1862.] Local Attraction. 147 



or astronomical amplitudes* were, the one 5".236 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^ 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 

 Papee of the series, Phil. Trans. 1854, p. 85, art. 43, (see also 

 Phil. Trans, for 1858, p. 769, art. 22 of the Second 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 Royal, sug- 

 gested that there is probably a deficiency of matter immediately 

 beneath the mountains, such as to counteract their effect tipon 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 tbe benefit of non- Scientific readers I will mention that the amplitude of 

 an arc of meridian is the difference of latitude of its extremities. 



f 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 hang, 

 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. 



