GRADUATION. 
al the other as the opening, was + or —, will be 4, 3, 
ti pan ¢ ofthe npace between, them and these Mr Ca- 
= yendish would use by estimation in the subsequent 
* of the work, Mistakes in making a wrong 
estimation of the spaces are to be fivebted, by making 
r matks upon the circle opposite to them. Mr 
ae ndish has given three different ways pal anereim 
but that which we have described, is the one which he 
himself thinks the best. 
883 
venth, and the value of each deduced from a compari- Original 
son with the are of 30° in which it is contained. Graduation. 
We will follow Professor Lax no farther in his inge- 7), 
nious and laborious examination ; suffice it to say, that, 2 
by we the same principle of comparing short arcs method of 
with their multiples, he obtains the errors of every in- examining 
dividual division of his circle, down to the ten-minute the “ivisions 
spaces into which it is graduated, pe ry 
~ Mr Lax says, that with his microscopes and his circle g--uments. 
To give a general idea of Mr Cavendish’s method was 
all that we intended. To follow him through his whole 
per would be useless ; for, notwithstanding that much 
ingenuity is displayed in pointing out such errors as he 
foresaw it would be liable to, and in contriving means 
to obviate them, we consider it as altogether inconsistent 
with practice, and inelegant in design. 
' Immediately after Mr Cavendish’s paper, we find 
one by Professor Lax of Cambridge in the form of a 
letter to Dr Maskelyne. 
examining the Divisions of Astronomical Instruments. 
» ‘The learned professor sees no reason why astronomers 
should trust to the ability and integrity of artists, when, 
by means of a proper apparatus, they have it in their 
own power to examine and note the error of every di- 
vision of an instrument. Mr Lax is in possession of 
an altitude and azimuth circle, of one foot radius, made 
by Mr Cary, and it is to this instrument that his exa- 
mining apparatus is. adapted ; but the computation of 
error is expressed in general terms. 
~ His apparatus consists of an arc fixed to the frame of 
the instrument, exterior to, and concentric with, the circle, 
and which stands still while the circle is turned round. 
The arc contains about 90°, and a microscope, which 
slides upon it from end to end, may be clamped to any 
part of it: The microscope regards the divisions of the 
circle, and is used in combination with one of the read- 
ing micrometers: the former has an inclination of about 
80° to the latter, in order that both of them may be 
made to coincide with one and the same division of the 
circle ; by means of which contrivance, any opening 
between them from 0 to 90° may be taken. Professor 
Lax finds the error of the division 186° by help of the 
two reading micrometers, exactly as Troughton did, 
but in every other step the examination is carried on in 
a way quite different from that pursued by the artist, 
' The second step is rmed when zero of the circle 
poh nae sks to one of the micrometers, and the micro- 
scope fixed to the exterior arc at the division 90°, by 
bringing in succession to the microscope the divisions 
180°, 270°, and 360°, and comparing the first arc of 90° 
with the other three arcs of 90°, the difference of which 
having been measured with the micrometer, and dis- 
‘tinguished by +4 or — affords data for computing their 
: ive errors. In like manner, the first are of 60° 
is to be measured against all the other five arcs of 60° 
ptecisely as the first arc of 90° was measured against 
all the other ares of 90°, And again, the first arc of 45° 
is to be measured against all the other seven arcs of 45°. 
So far the Professor proceeds before sunrise, in order to 
ayoid the effect of expansion ; the rest, on account of 
‘the small arcs that are used, may be done at any time. 
The are of 30° may now be measured against every 
succeeding arc of 30° in the first, third, fourth, and 
sixth arcs of 60°; and let the length be determined 
from a separate comparison with the arc of 60° in which 
it is comprehended, and not from a general comparison 
with all the four. The arc of 15° must then be mea- 
sured against evéry succeeding arc of 15° in all the 
mes 30° exeept the second, fifth, eighth, and ele. 
- = 8 
‘a 
It is entitled, On a Method of 
of one foot radius, he cannot commit.an error greater 
than three quarters of a second in reading off, and with 
this datum and that of the number of times that some 
divisioris have been dependent upon previous examina- 
tions, he reckons upon a possibility of error in extreme 
cases amounting to 9”.63. This is a very large quan- 
tity : the truth however is, that the examiner not only 
under-rates the ability and integrity of artists, but also 
the powers of his own method. To make out the 
above quantity, Mr Lax is obliged to suppose, that at 
every step he commits the greatest ible error, and 
that, in every course, the error lies in that direction 
which produces the greatest accumulation, After the 
examinations have been completed, and the calculations 
made, the Professor says: . 
« The time and labour required ‘for this examination 
are no doubt very considerable ; but it. ought to be re- 
collected, that it will render any great degree of pres 
cision, in dividing the instrument, totally unn 
Whoever, indeed, employs this method of examination, 
will be virtually the divider of his own instrument; 
and all he will ask of the artist, is to make him a point 
about the end of every five or ten’ minutes, whose dis- 
tance from zero he will determine for himself, and en- 
ter in his book, to be referred to when wanted. We 
may likewise observe, that, by this examination, we 
shall not only be secured against the errors of division, 
but against those that arise from bad centring, and 
from the imperfect figure of the circle, and which, in 
general, are of too great a ap er to be neglected.” 
Now, the greatest part o 
ble of performing the work ; and we think that they 
will continue, as heretofore, to demand of the artist the 
utmost exertion of his talents. 
Professor Lax has shewn the analogy between his 
method of examination and that of observing by r 
tition, as much practised abroad, which is but another 
way of reducing the errors of dividing. As, however, 
things do not easily get out of their usual course, we 
are of opinion, that the paper under consideration will 
have no tendency to relax the efforts of the artists of 
this island to approach the point of truth, any more 
than the improvement of the art of graduation will, upon 
the continent, supersede the use of the repeating circle. 
We are not satisfied with the inclining mi ‘ 
In order that this should occasion no error, the plane 
which bears the graduation should be almost a mira- 
cle of truth. Were the microscope so fixed as to be ca- 
pable of being inclined as much the contrary way, the 
effect of lax would be contrary too ; and if a suc- 
cession of the same angle were repeated in both posi- 
tions of the microscope, an identity of results would 
rove our doubts to be groundless, or a disagreement Captain Ka- 
ween them shew the thing we are afraid of. 
In the second part of the Phil. Trans. for the year 
cal, Circles, and other Instruments,” 
all this is certainly very Remarks on 
true; yet we doubt if astronomers in general will not save Mt Pars 3 
themselves the expence of the apenas and the trou. ™*"°* 
im . « thod of di- 
1814, we meet with a r by Captain Kater : ‘it is yigj Z 
called, «* An Improved Method of dividing Astronomi- noni 
circles, 
