_ mutal arch, from the year 1756 to the time of his de- 
cease: with it he settled the mean obliquity of the 
[ pape the heginitinig of the year 1756, at 28° 28’ 
6”; which Dr ley settled by his- observations, 
ide in the years 1750 and 1751, at 28° 28’ 18”, The 
: is le to what ought to arise fromthe 
ual diminution of the obliquity of the ecliptic at 
‘a rate of about } a:second inva year,” &c. “That:two 
a ea eetart _ “Fas aa of different radii, 
in different’ parts of Europe, ‘should so nearly e, 
: is matter of arlene astonishment, and sufficiently 
proves, that a’mean of several observations, made'b 
observers, with accurate instruments, properly 
justed, willalways lead us either to’the truth itself, or 
extremely near to it. 
ks on _ Excepting the means of rendering the common sub= 
;me- ‘ivision of the circle bisectional, his ‘care in»avoid- 
of ing errors from expansion, Bird's method of cutting the 
nation. 3 Was its most important deviationfrom: the prac- 
tice of Graham, The latter made his dots ‘inthe tan- 
igential line, which the resting »point ofthe 
; while the point, at a considerable dis- 
‘tance, traced the divisions. Bird, by making his dots 
extremely near to the outer ends of the strokes, and 
resting the point in an undivided tangential line, avoid- 
ed any error that might arise from an alteration of the 
Jength of the beam during,the operation, which was a 
serious objection to Graham's way of proceeding. We 
should, however, have been afraid thatthe resting point, 
on being simply dropped into the line, and,having ap- 
v1 tly nothing to hold it there, mi re been in 
enieer of slipping, did not we know that artists them- 
‘selves, provided the metal be sound, are apprehensive 
of little or no error on this account. 
' Duke Soon after the publication of Bird’s method, that of 
er ; the Duke de Chaulnes’ made its appearance, which has 
lradua, 10 the preceding Section been noticed as applicable to.a 
dividing engine. He was the first who, employed 
double microscopes in the graduation of the circle; a 
oeg which, in the hands of others, the Duke’s work, 
. n or unknown to them, has essentially improved 
the art. There are also two more peculiarities in De 
Chaulnes’ method, that deserve to be noticed. One is 
its being purely visual. ‘The whole is done by the eye, 
utting the real divisions ; and eventhis, toprevent 
the errors ‘hand, is performed by machinery. The 
roped geen Aer acer _ marks upon the limb, 
e ‘or his purpose, a competent 
number of thin piaienack brass, Pore pans ee 
inch long, and one-sixth broad, with a fine line upon 
the surface of each, drawn. perpendicular to its length. 
To make these pieces adhere, to the surface that was to 
receive the divisions, their under planes were thinly 
coated with wax,, and | y made capable of being 
easily ag eps Pe and of retaining, that 
tion un e divisions represented by them were 
fnseeted. F ‘ 
_ The circle to be’ divided moves round horizontally 
. pon a vertical axis, within a strong frame of wood, to 
ee ee 
RE 
GRADUATION. 
367 
which the microscopes are fixed, and applicable to any Original 
part of it. Y Graduation 
The first step is to bisect the circle. To this end one ha. 
of the brass pieces isto: be made fast with screws, atthe 4. chani- 
ace which is intended to be zero, the line upon its sur- nes’ method 
face being directed towards the centre. A microscope is of gradua- 
affixed tothe frame, with its radial wire coincident with tio. 
the line, and its cross one a tangent to the'circle. Another 
microscope is secured on the frame, by estimation or any 
better way, diametrically opposite to the first, and one 
of the waxed pieces placed under it, so that the line and 
wires may have to each other, and .to the circle, the 
same relation as above. Let the cirele:be turned half 
round within the frame, so as:to bring the. zero line ¢o- 
incident with the radial wire of the other microscope. 
If now the line of the waxed piece be found exactly un- 
der the wire of the-first microscope, it is evident that 
the circle is:bisected; but as this.can hardly happen in 
the first instance, the apparent error must be corrected 
one half} by sliding the -waxed piece towards the wire, 
and the otherhalf' by moving the:microscope to it. The 
circle must again-beturned half round, to verify the cor- 
rection, or, ifnecessary, to afford means for a second 
correction, and the operation repeated until:the lines 
exactly coincide with the wires in-both positions, of the 
circle. ‘This being done, the: microscope which -has 
under it the zero piece should be regarded as fixed, and 
let its name-be A ; the other, which we will call B, is 
to be taken off, and reserved for future use. In the 
room.of B there is to be fixed the tracer or cutting 
point, so-that if the piece.were taken off, which it 
must not be, the tracer would cut a line exactly in its 
place, or diametrically opposite to the zero line. By 
this contrivance, it becomes necessary only to divide 
half the circle ; for if the divisions of one semicircle are 
brought successively to the wire of A, the tracer will cut 
their opposites in the other. 
The second step is to trisect the semicircle, which is 
to be done by two more of the adjustable. pieces, and 
the two microscopes. . With. sero. under A, place B as 
nearly at an angle of 60° from it.as can be done by es- 
timation or otherwise, and put a waxed piece under it ; 
move back the circle so.as to bring the waxed piece to 
A, and put. another undgr B ;, again move the circle so 
as to bring tha,second piece under A, when, if B should 
pen to coincide with the line opposite to zero, the 
thing is done; but if not, as most likely will be the 
ease, then B.must. be. moved towards the line one-third 
of the quantity of apparent error, and the operation re- 
peated, as was.done for bisecting the circle. The third 
step is to. bisect the three, equal ares of the semicircle, 
which is done by,similar means; and at the fourth step by 
which those last are trisected, arcs of 10° are obtained. 
The Duke de Chaulnes’, microscopes. could not be 
brought near ai to each other to bisect the arcs of 
10°; he therefore had recourse to that. of 9°,. which he 
found. and used. in.the following manner. He obtained 
it by taking ten steps with nine additional waxed pieces 
for each of” the two quadrants, which he brought to 
their places by.frequent trial and adjustment. With 
this opening between the microscopes, from the tens he 
set off all b+ nines, forwards, and all the ones back- 
wards. .He then resumed the former opening of 10° ; 
and as the operation for ascertaining the are of 9° had 
left a waxed piece in every interval of 10°, which would 
in their respective places represent 8°, 7°, 6°, &c. to 20 
in each quadrant, with the opening of 10° from eight, 
he set of all the eights, from seven he set off all the 
sevens, &c. and in this manner put in every single de- 
gree of the semicircle. 
