Local Attraction. 
147 
1862.] 
or astronomical amplitudes* were, the one 5".23G less and the other 
3".791 greater than the calculated or geodetic amplitudes, the cur¬ 
vature of the Indian Arc being taken the same as that of the mean 
figure of the earth. This discrepancy was supposed to arise from 
local attraction,f deranging the position of the vertical determined 
by the plumb-line. This was a highly probable conjecture: but it 
required demonstration. The problem, then, which I set myself to 
solve was, To calculate by some direct method the actual amount 
of the attraction of the Himalayan mass, and of the deflection 
caused by it in the plumb-line. The result is shown in the First 
Paper of the series, Phil. Trans. 3854, p k 85, art. 43, (see also 
Phil. Trans, for 1858, p. 769, art. 22 of the Seoond Paper). The 
result therein obtained is very much larger than was expected 
or was required to explain the differences in the astronomical and 
geodetic amplitudes which Colonel Everest had detected. This 
calculation seemed, therefore, to increase the difficulty which it 
was intended to remove; as, in the course of the investigation, this 
new fact came out, that the disturbing effect of the Himalayas is far 
greater in amount than any one had ever anticipated, and also of 
far more extensive influence, as its amount in the centre of India is 
found to be greater than it was supposed to be even at Kaliana only 
sixty miles from the hills. 
To meet this new difficulty, Mr. Airy, the Astronomer Koyal, sug¬ 
gested that there is probably a deficiency of matter immediately 
beneath the mountains, such as to counteract their effect upon stations 
in the plains. He assigns his reasons in a paper published in the 
same volume of the Philosophical Transactions and which I have 
introduced in this series for convenience of reference, (pp. 101—104) 
Objections to this hypothesis are given in the postscript to a paper 
I wrote on the English Arc in the volume for 1855, and which is 
also introduced on account of that postscript, (see p. 51). 
* For the benefit of non-Scientific readers I will mention that the ampliUide of 
an arc of meridian is the difference of latitude of its extremities. 
t If the earth were a, perfect spheroid and its materials as we descend down¬ 
wards were arranged in concentric spheroids, such as the mass would assume if 
it were fluid, then the total attraction of the earth’s mass at any point of its 
surface would be perpendicular to the surface and the plumb-line would bang 
in that perpendicular. But if there were any superficial masses, such as moun¬ 
tains, or hollows, such as oceans, or any defect or excess of density in any parts 
of the earth’s crust, a corresponding change would take place in the total 
amount and direction of the attraction. The resultant effect of these new and 
disturbing causes at any place is called the local attraction at that place. 
