MECHANICS. 
m 
and, laftly, fet Bp from M to E. Through the points 
r, t, v, E, draw the indefinite lines DN, DO, D P, D Q, 
and make DN equal to Dc; DO equal to D b\ DP equal 
to Da ; and DQ equal to D C. Then, through the points 
Q, P, O, N, B, draw the fpiral B, N, O, P, Q, which will 
be the proper form for the wing of the wheel when it 
moves in the dircftion EMB. 
That the fpiral BNO will raife the lever AC with an 
uniform motion, by acting upon its extremity c, will ap¬ 
pear from the flighted: attention to the conftruftion of the 
figure. It is evident, that, when the point q arrives at B, 
the point r will be in rh, becaufe Bra is equal to qr ; and 
the point N will be at c, becaufe DN is equal to Dc; the 
extremity of the lever, therefore, will be found in the 
point c, having moved through Be. In like manner, when 
the point s has arrived at B, the point t will be at n, and 
the point O in b, where the extremity of the lever will 
now be found ; and fo on with the re lb, til! the point M 
has arrived at B. The point E will then be in p, and the 
point Q in C ; fo that the lever will now have the pofition 
AC, having moved through the equal heights Be, c b, 
ba, ac, in the fame time that the power has moved through 
the equal fpaces q B, sq, us, M«. The lever, therefore, 
ljas been railed uniformly, the ratio between the velocity 
of the power and that of the weight remaining always 
the fame. 
If the wheel D turn in a contrary direction, according 
to the letters M II B, we mult divide the femicircle B H, 
EM, into as many equal parts as the chord cB, viz. in 
the points e, g, k. Then, having fet the arch Bra from 
e to d, the arch Bn from g to f, and the reft in a fimilar 
manner, draw through the points d,f, h, E, the indefinite 
lines DR, DS, DT, DQ: make DR equal to Dc; D S 
equal to D b ; DT equal to D a ; and D Q equal to D C ; 
and through the points B, R, S, T, Q, deferibe the fpiral 
B RSTQ, which will be the proper form for the wing, 
when the wheel turns in the direction MEB. For, when 
the point e arrives at B, the point d will be in m, and R 
in c, where the extremity of the lever will now be found, 
having moved through Be in the fame time that the 
power, or wheel, has moved through the divifion eB. In 
the fame manner it ni 3 y be fhown, that the lever wiil rife 
through the equal heights cb, ba, a C, in the fame time 
that the power moves through the correfpondiug fpaces 
eg, gi, i M. The motion of the lever, therefore, and 
alio that of the power, are always uniform. Of all the 
pofitions that can be given to the point B, the molt dis¬ 
advantageous are thole which are neareft the points F H; 
and the molt advantageous pofition is when the chord Be 
is vertical, and paffes, when prolonged, through D, the 
centre of the circle. In this particular cafe the two curves 
have equal bales, though they differ a little in point of 
curvature. The farther that the centre A is diftant, the 
nearer do thef'e curves refemble each other; and, if it were 
infinitely diftant, they would be exactly fimilar, and would 
be the fpirals of Archimedes, as the extremity would in 
this cafe rife perpendicularly. 
It will be eafiiy perceived that 4., 6, or 8, wings may he 
placed upon the circumference of the circle, and may be 
formed by dividing into the fame number of equal, parts as 
the chord B C, or of the circumference, inftead of 
the femicircle B F M. 
That the wing BNO may not aft upon any part of the 
lever between A and C, the arm AC fhould be bent; and, 
that the friction may be diminiihed as much as poffible, a 
roller fhould be fixed upon its extremity C. When a roller 
is ufed, however, a curve mull: always be drawn parallel to 
the fpiral defcribed according to the preceding method, the 
diltance between it and the fpiral being every-where equal 
to the radius of tile roller. 
If it fnould be required to raife the lever with an acce¬ 
lerated or retarded motion, we have only to divide the 
chord BC according to the degree of retardation or acce¬ 
leration required, and the circle into the fame number of 
equal parts as before. 
