+ sions, as well as its inner and outer edges, but especial- 
ly the latter, should be turned in the most exact and 
the limb, if the ; as is generally the 
ger than the diameter, those which 
extend farther, must be so applied, that may be 
removed during the operation of dividing. Fig. 1. and 
9. Plate CCLXX: 
ding parts, and both are 
drawn to a scale of half dimensions. AA is a of 
the circle, the surface of which is seen in the plan, and 
* the edge is seen in the elevation. BBB is the main 
the s, resting with its four feet a, a, a, a 
the surface of the arc; these feet, being screws, 
be adjusted to as to take equal shares of the weight, 
sialinaaed are fastened by nuts below the plate, as shown 
in Fig. 2. CC and DD are two similar re each 
__ attached to the main plate, one above and the other 
below, by four pillars ; and in them are centred the ends 
of the axis of the roller E. F and G are two friction 
wheels, the latter firmly fastened to B, but the former 
is fixed in an adjustable frame, by means of which ad- 
___ justment these wheels and the roller E may be made to 
____ press, the former on the interior, and the latter on the 
exterior edge of the circle, with an equal and convenient 
force. * At the extremities of the axis of the roller, and 
attached to the middle of the plates C and D, are two 
bri c, c, having a screw in each; by means of which 
an adjustment is procured for raising or lowering the 
roller respecting the edge of the circle, whereby the 
former, having its diameter at the upper edge about 
-001 of an inch greater than at the lower edge, (being, 
© as before described, a little a it may easily be 
‘brought to the position where it will measure the pro- 
‘per co of the circle. 
} roller. uch experience and thought upon the subject have 
taught me, that the roller should be equal to one six- 
teenth part of the circle to be divided, or that it should 
revolve once in 22° 30’ ; and that the roller itself should 
be divided into sixteen parts ; no matter whether with 
absolute truth, for accuracy is not at all essential here. 
Each of such divisions of the roller will correspond with 
an angle upon the circle of 1° 24 22.5, or +1,th part 
of the circle. This number of principal divisions was 
chosen, on account of its-being capable of continual bi- 
section ; but they do not fall in with the ultimate divi- 
sions of the circle, which are intended to be equal to 5’ 
The next thing to be considered is, how to make the 
roller measure the circle. As two microscopes are here 
, and those which I use are very simple, I will 
in this place give a description of them. Fig. 6. is a 
section of the full size, and sufficiently explains their 
f construction, and the position of the glasses; but the 
) micrometer part and manner of mounting it, are better 
rome. shown at H, in Fig. 1. and 2. The micrometer part 
consists of an oblong square frame, which is soldered 
into a slit, cut at rig les in the main tube; ano- 
ther similar piece nicely: into the former, and ha- 
f ving a small motion at right _ to the axis of the 
cy 
microscope, has at one end a 
' 
i 
f 
| 
this property, 
f GRADUATION. 
The surface of the circle which is to receive the divi- at the other a micrometer screw ; a spring of steel wire 
~ revolutions. 
ndrical guide pin, and . 
378 
is also applied, as seen in the section, to prevent play, Graduation. 
by keeping the head of the micrometer in close contact “~Y—"” 
with the fixed frame. This head is divided into one 
hundred parts, which are numbered each way to 50; 
the use of which will be shown hereafter. A fine wire 
is stretched across the moveable frame, for the purpose 
of bisecting fine dots. Two of these microscopes are 
nece: ; also a third, which need not have the di- 
vided head, and must have in the moveable frame two 
wires ing each other at an angle of about 30°: this 
miscroscope is shown at I, Fig. 1. In the two first mi- 
crometers, a'division of the head is of the value of about 
0.2, and the power and distinctness such, that when 
great care is taken, a much greater error than to the 
amount of one of these divisions cannot well be com- 
mitted in setting the wire across the i of a well 
made dot, The double eye-glass has a motion-by hand, 
for producing distinct vision of the wire; and’ distinct 
vision of the dots is procured by a similar adjustment 
of the whole microscope. 
The first towards sizing the roller, is to com- Adjustment 
pute its diameter according to the measure of the circle, p hn — 
roller. 
and to reduce it agreeably thereto, taking care to leave 
it a small matter too large. The second step is, after 
having brought the roller into its place in the plate BB, 
to make a mark upon the surface of the circle near the 
edge, and a similar one upon the roller, exactly oppo- 
site each other; then carrying the apparatus forward 
with a steady hand, until the roller has made sixteen 
If now, the mark upon the roller, by ha- 
ving over-reached the one upon circle, shows it to 
be much too large, take it out of the frame and reduce 
it by turning accordingly : when, by repeating this, it 
is found to be very near, it may be turned about .001 
of an inch smaller on the lower edge, and so far its pre- 
paration is completed. The third and last step is, the py. ana 
use and adaptation of the two microscopes ; one of these adaptation 
must take its position at Hin Fig. 1. viewing a small of the two 
well-defined dot made for the purpose on the circle ; micto- 
the other, not represented in the Figure, must also be ““°P** 
fixed to the main plate of Fig. 1. as near to the former 
as ible, but viewing one of the divisiens on the 
roller. With a due attention to each microscope, it will 
now be seen to the greatest exactness, when, by raising 
or d ing the roller, its commensurate diameter is 
found. 
Fig. 3: is a representation of the apparatus for trans- Apparatus 
ferring the divisions of the roller to the circle. It eon- for making 
sists of two slender bars, which, being seen edgewise in the dots in 
the figure, have only the appearance of narrow lines; but, ‘ “te 
when looked at from above, they resemble the form of 
the letter A. They are fastened to the main frame, as at 
W and Z, by short pillars, having also the off leg of the 
angle secured in the same manner; Y is a fine conical 
steel point for making the dots, and X is a feeler, 
whereby the point Y may be eq down with a uni- 
form force, which force may be adjusted, by bending 
the end of the bar just above the point, so as to make 
the dots of the proper size. The point Y yields most 
readily to a perpendicular action ; but is amply secured 
against any eecentric or lateral deviation. 
The apparatus, so far described, is complete for lay- Primary 
ing our foundation, 4. e. making 256 primary dots; no dete. 
matter whether with perfect truth or not, as was said 
respecting the divisions of the roller ; precision in either 
* Sufficient spring for keeping the roller in close‘and uniform contact with the edge of the circle is found in the apparatus, without any 
contrivance for this purpose, The bending of the pillars of the secondary frames, and of the axis of the roller; chiefly supplies 
