356 
Engine and how it is stopped atevery division, The chief parts 
Graduation. of which this apparatus consists, are more or less seen 
Method of im all the Figs. ; but the manner of its being supported 
graduating upon the platform of the stand by the intervening 
the limb in block I, is seen only in Fig. 2. The principal piece is 
Mr Edward a cock J, the horizontal part of which has two branches, 
fon (one shewn in the Figure, ) between which the strings 
ve dividing pass. The vertical part supports a cylinder of steel, 
which, when the screw is in action, forms a right line 
with its arbor ; but there is left between their ends a 
space of about half an inch: this affords easy means of 
p tats Poh the ratchet-wheels, which are placed upon 
the screw-arbor, and move round or stop with it. A 
barrel about 2 inches long, and 11 diameter, is fitted 
upon the cylinder, but so as to admit of its being turn- 
ed round and moved upon it with perfect freedom 
from end to end. The middle part of the barrel is 
formed into a spiral worm or screw, the groove of 
which receives a cord or cat-gut of one-tenth of an inch 
in diameter. There is a sli fit frame dove-tailed upon 
the horizontal branches of the cock, as shewn in front 
of Fig. 3. which has steady and free motion in the di- 
rection of the cylinder; to each side of this frame is 
attached a pallet, one of which enters in front, and the 
other behind into the spiral worm of the barrel, by 
which means, when the latter is turned round, rectili- 
near motion is given to the frame. The barrel to the 
right is large, and excavated, so as to admit the ratchet- 
wheel, which latter is driven by a catch and spring, 
planted in the edge of the cavity inthe former. . The end 
of the barrel to the left is embraced by a ring, which is 
capable of being turned round or set fast at pleasure. A 
stopping piece is fastened to the frame by a finger-screw, 
and by means of a slit, through which the screw passes 
from the ring of the barrel, varied through a consider- 
able extent. The elevated part of the stopping-piece 
resembles an anvil, and the hither side of the ring of 
the barrel, a hammer: the contact of these determines 
the point from which divisions begin: each division is 
terminated by similar means; an anvil is found in the 
elevated part of the frame behind, and a hammer in a 
screw-head, projecting from the enlarged end of the 
barrel: a string occupying four or five turns of the 
groove of the barrel, at one end is attached to a treadle 
near the floor, and at the other, after passing over two 
pullies, toa weight behind. When the treadle is pressed 
down withthe foot, the hammer in front leaves its 
anvil; and as the barrel is carried round, the frame is 
moved forwards by the pallets; so that in the second 
turn they pass clear of each other, and the motion is 
continued until the anvil behind is struck by the other 
hammer: during this time the catch, by the pressure 
of its spring, has hold of the perpendicular side of a 
tooth of the ratchet-wheel, carries the screw round alon 
with it, and moves also the engine plate through the 
proper angle. On the pressure of the foot being gra- 
dually withdrawn from the treadle, so as to let the 
weight prevail, the barrel will be brought round in a 
my direction ; the hammer and anvil on the far- 
ther side leave and pass each other, and then those on 
this side pass and meet as at first, ready for a second 
tread, During the time that the barrel runs backwards, 
the screw and Sener stand still ; for the sloping 
sides of the ratchet-wheel allow the catch to escape 
freely over them. As things stand in Fig. 3. a tread 
gives only two revolutions of the screw, but the num- 
ber may be varied at pleasure as far as six; for let the 
anvil in front be placed by its finger-screw so much to 
the right as will allow the hammer to escape it, the 
weight will then draw the barrel back through another 
engine. 
PLATE 
CCLXXIX. 
GRADUATION. 
revolution, and the parts will meet again. Parts ofa © 
revolution are obtained with equal ease. It was said @t@ 
before, that the ring of the barrel, to which is attached =~ 
the hammer in front, might be turned round and fixed 5.9, 
at pleasure ; now it is evident, that if the hammer were the! 
brought down so as to meet the anvil sooner, the tread Mr 
would be shortened ; and, if shifted the contrary way, Tr 
it would be lengthened. Thus, by changing the position } 
of the anvil, we can vary the number of 'T@* onoine 
volutions ; and as parts of a revolution are obtained by ~*~ 
shifting the hammer, we have the power of varying 
the angular value of a tread from six revolutions of the 
screw, down to a si tooth of the ratchet-wheel. 
The most useful number for the teeth in this wheel 
is 120, for it answers to the division of the vernier that 
gives 5” of the asual degree, or 10” in instruments of 
reflexion, as well as to many others. To divide the 
vernier of a reflecting one that shews 15”, requires a 
ratchet-wheel of 80 teeth ; and this number, were it of 
any use, which it is not, would give the usual subdi- 
vision of the 96° arc. To divide the centesimal de« 
gree of the French, and its first decimal subdivision, 
uires a wheel of 100 teeth. To the division of odd 
and prime numbers, a near approximation may be made 
by an artifice contrived by myself, and I believe un 
known to any except those who have been my assist~ 
ants: an example will be the best way of teaching it 
to those to whom it may be useful. Let the number to 
be divided be 331, and let the ratchet-wheel with 80 
teeth be chosen ; if we divide 2160, the whole number 
of turns the screw makes in one revolution of the plate, 
by 331, we shall have a quotient of 6, with a remain- 
der of 174, which latter being multiplied by 80, to 
reduce revolutions of the screw into of the 
ratchet-wheel, gives 13920, and this also being divided 
by 331, quotes 42 with a remainder of 18; that is, a 
division will be equal to 6 revolutions of the screw, 
and 42 teeth of the ratchet-wheel nearly. But as we 
cannot at one tread exceed 6 revolutions, we must be 
content with half of it = 3.21, and tread twice for one 
division ; but as in our arithmetical operation we had 
a remainder of 18 teeth, in order to make ends meet, 
these must, as we proceed, be di ed of in their pro- 
per places: now, as 18 is the 20th part of 360, if at 
every 20° of the circle we set the screw one for- 
ward by hand, the thing will be accomplished, and no 
greater error than 1 tooth = 7”.5 will enter the work ; 
a precision fully sufficient for any purpose that such 
numbers can require, and in my opinion greater than 
can be come at by any other means. 
On the end of the screw arbor to the right, as exhi- 
bited in Fig. 5. is attached a milled-head and divided Fis 
micrometer ; the latter, like the rachet-wheel, is 
able at pleasure, and carrying the same number of di- 
visions that the wheel does teeth ; the micrometer turns 
round with the screw, and a cock, fixed to the frame, 
bearing a fiducial line, serves as an index for counting 
the divisions. By the help of this we are enabled at 
once to set the stopping apparatus to any of a 
revolution of the screw, without the trouble of a second 
trial ; or by it in case of a false — or other accident, 
we can adjust the in to due position, x 
The teams and pastas 8 for ast the divisions, 
and their connection with the engine, remain to be de- fo; 
scribed. Upon the two remote branches of the tripod, the di 
and beyond the border of the wheel, are erected two sions. 
illars, the upper parts of which are formed into serews. 
‘our screw nuts work, two and two, upon the’screw . 
pat of these pillars, and embracing the ends of a 
ar of brass KK which they support, enable us to . 
