Original 
Graduation. 
Captain Ka- 
ter’s pro-"* | 
posed mee 
thod of di- 
viding < siro- 
nomical 
ercles, 
~ deter 
so 
'To give a gerieral idea of this method, which is itself 
ideal, 4s all that we think necessary ; and with it, and. 
a general remark or two, we shall close our article, 
This method is extremely like that of the Duc de. 
Chaulnes: the chief difference between them is, that, 
instead of the waxed pieces, Captain Kater proposes to 
perform the work by means of two pieces which are to 
be clamped upon the circle to be graduated, and ad- 
justed to their places each by two appropriate screws. 
He would use three double microscopes, one plain with 
cross wires, the other two with micrometers: they are 
to be applied to an-exterior are exactly like that which 
Professor Lax used in the examination of his circle. Cap- 
tain Kater'leaves the manner of fixing the arc to the 
frame of the instrument, to the ingenuity of the artist, 
. who may. practise the method; a task by no means 
Remarks on 
Captain Ka- 
ter’s me- 
thod, 
easy, considering the stability that would be required. 
The cutting-frame of Hindley is to be used, which, 
being properly placed at one extremity of the exterior 
are for tracing the divisions, the plain microscope should 
be fixed over the tracer, and adjusted to a line drawn 
with-it exterior to the circles which are to bound the 
length of the divisions: this is called the line of verifi- 
cation. The fixed microscope not only regards this line 
and a dot upon the cutting apparatus, but also assists 
the eye in tracing the divisions. This is altogether a 
good contrivance; for by it the stability of the several 
parts. may be examined at pleasure, and, if necessary, 
xectified, The two micrometer microscopes are also 
applied to the exterior arc, and have a range.upon it from 
contact to a distance of one-fifth-part of the circle. After 
being clamped, they. have each a screw-adjustment in 
the line of the radius, and the adjustment for, the cor- 
rect angular opening is found in the micrometer wire. 
Captain Kater would first divide-the-circle into fiye 
equal parts, then trisect each of these, and then would 
perform another trisection. This is not the course that 
an artist would take: his instruments are to be read off 
at opposite divisions, and he would not toil through the 
most difficult part of the work .without a trial, De 
Chaulnes, in the first instance, bisected the circle, and 
whatever course he afterwards followed, every division 
would have its opposite; but- Captain Kater’s scheme 
admits of no opposites until his ares of 8° are bisected. 
The Duke, in every subdivision, left waxed pieces at 
every step of an interval, which he could examine again 
and again, before he cut the divisions, But Captain 
Kater, by using but two adjustable pieces, deprives his 
method of that advantage; for, in order to obtain a 
proper 
are set alternately in advance of each other, and a blank 
space is left behind. : 
Tn all.operations of this kind, there’is a certain 
that one may either see or not see, and which Mr fos. 
in his cirele of one foot radius, which is the same that 
Captain Kater proposes to divide, states to be three 
quarters of a-second. Now if, at the time that the 
opening of 72° for quimquisecting the circle was ad- 
justed;.a succession of five -- errors to that amount 
were committed,. the circle would appear to, be equally 
quinquisected, by an opening of ".75 — its proper 
measure, And with this error of opening in the simi- 
lar operation for cutting the divisions, let it be supposed, 
that at each step of shifting the adjustable pieces, a — 
error to the same amount were committed, then it is 
evident, that the division 288° would err by a quantity 
8 x ".75 = 6". This is Professor Lax’s. way of reckon- 
ing the amount of error, which is indged. too, severe; _ 
but, in the case which we have. exemplified, there is 
nothing improbable in the supposition, that the error 
GRADUATION. 
opening between the microscopes, the two pieces . 
‘this view. before us, we. ai wher 
might amount to more than half that quantity, and yet. Ox 
neither the apparatus. nor artist:be at all to blame, ‘ 
Captain Kater observes, that, errors, if any, would be “= 
seen: True; but divisions havebeen eut,and what is to be «., 
done with them? They ave of course to be rubbed out, ter's 
anid a trial again made, in hopes of better luck. _—_‘the 
Besides this, the method before us is stillfarther very 
objectionable. A division, when cut, whatever its er- 
ror may be, communicates that error to others. made 
from it, through every course of subdivision ; and thus’ 
the sins of the fathers are visited upon the children 
down to the seventh generation. ‘ 
There is another thing that is not adverted to by Cap« 
tain Kater: no division can be viewed. by the micro« 
scopes, to any useful degree of accuracy, until the-bur 
is polished off ; and the frequent recourse that must b 
made to this operation, which could not be done with- 
out carrying the circle round, to get it out of the way 
of the apparatus, would prove a.source, not indeed of 
inaccuracy, but of very much embarrassment and de- 
lay. It may be observed, that the method of coaxing »— 
is fully as much liable to this objection, and that Trough- 
ton’s 1s the only one that is perfectly free from it. 
_, Captain Kate's apparatus is the most complex,. and, 
if made, would be-the most expensive, that has been 
either used, or proposed for graduating ; and we should 
remark, that the method would turn out to be extreme~ 
ly tedious. The Captain expresses himself upon b 
these matters as being of quite a different opinion : we 
are not surprised at this, considering, as we do, how 
much faster the nimble ideas of a speculator get on, 
than the fumbling fingers of an artist. - 
The gentlemen graduators have one and all rejected op 
the maxum of Graham; they know that it is not geo- tions 
metrically true, and.to what extent itis practically so th 
are perhaps incapable of judging. The bisection of an ™ 
~ 4 _ ~ 4 
SL =, Orca ee Seah 
meant endeavours should be 
duators of. instruments shall be ine 
