OF THE PLUMB-LINE IN INDIA. 
763 
I proceed now to make use of the calculations of this Paper to show how some idea 
may be formed of the effect, which the possible and not improbable existence of exten- 
sive tracts ivithin the mass of the earth where the density is, though perhaps very 
shghtly, either greater or less than the density of those parts as required by the fluid 
theory of equilibrium. 
5 6. General cmoltmom regarding the effect of a defeat or excess of dmaity in any fart 
of the mass of the earth. 
17. It is quite possible that extensive tracts may exist in the interior of the earth's 
mass throughout which the density is somewhat less or somewhat greater than the 
ensity which the fluid theory would requiie for those parts, and upon which the theo- 
retical du-ection of gravity is determined. I can conceive of a vast tract beneath in 
which the development of local heat had by long action expanded the material of the 
mass, and compressed it in a region beyond where no sufficient heat was developed to 
counteract this effect. Suppose this took place chiefly in a direction parallel to the 
the sLe ” TT Keliaapur, is known aocnrately by 
thL r I ; ^ by ‘be fe™nla. Bnt X comes out iLer 
O’ 1 t tT w '“■“'erence ansing from mountain attraction. Now X+ dx is used in formula 
(d.) to and how much A is affected by taking the ohm-ved, and not the calculated, value of X. Hence dx 
must be negative. Let I be the number of seconds in the deflection ; then d\=-l, and 
52-3 V 30 
30o)’ 
(y-) 
TUs formula agrees with the statement of Colonel EvnarST in clarvii of the Preface of his volume of 
S47. for by putting d,_0 (as he calcidates with the mean ellipticity), and l=5»-28 the error he gives, 
“id fathoms, the error in the arc which he deduces. If then a place between Kaliana 
and KaUimpim be laid do™ on the map. tost by reckoning from Kaliana and then from Kalianpur, the two 
’’ by .Jiith of a mile. Colonel Evmnsp avoided this by dis- 
n uting the error among all the stations of the arc, and shghtly altering all the latitudes accordlnglv. 
ut the natural way of correctmg it, as it appears to me, would have been to find an ellipticity which would 
have reduced the error to aero, and to have worked with tta, and not with the mean. In doing this it 
would also be necessary, as shown in the calculations of these Papers, to correct for mountain attraction. 
oart of re s'''’ of formula (y.), and to show the influence of errors on the mapping 
part of the Survey, suppose that the dedections, after all. owing to the compensating cause, make 1 Ly 
0«-523. and that the curvature of the arc is measured by the ellipticity jL (which is not impossible), then 
Kio~lob’ 'fA = l'l-0-01-0'825=0'26, and the error in the places would bo more than a quarter 
of a mile, and in the opposite direction. 
he r 0“"00t. as is evident from 
akel 7f of diatorbance near Kalianpur or Damargida, or both, are not 
5 H 2 
