NUMBERS. 
negative fign is prefixed to the fractional portion, donor 
confifts of the central wheel for a numerator and the w eel 
an 
_ Alfo, 
al n 
added or fubtra&ted, accordingly as the arm and wheel b 
by it are circumftanced with refpe& to the direGtion of their 
motions. 
Cafe ed. —When an apparent progreffive motion is to be 
avr nile a the difference of two comparative motions in 
ftancé, if g% years were the period in which an index is re- 
quired to advance ie aaa ely round the little ecliptic of 
an orrery or tellurian, whilft the ecliptic itfelf is movin 
backward once ina ane to preferve its parallelifm; in the 
firit place gi, reduced into a fimple fraQion, gives 3 2, which 
would be 
ecliptic were not pla 
59 
59— 
If it iad fo happen that a pair of wheels thus lie 
fhould be too large to be conveniently conftruted, t 
be converted into a train of the fame value by the dncdion 
laid down in the fecond cafe of this hea 
— When we are to exhibit an apparent phe sd 
the proper wheels, by Cafe 1, if the 2 iaidl 
laced on a revolving arbor, but in this 
eafe 
a? oF = will be the wheels required. 
3 
& 
will be the driven wheel ; he /um of the numerator 
and denominator will be ‘the diver, fo that if 9% were the 
59 
59+6 
In this cafe alfo a train may be conftituted of 
period as before, the wheels would be equal to 
namely ¢ 39, 
two wae which are in themfelves too large for ufe. 
hen the parallelif{m of a wheel’s axis is to be 
preferved in in every part of the revolution of the arm that 
bears it, nothing more is neceffary than to make the whee 
revolve by any contrivance aah. ence in each revolution of 
the arm, but in a contrary reera as has been already ex- 
0 “the inftrument maker to 
learn how, from one or other of thefe feven cafes, any wheel 
or portion of a train, which has been miflaid or loft, may 
be replaced. 
As it is always known what period of time is intended to 
be repre by any part rticular train in every inftrument, 
refented 
the general ‘vale will be, to afcertain, firft by the proper cafe 
in our laft head, what the value is, in time, of that a 
of the train which remains, and then divide ‘the whole know 
period by this value, and the quotient will reprefent the alu 
of the pee oa to be replaced by the correfponding 
cafe in this 
For an example of this kind we may take the annual 
train of the old aftronomical clock at Hampton Conrt, in 
the calliper of which we have feen that two deficient wheels 
are reprefented by dotted circles, which are faid to have 
been fomehow fupplied by a man cf the name of Lang. 
Bradley of Fenchurch-ftreet, but in what manner 1s not re- 
Jated: in our notice of this clock we put down the whole 
train thus, = x = reece out of which we may take 
8 = 12 
. J = ne or 39.875 for the value in days of the 
entire alae ; and if the whole year 365.24222 be divided 
by 39.875, the quotient 9.15943 will exprefs the value of 
the two eens a or vane pe a which we now * 
have to afcer of t odes of 
calculation, which will be ae ee def ctibed and illuftrated, 
that the valu the decimal portion, 15943, if exprefled 
in vulgar ae will be, according to the cada: we 
1 3 
may require, fome one of thefe, viz. ra ie ne or a 
and the mixed numbers 91, 9,35 9.4, and gi4, when con- 
verted into fimple ratios, will be refpedtively 3 », a 
2, and 238 3 the molt accurate of thefe of courfe is the 
laft, but is - no means of a praétical fize; in the calliper 
it appears that the wheel is a little larger than the one 
marked 132, which circumftance points out that <4 mutt 
be the numbers to be adopted in order to fly the de- 
a aid of the train before us ole train, however, 
s by no means fo accurate as Fergufon’s, who adopted for 
this conftru€tion of a clock i e ps yas which he calcu- 
lated for his orrery: according t 2 of our ae nd 
head, the value of the a a thus fapplied, will be 
174, 29, 132 _ 666072 
8  I9 12 1824 
more exact period be required to be reprefented, either one 
of the larger pairs muft be ufed, or the whole train muft be 
reformed. 
If, however, we take 365 days for the year, which 
bably was the time intended, then we fhall have as fucceflive 
fra€tions 2 5 oe ao. and ~22 = the laft of which is the 
= 3654 4h 6™ 355.184; and ifa 
exact ie but too a for wheelwork, on which 
account, moft likely, -2 were the numbers, which makes 
the whole movement 29 x 5% x ae == 465" oh 34" ie rE 
as the period of the frf 
an inftrument, provided the wheelwork of all’ the 
an sine are proper ratios of that period: in the common 
planetarium the period affumed is one year, but if, inflead 
of this, a period which is nearly a mean between "the two 
extreme periods of ape and Geor Bian, were {ubftituted, 
then eleven pair of wheels, or wheels and pinions for the 
eleven primary planets, would be futiricct for the ah 
tion 
