of the cube and square.” Or if the 
ocean ran in parallel canals belting the Earth and were of uniform 
depth then the theory of tides and calculations as to tides would be 
of the most charming simplicity and the happy peoples who would . 
then inhabit the dividing banks could delight themselves with the 
most gentle exercise. But we must take things as they are and we 
find most irregular distributions of land and water and varying depths 
of ocean, and hence the prediction of tides by calculation is one of 
the most complicated problems of practical astronomy. ‘Theoreti- 
cally at new and full Moon high water would be exactly at noon 
and at midnight, but roughly speaking the tides follow the Moon’s 
course so that high water always occurs about the same time after 
the Moon ison the meridian And as the Sun crosses the meridian 
with the Moon at new or full Moon the hour of the clock at which 
high water occurs at such periods is in effect a statement of the num- 
ee a 
