HIMALAYAS ON THE PLUMB-LINE IN INDIA. 
95 
in art. 62. establishes a relation between the two quantities on which the figure of the 
earth, supposed to be a spheroid of revolution, depends, viz. the semi-axis major and 
the ellipticity. As there are two quantities to be determined, a single arc is not 
sufficient to enable us to find them, unless the lengths and amplitudes of portions of 
the arc, as well as of the whole, are known. Bessel, in a paper which has been 
translated in vol. ii. of Taylor’s ‘ Scientific Memoirs,’ has shown from ten arcs 
measured on various parts of the earth and from portions of five of them, by an appli- 
cation of the principle of least squares, that the mean ellipticity ; and that 
the semi-axis major =3271953*854 toises, the length of the toise being to that of the 
fathom as T06576542 : 1. This result coincides almost exactly with the ellipticity 
which theory assigns, upon the supposition that the earth was once a fluid mass, its 
strata increasing in density from the surface to the centre, the density of the surface 
being that of granite, and the mean density being 5f rds that of water — a fact which 
is generally considered to be a strong argument in favour of the original fluidity of 
the earth’s mass. 
61. But by the process described above, the peculiarities of the several arcs are 
all merged in the mean result. When the calculations for the separate arcs are exa- 
mined, the values are found to vary on either side of the mean. This variety indi- 
cates that the several parts of the earth are not curved precisely according to the 
same elliptic law. Some may think that this militates against the original fluidity of 
the earth’s mass. I do not think this is a fair inference. If the earth’s surface ever 
were fluid, the science of geology shows us that it must have ceased to be so for 
many ages : and the interval affords time enough for the operation of that well-esta- 
blished law — that gradual changes of elevation and depression are unceasingly taking 
place in the surface, arising no doubt from chemical and mineralogical changes in 
the mass — to modify the original curvature of the various parts, making some greater 
and others less than before. The argument of the earth’s original fluidity lies in the 
fact, that the present mean form is that which the earth must have had when it was 
fluid, 
62. I will conclude this paper by calculating the form of the Indian arc between 
Kaliana and Damargida and its two subdivisions. The result affbrds, I think, the 
only explanation of the discordance between the difference of amplitude as brought 
out in Colonel Everest’s work, and by my calculation of the amount of deflection, 
ITe lengths of the three arcs, Kaliana — Kalianpur, Kalianpur — Damargida, and 
their sum, Kaliana — Damargida (which I shall call arcs I., II., III.), are shown by the 
Survey to be 326859*52, 367154*37, and 694013*89 fathoms. 
From these the amplitudes may be deduced by assuming a form of the meridian. 
Colonel Everest assumes 
semi -axis major =20922931*8 feet, and ellipticity = 3 ^^* 
