88 
ARCHDEACON PRATT ON THE ATTRACTION OF THE 
of these two regions is found by the following formula of spherical trigonometry ; — 
Area of portion of a lune 
9r(3/'^ * 
= Y^(sin sinaj, 
the portion being bounded by arcs of great circles at distances and from A, /3 
the angle of the lune expressed in degrees, and r being the radius of the earth. The 
values of and for the several limes are obtained from arts. 40. and 25. The 
results are, that the superficial extents of the Known and Doubtful Regions equal re- 
spectively 0-1679616r^ and 0 /555430 square miles, r=4000 ; and therefore putting 
the density = half that of the earth’s mean density, and the respective heights =4158 
feet or 0*7761 mile, and 5730 feet or 1*0852 mile, we have the following results: — 
mass on Known Region 3 0’1679616 x 0*7761 
mass of the earth Stt r 
= 0*000003890 
mass on Doubtful Region 3 0*7555430 x 1*0852 
mass of the earth Stt r 
= 0*000024367. 
Hence, also. 
mass on Doubtful Region 
mass on Known Region 
6*264, 
or the mass on the Doubtful Region is greater than that on the Known Region in a 
ratio higher than 25 : 4. 
Also 
mass on whole Enclosed Space 
mass of the earth 
0*000028257. 
49. By means of this last result we can determine at what distances from A, B, 
and C, the whole attracting mass must be imagined concentrated in a point, so as to 
produce the deflections at those three stations found in art. 43. If, instead of mul- 
tiplying the totals in art. 42. by l"*]392, we multiply them by 0*000005523 g (see 
art. 21.), we shall have the attractions in terms of gravity. Hence 
attraction at A in meridian =24*452 X 0*000005523g ; 
attraction at A in prime vertical = 15*078 X 0*000005523 g ; 
total attraction on A ... =28*72 X 0*000005523g 
=0*00015862g. 
In the same way I find 
Total attraction on B ... =0*00006245 g. 
Total attraction on C ... =0*0000360 g. 
Hence 
distance from A of point of concentration 
radius of earth 
attracting mass 1 
mass of earth ^0*00015862 
0*000028257 
0*00015862 ~ 
distance from A of point of concentration =1688 miles. 
