NUMBERS. 
WX 7 
mx I9—1 
ingly = 37019 gives us 14705 = 
8 
at aa » and when this is inverted, we fhall have a train of 
49 _ 61 
16 * 33 
error is little more than three feconds. If it had become 
neceflary to ufe 13 as a multiplier inftead of 11, the procefs 
been 13. X7 
13 X 19-1 
208 
— 
252 g® co™ 565.995, in which time the 
would have = = .36992 nearly ; 
ot. 
246 
2", when inverted, will afford the train 
3535 
the value of which is 254 10" o™ 4%, in which 
and 149% 
6 
— xX se 
1oIr 
_— error is belt four oo in ae oppofite extreme. 
igh nu 
of sae in m detcreing a train 
for the fun’s ibn. it will be unneceflary to be fo minute 
in eee the whole procefs in the oe which 
“The tropical period of Mercury, as we have feen 
79 235 14” 355.2, or makes 4.151967, &c. ui in 
a tropical year. Now if 152 0n A be put to 1000 on B, 
15155 
on the fliding rule, we fhall have the mann 5 
7 
—, = 1521, &c. and - aa 
6 7 
The Jat of thefe three ratios is a of fas a train 
a 2(- ax 2 -), which pro- 
duces an error of on i a” : too cae in 7 Be Ai 
But exa& as this train is, compared with the 
firuments in general, our method of eo will 
procure us a much more accurate one. Let us take the firft 
1519, as nearly as — 
equal to —~, namely, = ae mee 
ratio, 3 for this purpofe: the wheels compofed of 4,3, 
are 74 and as 33 is too large for the 5, unity muft be 
added to the 137. After both parts are multiplied an 
equal number of times, fe multiplier we find by a few 
. ; 33x 67 2241 
trials to be 67; fo that ee ee = 4.15196 
&e. gives us a very convenient train of > & 2 
9° 34 
33 x 67 
02 X go 
): the value of which i is 879 23" 14™ 355.706, 
(= 
in which the error in a whole revolution is little more than 
d. 
_ half a fecon 
ers are panciipeee 
Wheels for the shah Revolution of Venus. see pre 
pelqen of Ven s been afcertained to be 164 
90" ceeeedine to ane data, this planet will make 
es 25498, &c. revolutions in a folar year. Now the neareft 
{mall fra@tion, which correfponds to the decimal oben, 
is - = 625 exaly, and the ratio = = 1% inverted, is 
the fame ratio which was ufed for Venus in Huygens’ 
automaton, and the inftruments copied from it. But thefe 
numbers are by no means fufficiently correct for an infru- 
ment of great accuracy; they mu y be brought, 
by our approximating proce into higher numbers fuitable 
for a train. e numerator of this fra@tion being too large 
for its denominator, le us aflume ee glk a ueve dd 
add unity to the denominator; for ore acc 
{mall fration is aleady, the greater will iz mult lee ce re- 
X 312 
quired to be, and vice verfa : thus we fhall have -2— 
13X 31241 
2496 _ 
4057 
be too great, let us try 305 initead, from which we fhall 
1.6254006. Again, this multiplier proving to 
8 X 312 440 ar 
There te Sone 1.625409, &c. which is 
a Bee Bearers The former of thele periods is equal to 
h y™ o§, and the latter to 224% 165 s9™ 1015: now 
cy alee of cate two periods being about 2™, and the 
meniag e of the multipliers 7, we can 
have 
that the decreafing inter 
tion; 246, therefore, 
rom whi in a e error is much lefs, 
and of an oppofite denomination. In order 1.0w to gain a 
great variety, from o fele&t an accurate practical 
train, we will {ubjoin a table of ratios, with their values 
attached, till we arrive at the truth as nearly as may be. 
TABLE of Ratios for the Train of Venus. 
Procefs. Ratios. Values, 
8 x 246 _ 1968 | 
ia sO 15 aco 1.625508. 
8X 247° 2 _ 1976 __ 
cers 1.625506. 
8x 248 2 «+1984 
13 xX 248 + t ~ 3225 aes 
Se ee a 
gx aip dS 32387 1.625502. 
8 x 250 2000 
oo = = 1.625500. 
13 x 25071 325% 
8 x 251 _ 2008 _ 
13 X 251+ i 3264 tO2549%: 
8 x 252 2016 
= = 1.625496. 
13 X 252 + t 3297 349 
8 x 253 __ 2024 
13 X 253 + i = gago — 625494 
