JOURNAL AND PROCEEDINGS, 33 
west of the Sun, and so at each of the two half-moons in the month, 
that is, at the first and third quarters, the neap-tides, which are the 
lowest, occur. 
Furthermore, the lunar tide is the highest, for although the 
mass of the Sun transcends that of the Moon, yet the Moon is so 
much nearer that its effect is greater. It must also be remembered 
that the tidal effect is produced not by the attraction of the Sun or 
Moon only but by the difference of the attractions exercised by each 
of these bodies upon the nearer and further sides of the Earth and 
the water envelope. And as the proportion of the Earth’s diame- 
rer to the lunar distance is much greater than the proportion of the 
Earth’s diameter to the solar distance the lunar tide is the stronger. 
These fractions roughly are :— 
8000 8000 
and 
240,000 92,000,000 
As this is an important matter let us get at this proportion 
more closely. As the tides are occasioned by the attraction of 
gravitation it is easy to premise that for equal distances the tidal 
effect must vary as the mass of the attracting body. And if the 
problem of the tides was simply a question, what is the attractive 
force exerted by a heavenly body upon another heavenly body as 
the Earth? The question would beanswered by the statement that 
the effect on the ocean would vary directly as the mass of the attract- 
ing body and inversely as the square of the distance of the attracting 
body. But as has been already said the tide depends not on this 
but on the differentiation between the attraction on one side of the 
Earth and the attraction on the other side of the Earth. This is 
more complicated. Let me proceed to demonstrate the true law 
without having recourse to anything but ordinary school arithmetic. 
Let C MM represent the distance from the centre of the Earth 
to the Moon, which is 60 times the semi-diameter of the Earth 
which we will take as a unit of measurement. 
