356 Mr. Woolhouse on the Deposit of Submarine Cables. 
log c,=7'87966. 
é. r. pe loge. | loge. | logey. | loges. | log cg. 
° 4 oO é | 
0 | 90 0:0} 0 0:0] 0-:00000| 0.00000; —« | 0-00000} 8-18069 
1 | 51 49-6) 31 43:0 | 9°65052 | 9°37304 | 8-91908 | 9°68652 | 8:56267 
2 | 28 1:3) 41 26:2) 9-:09355 | 8-79424 | 8-16171 | 9-39712 | 8-80811 
3 | 18 55:2) 43 24:6) 8-74406 | 8-44348 | 7°65260 | 922174 | 8-97051' 
4 | 14 15°0| 44 63) 8-49464 | 819382) 7-28361 | 9:09691 | 9:09040 
5 | 11 25:0! 44 25°6| 830094 | 7:99965 | 6°99514| 5-99983 | 9-18513 
6 | 9 31-0) 44 36-1} 814263 | 7-84067 | 6°75820| 8-92034 | 9-26335 
7 | 8 31:0) 44 42-5 | 8-00875 | 7-70903| 6-56034| 8°85452 | 9°32837 
8 | 7 9:0) 44 46-6} 789278) 7:59143| 6-38534| 879572 | 9:38670 
9 | 6 215) 44 49-4| 7-79047 | 7-48928 | 6:23266| 8:74464| 9-43738 
10} 5 43-0 | 44 51-4) 7-69896 | 739670 | 6-:09583| 8-69835 | 9-48342 
For brevity put k= ie and 
Po 
dw sin w 1—2«? J—a acoswo+l1 
h= Sate Nee ad SOON Se a oa 
cosm@—e*sin?a@ Ite lt+e cosw—a 
es eo eee 
=c, log fan O—p) 
h 
0 tan (O—p) — (oe “1. . . e . . . (9) 
Then employing / as an independent auxiliary variable, we shall 
have 
1 ds_p.dw_p cosw—esin®w Ta k 
fgrah- “py ho Py sin @ ~ posing” sinw’ 
Hence by assuming a uniform succession of values of / and 
calculating values of @ from (9), and thence values of w from (7) 
and k& from (8), the corresponding values of a fk dh can be 
obtained by the method of quadratures. Thus, if the values of 
k be differenced twice, and (k) denote the arithmetical mean 
aye yee! o. Hence also in this case, 
0 
2s =[P@=S do sec? a=tan @. 
Po Po 
mi = (ee cosa= {de sec o= log tan (45°+3 0). 
Po Po 
¥ =(ee@ = fideo sec wtah w= sec a—l]. 
Po Po 
