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DISTANCE, SIZE, AND MASS. 21

on a smaller scale, M being the moon, G Greenwich ,and C the Cape of Good Hope ; then GCM is justsuch a triangle as we considered at page 8. Thebase-line G C is of course known; and it is very easilyseen that the angles at G and C are known fromthe observations pictured in fig. 8.* Thus M C andM G can be calculated.

Such is the general nature of the method for deter-mining the moon’s distance by observations made atdifferent stations, and either simultaneously or sonearly simultaneously that the correction for themoon’s motion in the interval can be readily made-t

* The distance from Greenwich to Cape Town is not in question,but the distance between Greenwich and the point C on the meri-dian of Greenwich ; for any effects due to the difference of longi-tude of Cape Town and Greenwich are readily taken into accountastronomically. Now the distance C G is the chord of a knownarc of a great circle of the earth, if we neglect the earth’s ellipticity,or is a known chord of the elliptic section of the earth through heraxis if we take the ellipticity into account (as we must of coursedo in exact measurement). Thus C G is known, and the angles0 G C, 0 C G, are equally known. Now the angle M G C is thesum of the angles M G H and H G C ; and of these M G H isthe moon’s observed meridian altitude at Greenwich , while H G Cis the complement of the known angle O G C. Hence M G C isknown. In like manner M'CG is known. So that we have thebase-line and the two base angles of the triangle MCG known,and therefore M C and M G can be calculated. In reality theangle M C G is about If degrees.

t If such an instrument as the equatorial were as trustworthy asa meridional instrument, it would be easy to make the observationssimultaneously, determining the polar distances of the moon atGreenwich and Cape Town respectively. But as a matter of fact,it is absolutely necessary to observe the moon when she is on the

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