169

in Mechanics atid Phyjical AJlronotny.

the cube thereof, sew of the terms will be found considerableenough to deserve notice, the only ones of any consequence tobe collected from th ence, b eing —,000046^0,76 ’ X cos./>—.*—o, 1 iB 1 x cosine p —3./3.Z —,08 B 5 x cos. 2 p —3/3.2:

—>°55^ ! X : But, from the biquadrate, we shall only have

one term (i,iB + cos./>—2/3 .z) that can produce an equation ofmore than a second, or two; though the effect of this one termwill, alone, amount to near a minute-, which is owing to thesmallness of the exponent p —2/3, consonant to what has beenbefore inculcated (at page 157). And it may be worth whileto take farther notice here, that all the terms hitherto deter-mined, except two or three, belong to one, or the other ofthe two kinds there specified.

If, now, the several quantities above brought out, be collectedinto one sum , we shall have 0,036* cof./>*-{-,0005 iB—0,76'

x cosine p—( 6 .z -s- 0,30286* -j- 1,16^ X cosine p —2,3.*_

-j-,oo72B*cof.2/3z-J-,oo7oB*cof zp —2/3 .z —0,1 iB cofp —3/?.z

>—-,o8B'cof.2/>—3/3.z-j-,oooi6B—,o55B’x^-^; of all which

terms, 0,30286* -s- i,iB + x co Lp —2/3 .z is by far the greatest,and so considerable as to produce other terms, or correcti-ons, of consequence enough to be regarded here. The newterms arising from the entering of this term into the firstpower of the series, for the value of 1 — w, will appear to be—,00326 cos.2/3*—,oo47B*cof.2/»—2/3.z-|-,oo26B*cosi/>—2/3.*(which are found as above, by making hd—3X—0,30286*,N=4X'—0,30286*, ct=p —2/3, and neglecting 1,1 B + ) :And by the entering thereof into the square of that se-ries, from the double rectangle under it and the first term,there will be had -j-,088 6* cos. 2/>—3/3.* —

,oi96'cof./»—Z^.r:-s-,036' X^^: which, together with the

quantities before found, being joined to the former value of1 — iv, we have at length

Z