of the Plumb-line in India. 23 
as we have seen, gives the attraction of the visible masses 
rather too little. 
Where the outer ranges rise from the plains more abruptly, 
and their trend is more nearly east and west, it is evident 
that the meridian deflexion at their foot will be increased. 
The numerical calculations have been tedious. I have 
happily been able to obtain the help of A. R. Hinks, Esq., 
M.A., chief assistant, and of Miss Bell of Girton College, 
computer, at the Cambridge Observatory. They have verified 
my formule and corrected the numerical results, and to them 
my best thanks are due. 
MATHEMATICAL NorEss. 
I.—Alttraction of the Mountains. 
The diagram (fig. 3) represents a section perpendicular to 
the range. It is drawn approximately on a scale of 1) of an 
inch to 5 miles. KMCEFB is the crust, out of which the 
Fig. 
to) 
oo 



mountains and their roots were formed, and is supposed to be 
25 miles thick. GHODK is the Tibetan plateau, three miles 
high and 400 miles across. DAH is the slope of the moun- 
tains, A D being 124 miles. DH is 3°3 miles)s MLEE is 
the root of the plateau. ER equals 28°71 miles. ERC is 
the root of the slope. 
We require to find the horizontal attraction at a station P 
on the surface of the crust. P may be either to the right or 
left of B. Sphericity is neglected. Then the horizontal 
attraction of the mountain and root together at P equals the 
horizontal attraction positive of the slope, plus that of the 
plateau, combined with the horizontal attraction negative 
produced by the substitution of their less dense roots for the 
more dense substratum. The crust, whether disturbed or 
not, will produce no horizontal attraction. The negative 
attraction of the root will be the same iu amount as if the 
root was composed of matter whose density was equal to 
