HIMALAYAS ON THE PLUMB-LINE IN INDIA. 
55 
shows that in passing from north to south there are twenty-five elevations of one 
station above the level of the preceding one, amounting in all to 3901’1 feet; and 
twenty-three depressions, amounting to 2965*2 feet (see pp. 269-273). The difference 
between these =935*9 feet, which is the height assigned toKalianpur above Kaliana. 
I will take these, then, as the values of in my present example; so that 
the sum of the positive quantities among feet, and the sum of the 
negative =2965*2, and w=48. Now is the greatest and is the least of the 
quantities Hence it follows, that 
is less than 390riv„— 2*965 .2i/o, 
and therefore, much more, less than 3901*1{'„ feet. 
Now by the Survey t'o=5''*236, or in arcs =0*000025 ; 
.*. Ao<'o+^i‘'i+ 3901*1 X 0*000025 or 0*097527 foot. 
If in this extreme case of supposing the attraction to equal its greatest value at more 
than half of the stations, and that at stations where its effect would be greatest, 
the result is so insignificant, what must it be in the actual case*? The same may 
be shown with respect to the other term in the expression for the shortening of 
the arc, viz. ...vl). This quantity is less than -y" a-vl; or, if we reckon 
the distance between Kaliana and Kalianpur to be 370 miles, and therefore 
w.tt=370X 1760x3 feet and w=48, this quantity is less than 0*008 of a foot, which 
is utterly inappreciable. Hence mountain attraction may have a sensible value at 
the stations on the arc, and yet not affect the geodetic calculations in the slightest 
appreciable degree-i-. 
7. I can see no ground, therefore, whatever for the process of dispersion which 
Colonel Everest describes at page clxx of the Introduction to his work, by which he 
distributes the error 5"*236 among the triangles. It appears to me to be unquestionable 
that the geodetic operations are in no way sensibly affected by mountain attraction, 
and therefore need no correction whatever on that account. It is the astronomical 
operation of observing the difference of latitude which requires the correction. That 
it is here that the correction must be applied appears again in attempting to deter- 
mine the azimuths of the arc at seven stations astronomically (see p. xlii). It is only 
when the plumb-line is brought into use to determine the vertical angles of stars that 
the effect of attraction becomes sensible ; and never in the geodetic calculations, 
where only horizontal angles or extremely minute vertical angles (viz. the elevations 
or depressions of are observed. 
8. The importance of accounting satisfactorily for the difference between the geodetic 
* If the triangulation be carried into elevated regions some of the values of ••• will be large; and 
therefore the conclusion in the text will not in that case stand. 
t In this paper I show that the difference caused by attraction in the latitudes of the extremities of the 
northern division of the arc, viz. Kaliana and Kalianpur, amounts to 15"’885, which is more than three times 
the angle 5"‘236. But the conclusion arrived at in art. 6. is still true. 
