358 Mr. Woolhouse on the Deposit of Submarine Cables, 
Also, if for brevity 
pee Sora, ee — pit dere 
the values of these integrals may be deduced from the forrnulee 
(0) =2{ Vq+1—¥q}, 
(1) =3{Yg+1—g(0)}, 
(2)=3{Vqg+1—29(1)} 
(3)=7{ Vq+1—89(2)}, 
&e. &e. 
Hence the coefficients of Q, A;, Aj, &c. in the value of AS 
0 
may be found with the use of a Table of square roots. Those 
of the first two will be sufficient for our present purpose, pro- 
vided that A, be diminished in each case by one-sixth of the 
mean value of A,; and the values up to g=30 are exhibited in 
the following Table :— 
Coefficients for integrating QZ. 
vq 
Coeff. of | Coeff. of Coeff. of- | Coeff. of 
Q | Ay—3(4a)- 4] & Q. A, —4(42). 
200000 | 06667 || 16 | 024621 | 01225 
0:82843 | 03905 || 17. | 023907 | 01190 
0:63567 | 03071 18 | 023952 | 0-1157 
053590 | 0-2615 19 | 0-22647 | 0-1128 
047214 | 02317 || 20 | 022088 | 0-1100 
0-42684 | 0-2102 || 21 | 021568 | 0-1074 
039252 | 01937 || 22 | 021083 | 0-1050 
036535 | 01806 || 23 | 0:20630 | 0-1028 
034315 | 01699 || 24 | 020204 | 0-1007 
032456 | 01609 || 25 | 0-19804 | 0-0987 
10 | 030869 | 01531 || 26 | 0-19427 | 0-0968 
11 | 0-29495 | 01464 || 27 | 019070 | 00951 
12 | 028290 | 01405 || 28 | 018732 | 0-0934 
13 | 027221 | 01353 || 29 | 018412 | 0-0918 
14 | 026265 | 0-1306 || 30 | 0-18108 | 0:0903 
15 | 0:25403 | 01263 
COND oP DO =— oO 
The value of the integral might be otherwise found by putting 
it under the form 2/Qav h), and considering “/ as the auxi- 
liary variable. 
If we examine the foregoing equations, it will appear that 
the longitudinal friction which introduces the terms containing ~ 
