NUMBERS. 
periods; which, aan we — for the prefent till more 
accurate ones are dedu 
D. H. M. 
“ Of Vefta 1335 oO 23 
Juno 1sgo 17 35 
Ceres 1681 6 15 
Pallas 1681 10 26 
The Sun.—The period of the fun’s oo as it r 
ntly by different 
h gm, and 
read at the public fitting of the French National Inftitute, 
in which the fpot is ftated to have returned to the fame fitua- 
tion relatively to the earth in 274 7" 37™ 285; from which 
s deduced the period 254 104, for the exa& time of a 
8 
& 
quantity not the ae 8 apparent motion in the ol tic, cor- 
refponding to 274 78 37™ 28°, was afcertained from the folar 
tables, which 7 be called ¢; then as 360° + @: 27% 7% 
4d yoh om, for the exact time of a rota- 
as fnfficiently — tll 
which we * will confi der 
M nae to enter 
e fubjeét here, oe ided the years ie {tated had been 
opi years of 3654.24222, inftead of civil gi of 365% 
ach; but as the tropical or folar year is taken in our cal- 
ein of placa numbers, as the ftandard b oie h the 
periods of the planets are meafured, it is ae to eta 
the lunar numbers into terms o mination. 
duc ae ee ToP 4™ 45s 
which periods, lunar wheel muft be calculated, in ores 
the moon’s motions may be referred to the vrei 
re now 
with great accuracy, agreeably to the fubjoined table, 
Sat. D. H. M. 
I. 1 18 28 36 
2. 3 13 17 54 
3: 7 3 59 36 
4. 16 18 5 
We omit giving, in this place, the periods ef the other 
fecondaries, which wi ill be given in their places; becaufe 
their motions afford no phenomena of fervice in navigation 
periods of the planets, as ced a wheelwork already 
conftruted, and which a able the reader to appreciate 
Vou. XXV. 
the caine of any numbers adopted by the mathematical 
inftrument m 
T hich have occurred, in our examination of 
different eet may be cl alled into feven, according 
to the fubjoined arrangement, viz. 
. When a fimple motion is nodiee by means of one 
wheel and a ecerelpoadine pin 
2. When a fimple motion is produ by a train of wheels 
and pinions. 
. When a fimple motion is ‘aimee by the agency of a 
4. 
action of wheels and pinions, and part 
or box, which fupports fome portion of the mechanifm. 
5- When an apparent bahar motion is caufed by the 
difference = two comparative m 
nan staat retrograde motion is caufed by the 
di ifference = two c aise arativ 
. And laftly, when by means cae two equal, contrary, 
or counterating aa the parallelifm of a wheel’s axis 
is preferved, as a regards a given original pofitio 
e we treat thefe feven cafes Gece. let it be 
premifed, that the wheel or pinion, which aCtuates or drives 
its fellow, will be invariably called the driver, and the other 
The different methods of com- 
Cafe. 1.-—Whe fope a mo tion is produced by mean 
of one wheel and a corre{ponding pinion, let the number of 
teeth, which each contains, be carefully counted and noted 
0 is driver > t en, what- 
cording as the driver is the 
which driver mutt be, in all inftances, the denominator. 
value of the fraction thus conftituted, it will be fuperfluous 
to {cientific readers to fay, is found by multiplying the af- 
fumed time of a revolution of the firft mover by the nume- 
ren 
of tim 
after every fuccefsful — ample will render this 
fimple ae rape aay 
that a wheel, confilting off : 5 teeth, and revolving 
rive a pinion of 6; and that it be 
requi n what tim ate pees sales the work 
at fall or will ftand thus : 
D. He M. S&S 
365.24222 = 365 5 48 48 
6 
75)2191.45333(29 Days. 
150 
691 
675 
16.45333 
24, 
6581333 
she suka 
Carry over 75)394. S7999(g 3 5 Hours. 
