70 
ARCHDEACON PRATT ON THE ATTRACTION OF THE 
a , 7 
68°-94, (p,y=l0°-33 i 
<p=\og~^ 
fl 1-0379639 ~ 
9-7799655 
< 20-8179294 !> 
19-8041256 
. 1-0138038^ 
10°-33. 
«,, = 79°-27, <p48=14°-03; 
^=log ' 
f 11-0379639' 
9-8348646 
<( 20-8728285 > 
19-7263656 | 
. 1-1464629J =14°-0I. 
^49 
= 93°-30, <p49=23°-38; <p = \og- 
11-0379639 
9-8995636 
20-9375275 
19-5685648 
L 1-3689627 
= 23°-38. 
a 5 g= 116 °- 68 , and reaches beyond the antipodes. For let us find a, supposing 
that just reaches to the antipodes; then a4-(p=180°, ^a-\-^p = 90°—^p, and equa- 
1 
, cos -a 
4 4- 
tion (3.) gives <p = ^ — p’ 
sin^ - 0 
4 
an equation which is satisfied by p — 82° 30', and therefore the corresponding value 
of cc would be 180°— 82° 30' = 97° 30'. But this is less than as above determined. 
Hence will reach, as I have said, beyond the antipodes. The reason why the 
compartments increase in length with such excessive rapidity when they are more 
than 90° from A, is, not only the increasing distance of the attracting mass, but their 
convergfency towards the antipodes and the consequent contraction of their width, 
^and also the great angle at which the attraction acts with the tangent at A, and the 
consequent smallness of its resolved part along that line. 
28. The following list of values, then, of a and p will form the continuation of 
those in Art. 25 ; — 
Distance from A of the 
nearer ends of the 
compartments. 
Lengths of the compartments. 
Distance from A of 
the middle points of 
the compartments. 
43. 
/ 
4°3-l7 
4*980 
45*66 
44. 
a ,^=: 48*15 
0^= 5*783 
51*04 
45. 
53*93 
< p ^— 6*800 
57*33 
46. 
60*73 
^46= 8-210 
64*83 
47. 
aj7= 68*94 
,p.^= 10*330 
74*10 
48. 
^ 48 = 79-27 
^>48^14*030 
86*28 
49. 
50. 
a49= 93*30 
116*68 
^^g=23*380 
is imperfect. 
104*99 
