50 ON THE EFFECT OF THE INTERNAL FRICTION OF FLUIDS
and substituting in the above equation, we get
- ma - LA, (ma)'1 - 2^2 (ma)"2 - 3 A. (ma)-3 • • • . + {- 2ma + A, + A, (ma,)'1 + • • -HA + A W + • • -1 = °> which gives on equating coefficients, Aa = - \, and for i > 0
24W = - *4( + A4 + A4-i • • • + -4 A, or, assuming to avoid fractions,
whence if we calculate
MI= 2m'1, Ğ, = -
(1 1 0).
a formtila by means of which the coefficients J?,, U2, /?3 ... may bo
readily calculated one after another. We get
£, = -!, A = + !' '5,=- 4, #, = + 25,
54 = -208, j?s = + 2146, 5. = - 2G36H, (111).
J5, = + 375733, J5, = - 6092032.
We get now from (100), (101), (108), and (109)
Tv,
we shall have, changing the sign of V^l in (112), ami writin 8 for ef V=i,
• If /t, ?2... be the common logarithms of UK; rurtH. •;,•! ttT1, tir2... in the last two of the formula! (1.13),
^ = ^•1505150; Z4= 2-4948500; Z, = 2-:ĞM.I5.m ; Ğ,= 1-6989700 ; 15 = 2-2371251 ; ZB - 270 1 <>:ğ 1 15 : Z3=2-6453650; Ze