or THE PLHI\IB-LINE IN INDIA. 
777 
and deflection, when the heights are known—this has been done in the Paper of 1855 ; 
secondly, to point out, from such trustworthy data as I could procure, that the amount 
of deflection is so great as to render it absolutely necessary to allow for it in finding the 
astronomical amplitude for geodetic operations; and, lastly, to suggest that such surveys 
and calculations should be made as to make it possible to determine the amount with a 
sufficient degree of precision. 
The only calculation I propose now to make, is to show that the deflection caused by 
this Table-land alow, as laid doum by Major Steachey, produces an error double the 
error brought to light by the Siuwey, in which mountain attraction is neglected and the 
eUipticity of the Indian arc is assumed to be the mean ellipticity of the whole earth. 
Much greater, then, will be the discrepancy, as I might easily show were it worth while, 
when the attraction of all the slopes — especially the parts nearest to A— is added. 
5. Through A I have drawn a straight line AD, and have marked otf certain divisions 
which indicate the Law of Dissection according to which the attracting mass is to be 
dn-ided. ^ From A several fainter lines are drawn dividing the attracting mass into lunes 
of 30^ width: the dark lines bisect these lunes, one of them being in the meridian of A. 
Now if through the points of dmsion of AD circles be drawn about A, they and the 
lunes will dnide the smLace into a number of four-sided compartments, like EF and c/: 
and the law of this dissection is so chosen, that if the height of the attracting matter on 
EF and < 9 / were the same, the attraction of these two partial masses on A along the dark 
mid-line of the lime would be the same : this may also be expressed by saying, that the 
attraction of the mass on any compartment thus formed is proportional to the height of 
that mass. In a former Paper the following formula has been proved: — 
Meridian deflection of plumb-line at A, caused by the attraction of a mass of height h 
miles standing on any compartment, 
Ji sin 15 X 1 139 cos azimuth of mid-line of the lune. 
6. I propose now to apply this formula to find the deflections caused at the three 
stations by the attraction of the Table-land alone. The height of the Table-land above 
Kahana I will take to be 2| miles; that is, about 14,000 feet, or 15,000 feet above the 
sea. Then the above coefficient becomes 2|x ’2588 x l"T39 = 0"-786 ; and 
Merid. Deflection=0"'786 cos azimuth. 
The calculation is rendered easy by the heights of all the compartments being the 
same , and the only difficulty is in finding how many compartments in each lune lie on 
the Table-land. This is done in the following manner : — A strip of paper is laid on the 
diagram along AD, and the divisions of AD marked upon it. This scale is then laid 
along the mid-line of each lune, and the number of divisions (and therefore the number 
of the compartments) which fall on the Table-land in that lune easily read off. In some 
instances the Table-land only partially fills a compartment ; in that case compensation is 
made by diminishing the number of the compartments, in the ratio of the deficiency to 
the whole space of the compartment. This is indicated in the following Table by an 
MDCCCLIX. 5 
