60 
ARCHDEACON PRATT ON THE ATTRACTION OF THE 
Let ABB' and ACC' be parts of two of 
the great circles forming these lunes ; 
BCC'B' one of the four-sided compart- 
ments. Let ^ BAC=|3, .^AOB=a 5 
ZBOB' = ^; Q an element of the 
compartment ; qQq' parallel to BC ; 
i!iQAN=4'j AN being a great circle 
bisecting the angle (5, and AT a tan- 
gent to AN ; AO=r, Z AOQ—0 ; 
distance of Q from AO=r sin d ; 
and r sin 6 and rd& are the sides of 
the element Q. Let /c' be the height 
of R, the earth’s surface, above Q ; 
^ the mean density of the superficial 
matter of the earth ; 
mass of prism QR=^/{’'r^ sin ^ 
ako chord AQ=2rsin^A 
Hence by the corollary in Art. 14, 
attraction of prism QR on A along the tangent to AQ 
sin ^ dp 1 . 
=f COS 2 ^ ; 
4r^ sln^ - 6 
.-. attraction of prism QR on A along AT 
sin ^ dp 1 . , 
j COS 0 COS -p. 
4r^ sin^ - 9 
Ji 
Integrating with respect to ”4/, from ' 1 ^=—^^ to ^(3, attraction on A of the mass 
standing on q(l in direction AT 
gsin9cos-9<f9l 2 gsin9cos-9rf9 ^ 
=. — \ Ji' cos \pd\}/= j • 2 sin 2(3 . A- very nearly, 
4sin2i9 ] , 4sin2-9 
h being the average value of k' on the arc qq ' ; 
=g’sin2i3. j— cfAA:. . (1) 
sin -9 
16. The degree of error incurred in thus taking k for A:' may be judged of by apply- 
ing the formula to an extreme case. For example, let us suppose that the surface of 
