NUMBERS. 
of a fimilar nature, will happen on the fame day of the 
month, and even Jour, if we take one of the moft accurate 
ratios. 
Train 
for the Earth's annual and diurnal Motions.—The 
annual and diurnal motions 
of the earth conftitute the frac- 
‘ : 24222 ; : 
tion or ratio Sei from which we thus approximate : 
1.0000 
Procefs for a folar or tropical Year. 
Divifors. | Dividends. hoa Formule. Ratios 
. 
I 
I 
° 
1.00000] 365.24222| 365 365 x 1 +0 365 
36500000 305 xO+T I 
24.222 | 100000 4 4x 365 +1 1461 
96888 4X1 +0 4 
61 + 36 2 
3111 | 24222 7 ee 
21777 et are 29 
7 IX 10592 + 1461 | 12053 
2 I ate 
444 rr I ew - 
666 | 2444 Py | momo H 10592) 46751 
1999 3 X 33 + 29 128 
444 ae Ix 46750 + 12053 58804 
444 Ix 128 + + 33 “161, 
saa |, , |? % 58804 + 46751] 163359 
“ op) 2X 161 + 128 450 
By retaining the value of the recurring decimal through- 
eut the procefs, we have obtained in this example a ratio equal 
to the truth itfelf, which is precifely i. = ne as we before 
SED 2 209 47 which in a 
afcertained, namely, x—- x 2 
9 
aes form will be better das, by inverting the fraétion 
Ke) 
ora 5 4s" 
5 or thus, — xs 
26° «94. 
pares 
- . 269 
re 47° 39 
485. 
58804 
161 
= 365% 5” 48™ 19%.192128, &c. in 
If we take the laft ratio but one, , we fhall have the 
train 2 x = x 2 
which the largeft wheel is — more praCticable, with 
refpeét to its number of teeth ; which movement proves to 
be the fame that A. Janie ee pany in his famous {phere 
lately sears Ged at Par 
A train, however flr more converient in point of fize, and 
oo more accurate than the latter, may be obtained by 
705559 
298 ” 
’ fub{tituting unity for the laft quotient 2, for the ratio 
Pig 17 
62 * 60 
has been before obferved, is 3654 5" 475.3 
Here the artift has his choice of ee "different calcula- 
which is equal to = x , the value of which, as 
227 
tions, any of which will be fufficiently accurate for any in- 
ftrument whatever. 
segs 
The laft ratio in this feries, vzz. points ovt 
what is the proper correction for our calendar, to make the 
folar and the civil years convertible into one another exactly, 
on a fuppofition that the year confilts of 365% 5" 48™ 48°, 
an or determin ation. if we di iss 
each of ¢qvo, out of every ni 
years would become coincident at the aime of each 
ninthcentury, for 7 x x 25}= 218 exadlly. oe 
ame refult will a see if we take 11™ 12>, the 
difference between a folar and civil ear, and multiply ne 
thereby, the product lo i juft feven days, which fhews that 
feven centenary lea s fhould be se ciel in sue years, 
Wheels for the roped alien of Mar reduce 
the tropical period of Mars, 686° a2" is, aa a a folar 
year into a we fhall have the ratio 989178 : 525948.8 
to approximate from, thus ; 
Procefs for the tropical Period of Mars. 
Divifors. Dividends. hae Formule. Ratios. 
fe) 
r 
I 
O 
gee gsoree.| a) «= | 
5259488 Ixo+t I 
Ixrt+y4 2 
2 88 edema ane 
wosr0gr | sasoa8® Pr) | i 
624196 | 4632292 7 (Ee Saste es . 
4390372 Cane 
2 Ig + 2 32 
241920 | 627195 @) sae 2 eee iy 
— Pr 2x 8+1 17 
p IX B2+ 15 47 
I 6 | 241920 Lo eee ue 
4335 ie ieee He 
1 xX 47 + 32 79 
S°6 I 6 1 Toe eA 
oe ones IX 25+ 17 42 
2 | 9856 | toe, | 
oe 30084 2X 42 + 25 10g 
4.x 205 +179 | 899 
808 2 age eee © eee 
ae +) gx 109 +42 | 478 
8872 | 8980 eo 
8872 1 x 478 + 109 | 587 
108 | 8872 $2 
8356 
eT If 
