178 

 it reduces itself without sensible error to 



-j cos 1-5 



where M is the attracting mass, a the chord joining its base with A, 

 and 9 the angle subtended by this chord at the earth's centre. 



In applying this expression to the problem in hand, the author 

 divides the earth's surface into lines, by vertical planes passing 

 through at equal angular distances. These lines are further sub- 

 divided by small circles having A for their common pole, and in this 

 manner cutting the whole surface into curvilinear quadrilaterals. He 

 then investigates what the law of dissection must be, that is, accord- 

 ing to what law the radii of the small circles must be taken to in- 

 crease, in order that the horizontal attraction of the portion of the 

 crust standing on one of the quadrilaterals may be equal to the pro- 

 duct of its average height and density by a constant quantity, inde- 

 pendent of the distance of the quadrilateral from A. If a and a + <p 

 be the angular radii of two consecutive small circles, there results 



. ^~ l \^ ==Si constant quantity =e. 



To fix the value of this constant, the author assumes <p= a when 



4 

 and a are indefinitely small, which gives c=^r. The above 



equation may then be solved numerically with sufficient approxima- 

 tion. In this manner a table is calculated of the radii of the suc- 

 cessive small circles. 



These distances should be laid down, and the circles drawn, on a 

 map or globe, as well as the lines dividing the surface into lines. 

 Nothing then remains to be done but to ascertain the average heights 

 of the masses standing on the compartments thus drawn. 



The author's paper was accompanied by a plate representing an 

 outline of the continent of Asia. On this was laid down a polygonal 

 figure DEFGHIJKL, (which for convenience the author calls the 

 " enclosed space,") marking the boundary of an irregular mass, 

 which is the only part of the earth's surface that appears to have a 

 sensible effect on the plumb-line in India. The boundary of this 

 space is thus defined : 



DEF is the Himalaya range, having a bend at E from north-west 



