NUMBERS. 
due agian and thefe will bea feries of > alternately 
above and below the value of the original true ratio, con- 
verging ee the truth in proportion generally as the 
ratios are more or lefs numerous. 
raxis is extremely eafy, and thofe readers who wifh 
for a demonftration of the theory may confult the authors to 
whom a reference has been given, who have treated the 
fubje@& mathematically. 
In the examples of the fun’s rotation, and of the primary 
planets which follow, a folar year, as before, will be taken 
as the ftandard period, with which the other periods will be 
compared, to conftitute the true ratios, by which means we 
fhall, as we proceed, contraft the two methods of approxi- 
mation. 
The Sun's Wheels.—The true ratio between a folar year 
and the walt ss of the fun on its axis, as it nee ards the 
22 
or che aa 
25.41666° 
earth, is 25.41666 : 365.24222, from which 
we have the annexed 
Procefs for the Sun’s Rotation. 
Divifors. Dividends. is Formule. Ratios 
2 
I 
I 
© 
25.41666 365. 24222 | 14 772 at 
2541666 If X O+1 1 
“11107562 
10:66666 
axmti | 29 
940896 ae - 2x1+0 2 
IX 29 + 14 43 
6598 0896 I nea cee 33 
s9874 | guo8gs Ca is 
2X 43 + 29 | 115 
281022 | 6598 2 ies E- AD oa 2 
oa 2x3¢+2 8 
2x 115 + 43 | 273 
830 | 281022 2 af 
pes 195660 2x 8+ 3 19 
85352 | 97830 ee 
85352 I xX 19g + 27 
6 x 388 + 273 | 2601 
68 | 8 6 siesta 
aa ee 6 x 27+ 19 181 
10554 | 12468 ce z008 J 320 | 2980 
10554 1x 181 + 27 | 208 
As the laft ratio of the feries is in ae! inftance the moft 
ve a high prim of its fa@or 
ng ratio, or otherwife fubftitute another q 
in value to the one ufed in the formula, for inftance, either 
unity above it, or unity belew it, and try if the ratio fo 
procured be a practical or divifible one; but this fubftitu- 
tion muft only be made with the Jaf gerne and that when 
carried to eight fucceflive cies if, eed, the numbers 
do not run too high, nine or ten ts may be procured, 
and es many formula, but that extention will feldom be foun nd 
n the greater portion of 
the true ratio, in order that the ale of the laft figure may 
2989 
208’ 
is the fame as was obtained by our indire&t method of ap. 
49 
be involved. In the example before us, the laft ratio, 
proximation, and is capable of conftituting the train 
ze, the value of which has been fhewn to be 257 gf som 
56°.995 
The reafon why the ratio is here inverted, is, that the 
fun’s rotation is the fhorter hates and is to be confidered 
as the driven portion of the t The next preceding 
— , confifts not of practical numbers ; but a 
laft but two, proves alfo to be the fame as was procured 
2 
27 AS 
97 
ratio, the 
by the fliding rule for the train 
ae vi have been obferved, that the recurring decimal 
figures, beyond the a place, have been neglected in the 
tabular procefs, it having been confidered that the value fo 
excluded is too inconfiderable to be regarded, apienrtel 
as - laft ratio proves to be commenfurable in both i 
54 9° 
par 
Should it ever hereafter be ae, ie the fame = 
vice for eftablifhing the exiftence of fuch r 
115 
their occurrence. If, for inftance, we take the ratio 3° 
it implies, that in eight years the fun has 115 rotations ; 
for 365% x 8 are equal to 2992 days, alfo 25.416 x 11 
produce 2922.916, fo that atter a lapfe of eight ae years, 
d not amount to 
n hour, ance the cil years are made fclar ones by 
the‘ miffion of two biflextlies in the two centuries, for 
365.24222 x 208 are equal to 75970.382 days, and alfo 
89 are equal to 75970- -416, in which pe- 
48™ 
¥ 4 
7 s tropical Revolution—We have 
t ortion of velocity between che 
we fhall be enabled to determine an indefinite feries of ratios 
according to the foregoing rule, as in the annexe 
Procefs 
