580 
AECHDEACON PEATT ON THE INDIAN AEG OF AIEEIDIAN. 
from the arcs themselves. But, being hidden from our sight, neither the magnitude nor 
indeed the existence of this cause could be a priori ascertained, much less reduced to 
calculation. Whether, moreover, the errors brought to light by Colonel Eveeest arose, 
solely from local attraction, or from local attraction combined vrith some local peculiarity 
in the curvature of the Indian Arc, was not apparent ; so that the subject of local attrac- 
tion, and its influence on geodetic operations in this country, was still involved in obscu- 
rity, and the anomalies of the Indian Arc remained unexplained in the papers which I 
have hitherto forwarded to the Society. In the present communication I think ambi- 
guity is removed. It is demonstrated that no peculiarity in the curvature of the are 
can produce any part of the errors brought to light by Colonel Eveeest ; that those 
errors arise solely from local attraction ; that they are in fact the exact measure of the. 
difierence of the resultant local attraction at the two extremities of each arc, from what- 
ever causes the attraction may arise — mountains, ocean, or crust ; lastly, it is proved 
that there are hidden causes in the crust below the Indian Arc, and the differences of 
their resultant effect upon the stations of the arc are computed. An inference from 
these results is, that the relative position of places in a Map, laid down from geodetic 
operations, is accurate, being altogether unaffected by local attraction ; though the 
position of the Map itself on the terrestrial spheroid will be dependent upon the 
observed latitude of some one station in it, and that observed latitude will he affected 
by the local attraction at that place. To determine the absolute latitude in some one 
station connected with the geodetic operations is still a desideratum. 
§ 1. Suimnary of the Results of former Papers. 
2. The results of my former papers I may briefly sum up as follows : — 
(1) In the first of them* I calculated the effect of the Mountain-Eegion north of India 
upon the plumb-line at the three principal stations of the northern portion of the Indian 
Arc ; -viz. Kaliana (29° 30' 48"), Kalianpur (24° 7' II"), and Damargida (18° 3' 16"). The 
deflections towards the north were found to be 27"'98, 12"’05, 6"-79 ; and in consequence 
of these, the observed astronomical amplitudes would be 15"-93 and 5"'26 less than the 
true amplitudes determined by normals to the meridian line in the meridian plane. 
These quantities, as I showed f, are not materially affected by new information regard- 
ing the mountain mass communicated to me by Lieut.-Colonel Steachey. 
(2) In my second paper J I calculated the efiect on the plumb-line of a shght but 
nide-spread deviation of density in the crust of the earth, in excess or defect, from 
* PhilosopHeal Transactions, 1855 ; also 1859, p. 770. 
t Ibid. 1859, p. 774. The reader is requested to make the following corrections in that paper: — 
Fage 761, line 4, for multiply read modify. ' Fage 782, line 16 ah imo, after by insert 0T85 and by 
— 794, — 17, for 15-88 read 62-60 
~d — 795, — 4i ah imo, for 15-88 read 62-60 
— — — — for 514-57 read 561-29 
7 67, — 2 ah vmo, for — read 
r—d r 
— 781, — 26, for require read requires. 
X Philosophical Transactions, 1859, p. 745. 