As it is frequently more convenient to raife or deprefs' 
weights by the extremity of a conftant radius, f.urnifhed 
with a roller, inftead of wings fixed upon the periphery 
of a wheel; we (hall now proceed to determine the curve 
which mult be given to the arm of the lever which is to be 
raifed or depreifed, in order that this elevation or depref- 
fion may be effected with an uniform motion.—Let A B, 
fig. 107. be a lever, which it is required to raife uniformly 
through the arch B C into the pofition A C, by mead's of 
the arm or conftant radius D E, moving upon D as a cen¬ 
tre, in tire fame time that the extremity E defcribes the 
arch E e F. From the point C draw C H at right angles 
to AB, and divide it into any number of equal parts, lup- 
pofe three, in the points 1, 2 ; and through the points 1,2, 
draw 1 a, a b, parallel to the horizontal line A B, cutting.- 
the arch CB in the points a, b, through which draw a A, bA,. 
Upon D as a centre, with the diltance D E, deferibe the 
arc Eie F ; and upon A as a centre, with the di fiance A D. 
deicribe the arc cOD, cutting the arc EfeF in the point e. 
Divide the arcs Eie and Fsc, each into the fame number 
of equal parts as the perpendicular cH, in the points k, i,s, w; 
and through thefe points, about the centre A, deferibe 
the arcs k z, ig, qr,m n. Take zx, and fet it from k to ij 
and take gf, and fet it from i to h. Take rq aifo, anjd 
fet it from s to t ; and fet r m from 0 to p, and dc from e 
to O. Then through the points E, l, h, O, and O, t, p, F, 
draw the two curves E//1O and O tp F, which will be 
the proper form that mult be given to the arm of the lever. 
If the handle DE moves from E towards F, the curve EO 
mull be ufed ; but, if in the contrary direftion, we mult 
employ the curve OF. It is evident, that, when the ex¬ 
tremity E of the handle DE has run through the arc Ek, 
or rather E l. the point l w ill be in k, and the point z in x, 
becaufe x z is equal to k l, and the lever will have the po¬ 
fition A b. For the faine reafon, when the extremity E of 
the handle has arrived at i, the point h will be in i y and 
the point g in f, and the lever will be railed to the poli- 
tion A a. Thus it appears, that the motion of the power 
and the weight are always proportional. When a roller 
is fixed at E, a curve parallel to E O or OF mult be 
drawn as formerly. Appendix to Fergvfon's Ldlurcs. 
Of the Nature and Advantages of Fly Wheels. 
A fly is a heavy wheel or cylinder, which moves ra¬ 
pidly upon its axis, and is applied to machines for the 
purpofe of rendering uniform a defultory or reciprocating 
motion, arifing either from the nature of the machinery, 
from an inequality in the refiftance to be overcome, or 
from an irregular application of the impelling power. 
When the firlt mover is inanimate, as wind, water, or 
fleam, an inequality of force obvioufly arifes from a va¬ 
riation in the velocity of the wind, from an increafe or 
decreafe of water occafioned by fudden rains, or from art 
augmentation or diminution of the fleam in the boiler, 
pioduced by a variation in the heat of the furnace 5 and 
accordingly various methods have been adopted for regu¬ 
lating the aftion of thefe variable powers. The fame in¬ 
equality of force obtains when machines are moved by 
hories or men. Every animal exerts its greateft ftrength 
when firlt fet to work. After pulling for fiome time, its 
ftrength will be impaired; and, when the refiftance is great, 
it wifi take frequent though fhort relaxations, and then 
commence its labour with renovated yigour. Thefe in¬ 
tervals of reft and vigorous exertion mult always produce 
a variation in the velocity of the machine, which ought 
particularly to he avoided, as being detrimental to the com¬ 
municating parts as well as the performance of the ma¬ 
chine, and injurious to the animal which is employed to 
draw it. But, if a fly, confiding either of crols bars or a 
mafly circular i>im, be connected with the machinery, alL 
thefe inconveniencies will he removed, As every fly¬ 
wheel mult revolve with great rapidity, the momentum of 
its circumference mult be very confiderable, and will con- 
fequently refill every attempt either to accelerate or retard 
its motion. When the machine therefore has been put- 
in 
