Engine 
Graduation. 
Puate 
CCLXXIX. 
Fig. 4. 
354 
per end:of the axis an arbour of hardened and tempered 
steel, which, having passed through the plate from be- 
low, stands full two inches above its surface, and ends 
iman obtuse point: similar to that below. Upon the 
two points when revolving in the lathe, the surface of 
the plate was generated, and its outer edge made per- 
fectly circular. : ‘ 
A screw for making the teeth in the limb had previ- 
ously been made. It had 20 threads in an inch; and 
as it was intended that by one of its revolutions it 
should carry the plate through an angle of 10’, it fol- 
lowed, that the circumference of the plate should be 108 
inches. From the measure of the screw, therefore, the 
dimension of the exterior border of the plate was deri- 
ved, first by computation nearly, and afterwards by trial 
with the screw itself. 
A strong collar of bell-metal had been soldered upon 
the axis, and, when the limb was turned, made coneen- 
tric with it. The position of this collar is, respecting 
height, coincident with the body of the tripod. The 
centre of the tripod is hollow, in order that the collar 
should pass through, but does not form a socket for it 
to work in. Instead of that, two narrow pieces of steel 
are fixed vertically at an angle of 120° with each other. 
Against these, the collar is pressed by a steel spring 
planted at 120° distance from them. In this triangular 
bearing the axis-is supported at top, while the piece F 
receives the point at the lower end, and supports the 
whole weight. 
To that branch of the tripod which is in front,a strong 
late of brass is screwed fast, as represented in the plan. 
t extends inwards half way to the centre, and outwards 
somewhat beyond the border of the wheel. Its breadth 
is rather more than the length of the screw arbor. Im- 
mediately above this, and in contact with it, is an ex~ 
actly similar plate. To the under side of the latter are 
screwed three oblong pieces, the thickness of which is 
equal to that of the lower plate. These, one of them 
at the middle of the inner end of the plate, and the other 
two at the outer end near the edges, are received by slits 
cut in the lower plate, which are about one-eighth of 
an inch longer than the pieces, and allow a motion of 
the upper plate, in the direction of the radius equal to 
that quantity, but afford it no lateral play. 
The dividing screw is fastened to the upper plate, 
and partakes of its motion, the use of which is occa- 
sionally to disengage the screw from the teeth of the 
limb. Two pieces, which connect the serew with the 
upper plate, are seen, one or both of them, in all the 
figures, and marked with H; they extend towards the 
centre, as far as the plate, and form edge-bars to 
strengthen it. The shape of these pieces is best shewn 
in Fig. 4. especially as to the manner how they are 
brought from below, for placing the screw even with 
the edge of the wheel, and how the screw arbor is 
centered in them. The arbor of the screw is cylindri- 
cal; and a portion of each end forms a cylinder of 
smaller diameter. The shoulders, which near each end 
of the arbor, limit those parts, prevent lateral play in 
the pieces last described ; for the smaller parts work 
freely in the holes of those pieces, the shoulders being 
in contact with their inner edges. i 
The engine, so far Aeedeitied, is ready to receive the 
original graduation of its limb ; and as this operation 
was done, while work to be described eebidies was 
preparing, I will here explain by what means this most 
important part of the work was accomplished: to do 
this, however, within moderate bounds, I must sup- 
pose that the reader is already acquainted with my 
method, as published in the Phil. Trans. for 1809, or 
In the first step, a roller was ] 
a frame attached to the tripod, ; 
motion round its own axis; thi: i 
be carried exactly 16 times round, while the 
plate made one revolution, and was itself near the edge ! di 
upon its upper surface, divided into 16 parts. Now, "8 
upon turning the plate round, these 16 divisions 16 
times told = 256, 4 in eer te to the wire of a 
fixed micros , and were, a proper apparatus, 
transferred to the surface of the plate, in five dots, at a 
sufficient distance within the edge to prevent their be- ; 
ing disturbed by making the teeth. To | lish Methos 
the next step, an index was made to revolve upon the’ 8d 
arbor of the plate ; it was composed of two branches, je 
each of which carried at its extremity a microscope 
with a micrometer; these had a range of angular motion 
respecting each other, from a right line to a very small 
angle. By this index, and these mi , the 256 
fine dots were examined by a certain bisectional tee 
cess, from which their individual errors were inves 
ted by computation, and formed into a table. By 
help of the table of errors, the future work of racking —_ 
the limb was prosecuted with as much certainty as 
could have been done, had the original divisions been 
inserted without error. 
It has already been said that the value of a tooth of 
the limb should be 10’, and consequently their whole 
number will be 2160; now = 84, and just soma- 
ny revolutions and parts of the dividing screw will be 
commensurate with a mean s from dot to dot = an 
angle of 1° 24’ 22’’.5. In order, therefore, that a com= 
parison between the plate and the screw might be 
made at every original dot, it became necessary to pr¢ 
vide means to ascertain the position of the former at 
every 16th part of a revolution. To this end a micro- 
meter head, as large as could be admitted, divided into 
16 equal parts, was fixed upon the left end of the screw 
arbor ; and contiguous to this, was placed a fixed in- 
dex bearing a fiducial line. For the purpose men- 
tioned above, these were all that could be wanted ; but 
as our dots were erroneous, in order from their apparent, 
to determine their true places, a lower subdivision of 
the head became necessary. Each of the 16 spaces, 
therefore, was divided into 10 by actual division, ‘and 
as an eye, practised in such matters, can by estimation 
accurately obtain the value of the next decimal figure, 
it was into the last denomination of subdivision that the 
table of errors had been reduced, the value of an unit 
of which, in angular measure, is 3ths ofa second, 
The roller was removed when the 256 dots had been 
transferred to the plate, as were the double index and 
microscopes from the central arbor, when the position’ 
of those dots had been ascertained. Now, the dividing 
screw was placed in its frame; a micrometer, with a 
moveable wire, fixed to the tripod for viewing the pri- 
mitive dots, and a winch for turning the screw attach- 
ed to its arbour on the right: this change of parts be- 
ing effected, the screw with its frame having free mo- 
tion in the line of radius, and capable of being, by the > 
force of a spring, pressed into contact with the edge of 
the plate, or by a screw drawn backwards at pleasure ; 
and the plate itself having free motion round its axis, 
the important operation of forming the teeth, or rack- 
ing the circle, was commenced. Ps 
It should be premised, that to prevent pre A! 
beginning an interval at a wrong 16th of the head, 
which, by making false marks, would occasion muck 
