NUMBERS. 
tion of the eleven periods, more or lefs accurate, accord- 
ingly as the ratios confift of Jar ‘ie or ps all numbers. 
e fhall hereafter fhew how a mean periad may be af 
tained which w il become a common denominator to - 
fent he mean motions accurately 
with the leait — number of wheels and pinions; but 
in order to arrive at ie accuracy in all the periods, the 
numbers that compofe the fractions will neceflarily be large; 
for ions is gained i in fimplicity, will, in a certain degree, be 
loft in a 
Of pieeiney AB Numbers. —We have now explained the 
fundamental rules for determining wheelwork which fhall 
correfpond to any affumed commenfurable period, the applica- 
tion of which can hardly be mifapplied in the refpective cafes 
rime or incom- 
r the ae 
approximate “fall ae olhough omen Gakuen is 
by means of two pica aam lines for bea See 
which on the com — are ma ple d B; for 
ati 
ever 7 pair of oe dinding « or fabdividi a fee linés, 
mined like the and limb of a Hadley’s fextant, will 
conttitute fo age ne more or lefs ex a as the coin- 
args are more or lefs perfe& ; and . = Siseigasie lines 
arge radius, and we upon 
ee | — all the variety a ieee ate final ae os 
will be feen at one pofition of the flider, that can ore) 
be ernels after which their aL sraaH values may be afcer: 
t cceflively into diet and 
comparing them with the ee orginal fractio 
is fhort h er, ought not to ie depended 
upon in calculations where great accuracy is required, for 
ome nearer by truth, in the fraction of a 
“9 
“ 
we can fel 
year, than ras the fec figure in decimals ; whereas, 
the value of /z beads cee generally upon the fifth a 
i n the ' on of a day or other 
fhort period, it is very ufeful as a check upon arithmetical 
en and will fometines even fu uperfede the neceflity 
of them might now proceed to determine, by a direét 
method, pee: known to er eee ticilans than artifts, a 
feries of continual fractions, which approximate to the truth 
aa nearer the higher t ey hee ie are patpegh Abe ane 
a the true ratio 7 aw ten 
od occurred to the ace of “this article, ey i in 
advantages, before he was acquainted with the application 
of the one alluded to, it may be deemed aa to fome 
readers to fee it sea ap ie in ier a pla 
Indire Method of Approx When none of the 
{mall fra@ions or ratios indicated “< the fliding rule are 
saree accurate, take one of them and increafe both 
part mmon multiplier, and then add unity > 
or Lira unity se that part, whether numerator or deno 
minator, which is too great or too {mall f 
and by tying a ale of the new enlarged fradtio on in de. 
cimals, will be acne ee palate a ee 
affumed has been too large 
fecond, and a third Paulin hee be eee oe 
and it will foon appear what number is the moft accurate 
multiplier to be adopted. The 0 
or commenfurable Bere 3 indeed inftances have occurred, 
which better beeen bean have been procured by this 
method, than ca y the more dire& fcientific me- 
thod, which will | be. aheee : exemplified 
The Sun's Wheels—As the fun is the grand luminary 
i ole 
hich, laced n, or at age near, the centre of the w 
ftem, gives light and heat to the a bods, we 
will begin wi ro r pro- 
ducing a rot bere cada to 
the revolutions of the planets in their refpective order ; the 
period of a rotation of the fun, as it refpeéts the earth, has 
been giv as we have feen above, at 25 days 
d so hours, or 25.41666 a by which, if we divide 
=A is not to be divided lower 
pical year; here 14gvs = 
x : : ' 
than 272 x i on which account an approximate fraction 
3h 3; fet, therefore, 37 on A to 100 
on B, and the neareft imal ratios conftituted by the ap- 
» parently coincident lines will be . and ma the latter of 
which, converted into a decimal, aa £37037 &e. in 
which the variation from the tr uth is, as it happens, in the 
@ more accurate ratio might feem quite 
tions of the fun 
unneceflary, for 1412 = id or rather Boil as the mo- 
cd 29 388 
27 x 
tion to be produced is quick, is reducible into ons 
: and 
4 
2 I 
<I x = 254 gh 59 315 
to exemplify our method of approximating ftill nearer to the 
a train equal to this is but 
truth, let us take the ra and multiply both its parts by 10, 
hd 3 Now as wa 
190 19 
too large for its numerator; Jet, therefore, unity be fubtraGted 
from 1go, and we fhall have i = .370370, &c. the fame 
: 10 ; ae ; 
ratio as -—; again, try 12 for a multiplier, and there will 
lel ae 12x 7 ——— XY = 04 
ZX 1I9—1 
pe ae ale 1484, cannot be turned 
ny by reafon of 227 being a prime num- 
- wo sls one of “_ gives more, and 
the other lefs than the true value, we now know, that if 11, 
ufed as a multiplier, will produce a  conmenforabl cigs it 
will be proper for our train; not, we mult take 
as the next neareft to 12, for the eroeee aialliphers accord 
ingly 
making is equal to .36842 only, the 1g is 
37004, which is extremely 
near the truth, 
into 
