President's Address li 
in terms of the mass of the earth ; the eccentricity of the orbits of the 
sun and moon; the mean distances of the sun and moon from the earth; 
the inclination of the orbit of the moon to the ecliptic; the mean 
obliquity of the ecliptic; the regression of the moon’s node; the 
length of the year and lunar month ; and the precessional moment of 
inertia. 
This moment of inertia involves, besides the ratio of the centrifugal 
force at the equator to gravity, the knowledge of the ratio of the polar 
to the equatorial diameter of the earth, and the ratio of the mean density 
of the earth to its surface density. Unfortunately, we know very little 
of the internal constitution of the earth. But assuming the most 
probable hypothesis that the whole earth was at one time fluid, and that 
it has gradually cooled from the liquid to the solid state, and determining 
on one hand its mean density by the well-known Cavendish experiment, 
and on the other its surface density by determinations of the specific 
gravity of its average surface components, we can arrive at a law of 
internal distribution of density which, so far as can be judged, must be 
approximately true. If, however, we attempt to pass through the 
assumption of this law to the determination of the compression of the 
earth by the results of pendulum experiments, we are met with a dis- 
cordance of something like two per cent. between the results derived 
from the two methods ; a discordance, however, which is far from being 
incompatible with the uncertainties both in the pendulum operations 
and the results of the measurement of geodetic arcs of latitude and 
longitude. In fact, to make certain of an accuracy of two per cent. in 
the amount of the earth’s compression we must be certain of the lengths 
of both polar and equatorial axis within about 660 feet, and we have 
already estimated that uncertainty at 1,000 feet. In the present state 
of science, therefore, it seems almost as proper to proceed to determine 
the compression of the earth from astronomical and pendulum observa- 
_ tions, as to rely upon the value of it derived by direct measurements on 
the surface of the earth. But every year increases the geodetic data at 
disposal. I mention this fact here, not only as a guide in the future 
consideration of the subject, but to emphasize the fact that in the recent 
completion of the geodetic survey of South Africa a notable contribu- 
tion has been made towards the solution of our great problem. 
Of the data above enumerated, which are requisite for computing the 
theoretical values of precession and nutation, most of them are capable 
of determination by direct observation within all necessary limits of 
accuracy, and these need not be further referred to ; nor, for a moment, 
shall we consider the necessity for accurate knowledge of the masses of 
the planets, and the effect of their attraction, although the mass of 
Venus enters with a sensible factor in the expression for the luni-solar 
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