NUMBERS. 
TaBLeE of the Ratios of Mars. 
Procefs. Ratios. Values. 
pe maa. [Oe its = = 1.880769 
agx52 § 
arrears = as oe 1.880754 
25 X 52 1325 
47 * 54 + TY _ 7539 _ 1 880740 
25 X 54 1350 
Fortunately 249? the moft accurate of thefe three ratios, 
1325 
admits of the practical train 9 x = = 686% 225 20m 
25-53 
‘Ig; in this train the error is 2™ 415.19, or a {pace in 
the ecliptic of 33", which may be confidered nearly as ac- 
curate at a 
Mercury it will only be about an eighth part of this quantity 3 
for ve tropical Revolutions of the four little Planets 
ly ice rding to - eft information we a 
planes as they relate to the ecliptic, are thefe . tha 
of 655153 tropical years, that of June in 
4. eee. we ‘of Ceres in 4.603056, and that of Pallas in 
4.603616; but thofe of the two laft named are fo nearly 
alike, that a mean between the two may be taken at a 603386, 
‘in order to make one pair o eels, or one train, produce 
the revolutions of both plants i the aid of the fliding 
19 
‘rule'we ‘find the neareft {mall fra¢tion for Vefta to be Ps 
= 
655173 and 322 = 100 will conftitute the wheels proper 
to produce a ean in 3.65517 tropical years, o 
1335-023 : days. In like manner for Juno the {malle& fas 
135 
tion is — = .35484; and 4ii = will be proper 
wheels a a revolution to be performed in 4.35484 tropical 
years, or in 1590.56774 days. Likewife for Ceres and 
Pallas, the fra€tion = = .60 will be the neareft in fmall 
: 138 ty 
terms, and 4? = #3, or in a more practical form, will 
be wheels ae for effeéting a mean of the two revolutions, 
and two arm opening like a pair of dividers may be inferte 
on a tube Ged with wheel 138, when the 30 revolves 
in a folar nai in Which cafe each planet will make a revo- 
lution in the ecliptic in 4.60 tropical years, or in 1680.11421 
ys. 
We might approximate much nearer to the affumed pe- 
riods of thefe planets by our procefs for gaining trains, but 
until the en wef pea are more nicely determined, it 
would anfwer no ufefu 
Wheels for the ty Revie of Jupiter —We come 
3 
any of the preceding ; for during a revolution of 
next to Jupiter, which pe we have feen, runs through 
the ecliptic, according to La Lande’s tables, in 3309 14h 
403™, or in 4330.61145 days, which number divided iM 
365.242222 _ the fame equal to 11.856820tropical years; 
now if we take © for the {mall fraction, and 37% for the 
nearelt praGtical multiplier, we fall have oo a } es 
x 377 +1 
2260 
2640 
folved into 
== .856818; and 113268, or 3 ae may be re- 
ba caine which, if we take two-thirds of 
33 Xx 80 
each leading portion, and one-half of each following, in 
both the numerator and denominator, will afford us the con- 
venient train aes x ne the value of which is 43304 14 39” 
‘, during which time the error in time is onl 
1™ 25%, ora 
correfponding 
con 
{pace in the ecliptte equal to a quarter of a 
Whee ls for the tropical Revolution of Saturn.—We 
now to teers wheels proper for the panel eoladen “of 
Saturn, whi aoe ia beft tables of La Lande, is equal to 
10746% 195 ¢ 29-423777 tropical years; the feveral 
{mall ae Which the fliding rule gives, nearly inn 
3 
to the decimal portion .423777, are : = .428, &c.; x 
= .4230, &c. ; res 4242423; and = 423728: now, 
if we Ape from the firft of thefe, we fhall have the 
following ratios 
Procefs. Ratios. Values. 
3x 16 _ 48 _ 
yx 164 4 = 31g “4747 
a ee eee ee 
7X41 106 “4745 s” 
3x4 
oe eS 424242 = fs the third fra@tion. 
X1441§ 99 
2X38 7 99, 
are i} a2 423913 
3 
x 12 _ 36 > 
7 x roa ie g; “4°33 
Thefe nee are not exact enough here, and the numbers 
29‘2, which are the mo‘t accurate, have prime numbers for 
the faGtors of neue denominator, when reduced into a fim- 
11 
ple fra@ion; we mufl therefore have recourfe to rg the 
fecond {niall fra€tion for conftructing another table of ratios, 
th 
Vrosefs. Ratios. Values. 
11 X 25 
273 — 14300 
eae tal %6 4937 
11 X24 26, 
; — = 42 
26 xX 24 — i} ea 42375 
