752 
AECHDEACOX PEATT OX THE DEELECTIOX 
If 2 be a symbol representing tlie sum of the quantities /i sin ^ /3 cos Az for the five 
lunes for any given value of p and 2./isin-/3cosAz=S, 
Deflection in the meridian, for these five compartments, =1"-1392 ^ S. . . (o.) 
11. We must first obtain the values of S. The width f3 of the several lunes into 
which the Enclosed Space is divided, and the azimuth of the middle lines, are as follows 
(see par. 39 of my former Paper): — for A, widths, 24°, 30 , 30 , 30 , 20 , azunuths, 2i . 
0°, 30°, 60°, 85°; for B, widths, 8°, 30°, 30°, 30°, 10°, azimuths, 19°, 0°, 30°, 60°, 80^ 
for C, widths, 30°, 30°, 20°, azimuths, 0°, 30°, 55°. Hence the values of sin ^ (3 cos Az 
for the several lunes are — 
for A, 0-1852, 0-2588, 0-2241, 0-1294, 0-0151; 
for B, 0-0660, 0-2588, 0-2241, 0-1294, 0-0151 ; 
for C, 0-2588, 0-2241, 0-0996. 
By these numbers must the heights in the Table of Heights (page / 50) be multiplied ; the> 
must then be added together from left to right, and the totals, given in the Table in 
page 763, will be the aggregates for the several distances from the station, that is, the 
\'alues of S. The grand totals at the foot of the Table, reduced to miles and multiphed 
by 1"-1392, give the total meridian deflections at the three stations caused by the 
mountain-mass as it now lies at the surface. These differ but slightly from the results 
of my last Paper, as recapitulated in par. 22 of the present communication*. 
12. The values of t have now to be determined, in order to carry out the calculation 
K 
of formula (3.). By fig. 2 we have 
= 2 « sin ^ 
= 4ft® sin® ]^6-\-d‘' — A.ad sin® ^ ^ = fZ® + 4ft® sin® ^ 1 — 
Put ^'\Xl“^sin^^= tan-^/, /i;®=d®sec®'4', 
c 2a , . 1 
These formulse give 
2a 
log^ 
\/ 1 -p log sin ^ ^ = log tan \}y 
( 3 -) 
log ^ + log cos pp log sin ^ 20 = log j (5.) 
* To test the accuracy of these results, the totals of the thirteen coluinus oi the Table in page 7o0 ha\e 
been multiplied by the thirteen constants above given, and then the three grand totals taken lor the tliree 
stations. They are found to accord exactly with the three totals of the Table in page /53. 
