NUMBERS. 
ef 2 fcrew, is, therefore, fimilar to that of a pinion,—by 
ee 1, if there be only one wheel, but by Cafe 2, if there 
a trai 
The lunar train of Mr. Fergufon’s orrery, which we halt 
have occafion to examine under our article ORRERY, affords 
drivers may be either wheels, pinions, or 
provided they are put down as the nencnanien of their 
{pective fractions 
afe 4 he na compound motion is effected partly by 
the aoae of wheels and pinions, and partly by a moveable 
bar, which fupports fome portion of the mechanifm, the 
effet is not fo eafily computed as in the foregoing ae ; 
for befides the nen Pea produced by a train of w 
work, according to Cafe 2, it will be neceflary to sad or 
fubtra& an additional calculation, according as a wheels 
on the moveable bar are circumftanced with refpe&t to thofe 
which are not carried thereby ; a e inftances will cnet 
a 
this cafe. 
In Mr. Fergufon’s orrery, the train of wheels which 
produce a revolution of Venus, is “3 x 2 3 = = 2248 
20" 47™ 35, according to the rules laid down in Cafe 2, and 
Mercury’s revolution is occafioned by a of this train placed ° 
m of Venus, or is equal to 1.555 revolutions in 
one of Venue ; ; but - arm of Venus — ercury's laft 
wheel once round in the fame time, by means of “ con- 
nedlion with its teeth, as may be feen in the pene 8 ‘¢ Se- 
Je&t Mechanical Exercifes,” page 83—85 ; confequently 
244.86606 
I+ 1655555 
exad length of a revolution of Mercury, as produced by the 
joint aout! of the wheelwork and moveable arm. 
, which is equal to 87% 23" 47™ 245, is the 
the motion of the arm which {upports it 
be out of the queftion ; but if we confider that the arm 
and wheel B both revolve in the fame dire@tion, from e 
to welt, it is equally evident that this wheel will revolve 
twice in being carried round the wheel et even pape = 
wheel were at reft ; hat 100 + 2 » 1s 
number of revolutions that the wheel B ae whilf oc 
arm revolves o 
If, however we fuppofe the faid wheel A ; aparaee 
from eaft to welt, inftead of from weft to eat, eel 
B will in ‘this pred aeie ag in a di ore contra 
w it is peony revo- 
need from w » will m wo Pom walt to 
that 100 — 2 be <n number of revolutions 
effefted under theft fe In the former inftance 
the value will be — x — oe ae 4° ofa year, and in the latter 
50 ~ 40} 20 
= ee ae of the fame. 
50 
Let us again fuppofe B to be 16, and A as before 40, 
then one inftance will give . x = 4+ oe 1274, and the 
40 
16 
other — x Oe voges 1222, 
50 16 
From thefe examples the reader will be able, it is pre- 
fumed, to compute the effect of any wheelwork that ma 
fall under this cafe ; but it mutt be iaamare that in every 
elround acentral 
one, the central, even though the driving oe Aa uft be made 
the numerator of the additive or 1ubtractive dattion n, which 
is annexed to the calculation depend train, as 
y this cafe, the diurnal motion of fome of the modern 
urians. 
@ 5. n an a sa progreffive motion is caufed 
by a difference of two comparative motions, as is that ef 
the moon’s apogeal point, esos with the {mall piling 
ecliptic plate in Mr. Fergufon’s inftruments, called the ¢* Cal- 
culator »’ and the * Mechanical Paradox,’ fubtra@ the 
number of the fmaller of the two wheels from that of 
ag greater, and fee how often the difference is contained 
the greater: this nia will exprefs the sea 
* revolutions of the wheel during which o 
po progreffive ei ie will be gained by the 
‘oa 
Let us firft take oe the numbers of the calculator, for 
an example; their difference is 7, and aaa is oan to 8$ 
oie, on etrograde a 
pace ‘of ae teeth in the jane time; the {mall ecliptic iad 
alfo revolves in a retrograde dire@tion once in a year ; confe. 
quently, as the dg eeoageres of Hag ve wheel is finwer 
than that of the ecliptic plate, it appears to an obferver to 
advance Progreff my the fpace of feven fix ty-fecon nd parts of 
a circle in every y and by this apparent m pute eas 
the mean motion of ae oon’s apogee in the e 
As afecond example, let the numbers of Ae ene 
44 
cal paradox be taken, which are 30° here the difference is 
5, and 44 or 84, is equal to aperiod of 8 tropical years and 
292.1936 days. 
When a train of wheels and sone is employed to pro- 
duce the progrefve motion of the apogeal point, as is done 
in the common lunarium, it mutt frit be reduced into a fimple 
fraction by Cafe 2, and then eftimated by this cafe as though 
one ard of large wheels conftituted the fra@tion 
-—When an apparent retrograde motion is caufed 
by ie difference of two comparative motions, as in the cafe 
of the moon’s nodes, compared with the little ecliptic plate in 
the lunarium, and fome of the larger orreries, fubtra@, as 
n the laft cafe, the Geasiley of the two wheels from the larger, 
ae fee how often the difference is contained in the /maller s 
