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, A_a = - \, and for i > 0
24_W = - *4_( + A4 + A4-i • • • + -4 A, or, assuming to avoid fractions,
whence if we calculate
_mi= 2m'^1,  «, = -
(1 ^1 0).
a formtila by means of which the coefficients J?,, U_2, /?_3 ... may bo
readily calculated one after another.   We get
£, = -!,       A = + !'     '5,=- 4,      #, = + 25,
5_4 = -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. •;,•! ttT^1, tir^2... in the last two of the formula! (1.13),
^ = ^•1505150; Z_4= 2-4948500; Z, = 2-:«M.I5.m ; «,= 1-6989700 ; 1_5 = 2-2371251 ; Z_B - 270 1 <>:» 1 15 _: Z_3=2-6453650; Z_e