i6o Mr. Ivory on a new Method of deducing 
account it is convenient to denote the coefficients by means of 
their logarithms : v^hich is done, by writing, for instance, 
num. (9.482480) for the number whose logarithm is 9-482480. 
The formulas of this orbit, expressed in the manner here pro- 
posed, are as follows, viz. 
r* = 0-976625 — num. (9‘48248o) x p -j- P* 
r'" = 0-972873 — num. (0-163532) x p + num. (0-578429) x p* 
V = 0-959610 — num. (9*847341) X p 4 - num. (o-24924l)xp^ 
We are now prepared to approximate to the value of p; for 
which purpose we must seek a first value as near the truth as 
we can. Now, in this instance, ~ positive, and very 
small : hence, we may infer that r will be less than R, but, 
approaching near to an equality with it. Let us then suppose 
r* = R^= 0*976625; and we get p = num. (9*482480) = 
0-3037 ; or p = 0*3 nearly. By substituting 0-3 for p, we get 
^ = 0’9755o8 
z= O- 876635 
V = 0-908288 
6“ = + r ® — 2 V = 0-035567 
a* = 2r* -J- = 3-704286 . . log. 0*5687044 
log. a = 0-2843522 
6* — ^ = — o'0259sa. 
The error here having the same sign as in the supposition 
f = 0 (No. 9) ; we hence learn that p is greater than 0*3. 
Suppose p = 0*4, then 
r* = 1*015136 
= 0*996083 
V = o 962188 
