Chemistry and Physics. 403 
the equations form a s system of simultaneous differential equations 
which have to win solved in order to trace the changes in the sys- 
tem of satellit 
xpressions are also found for the rotation of the planet, and 
for the energy 4, in terms = the resultant moment of momentum 
of the system and of the & 
It is then shown how sibeb equations may be per by series, 
te by powers of the time. As, however, the series are 
t rapidly pase ie a dt are not sppemereas is tracing ex- 
boc changes of configura 
The case where there are oe two satellites is then considered 
in detail, and it is shown that, if a surface be constructed, the 
coordinates (47 being drawn vertically upward and the &’s being 
horizontal), then the solution of the problem is expressed by the 
statement that the point, representing on the gene the config- 
uration of the system, travels down the steepest p 
The contour-lines on this “ surface of energy” are illustrated by 
figures, = the graphical solution found therefrom is interpreted 
and — sed. 
mao i part of the paper contains a discussion of i part 
played by tidal friction in the evolution of the solar system. 
It is proved that the rate of expansion of the sigsuart orbits 
Tt a os red, ere rk ss that a knowledge of certain nu- 
merical walunbae wou w light on the question. Accordingly 
the moments of momentum of the orbital motion of the planets 
round the sun, of the sun’s rotation round his axis, of the orbital 
motion of the satellites round their planets, and of ‘the rotation of 
the planets about their axes are evaluated with such degree of 
tecuracy as the data ermit. 
comparison ua the orbital momenta of the planets 
and their rotational mo , it is concluded that tidal friction 
can ite & sensibly have enlarged the planetary orbits since the 
planets had as eee existence 
