376 
Original space between the dots, the errors of which have been 
Graduation. tabulated. Let, therefore, the arc of the sector be di- 
PLATE 
CCLXXxXUL 
Fig. 4. 
Dividing by 
the engine. 
vided into 16 spaces of 1° 20’ each, and let a similar 
space at each end be subdivided into eight parts of 10’ 
each, as in Fig. 4; we shall then have a scale which 
furnishes the means for making the true divisions, and 
an immediate examination at every bisectional point. 
I have aways divided the sector from the engine, be- 
cause that is the readiest method, and inferior to none 
in point of accuracy, where the radius is very short ; 
but, as itis more liable than any other to centrical error, 
the adjustment of the are by the screw E becomes ne- 
. cessary: by that adjustment, also, any undue run in the 
Division by 
lines prefer- 
able to dots, 
Apparatus 
for cutting 
the divi- 
sions. 
Invented by 
Mr Hind. 
ley. 
Lanterns 
employed. 
Fig. 7. 
action of the roller may be reduced to an insensible 
quantity. 
When the utmost degree of accuracy is required, I 
give the preference to dividing by lines, because they 
are made with a less forcible effort than dots are ; and 
also because, if any small defect in the contexture of 
the metal causes the cutter to deviate, it will, after pas- 
sing the defective part, proceed again in its proper 
course, and a partial crookedness in the line will be 
the only consequence ; whereas a dot, under similar 
circumstances, would be altogether displaced. But, on 
the other hand, where accuracy has loss out of the 
question, and only neatness required, I have used dots; 
and I have done so, because I know that when a dot 
and the wire which is to bisect it are in due proportion 
to each other, (the wire covering about two-thirds of 
the dot,) the nicest comparison possible may be obtain- 
ed. It may be farther observed, that division by lines 
is complete in itself; whereas that by dots requires 
lines to distinguish their value. 
On the upper side of Fig. 1. is represented the appa- 
ratus for cutting the divisions. It consists of three 
pieces JKL, jointed my ewe so as to give to the cutter 
an easy motion, for drawing lines directly radiating 
from the centre, but inflexible with respect to lateral 
pressure ; dd are its handles. The cutting point is 
hidden below the microscope H ; it is ofa conical form, 
and were it used as a dotting point, it would make a 
puncture of an elliptical shape, the longer diameter of 
which would point towards the centre. This beautiful 
contrivance, now well known, we owe to the ingenui 
of the late Mr Hindley of York ; it was borrow by Me 
Ramsden, * and applied with the best effect to his di- 
viding engine, 
It might have been mentioned sooner, that in the in- 
stance which I have selected as an example of my divi- 
ding, the operation took place when the season of the 
year, and the smoke of London, had reduced the day 
to scarcely six hours of effective light; and rather than 
confine my labours within such narrow limits, I deter- 
mined to shut out the day-light altogether. Fig. 7. 
shows the construction of the lanterns which I used. 
A very small wick gave sufficient light, when kept from 
diverging by a convex lens; while the inclining nossel 
was directed down exactly upon the part looked at, and 
the light, having also passed through a thin slice of 
ivory, was divested of ah lare. I enter into this de- 
scription, because, I think, I never saw my work bet- 
ter, nor entirely to so much advantage as in this in- 
* This I learned from that most accurate artist Mr John Stancliffe, who was himself apprentice to Hindley. , 
: P is carried on as if the roller measured the mean interval without error. 
was said (Page 371), that the roller, in a continmed motion quite round the circle, would, in some part of its course, err by 30’', or mores 
therefore, when this is the case, an extreme run of the roller cannot agree with a mean interval of the circle nearer than * = 0.23// 5 and 
most probably this kind of error will, on some intervals, amount to double that quantity. It, therefore, becomes matter of 
+ For the sake of simplicity, the 
of the 
GRADUATION. 
tion, to examine every interval previous to making the divisions; and, where necessary, to adjust the sector, so that its arc may 
measure the corresponding interval as corrected by the tabulated errors. : 
stance ; owing, perhaps, ‘to the surrounding darknese 
ale wiskg tiasep il of the eye to keep cr pa ex. 
ded, than when indirect rays are suffered to enter it. 
The heat from a pair of these lanterns was very incon- 
siderable, and chiefly conducted along with the smoke 
up the reclining chimney. . 
Previous to cutting the divisions, the parts now de- 
scribed must be adjusted. The cutting apparatus must for 
be placed with the dividing point exactly at the place 
where the first line is intended to be drawn, and clamp- 
ed, so that the adjusting screw may be able to run it 
through a whole interval. The mi H must be 
firmly fixed by its two'pillars 6, to the main frame, 
with its micrometer head at zero; and with its only 
wire in the line of the radius, bisecting the first of the 
256 dots. And it’should be observed, that the cutting 
frame and this must not vary respecting each other, 
during the time that the divisions are cut; for any mo-~ 
tion that took place in either would go undimin to 
the account of error. The microscope I is also fastens ~ 
ed to the main frame; but it is only required to keep 
its position unvaried, while the divisions of the sector 
pass once under its notice ; for it must have its wires 
adjusted afresh to these divisions at every distinct 
course. The microscope I has two wires, crossing 
each other at an angle of about 40°; and these are to 
be placed so as to make equal angles with the divisions 
of the sector, which are not dots but lines. The sec~ 
torial arc must also be adjusted to its proper radius by 
the screw E,.Fig. 5; i.e. while the. main frame has 
been cayried along the. circle through a mean interval 
shewn by H, the sector must have moved eX 
actly 162ths of its divisions, as indicated by I. t 
Things being in this position ; after having given the cy, 
parts time to settle, and having also sufficiently proved iyi 
the permanence of the micrometer H and the cutting 
frame with respect to each other, the first division may 
be made; then, by means of the screw for slow mo- 
tion, carry the apparatus forward, until the next line 
upon the sector comes.to the cross, wires of I; you then 
cut another divison, and thus proceed until the 16th 
division’ is cut, = 1° 20’: Now, the apparatus wants - 
to be carried further, to the amount of jths of a divi- 
sion, before an interval is complete ; but at this last 
point no division is to be made; we are here only to 
compare the division on the sector with the correspond~ 
ing dot upon the instrument. This interval, however, 
upon the circle, will not be exactly measured by the 
corresponding line of the sector, which has been ad« 
justed to the mean interval, for the situation of the dot 
1°.4 is too far back, as appears by the table of real er- 
rors, by — 4.8 divisions of the micrometer head. The 
range of the screw for slow motion must now be re- 
stored, the cross wires of H set back to —4.8 divi- 
sions, and the sector moved back by hand, but not to 
the division 0 where it began before ; for, as it left off 
in the first interval at ths of a division, it has to go — 
forwards 4th more before it will arrive at the spot where — 
the 17th division of the instrument 1° 25’ is to made, — 
so that in this second course it must begin at ¢th short 
of 0. Go through this interval as before, making a 
division upon the circle at every one of the 16 great 
§ 
ee 
y 
But it 
prudent precau- 
