872 
serves, may or may not agree. Bird, without doubt, 
used the radius and its parts, in order to secure an exact 
quadrant ; but Smeaton, treating exactness in the total 
are as of little value to astronomy, would, in order to 
secure the more essential property of equality of divi- 
sion, reject the radius altogether, and entirely 
upon the simple principle of the computed chord, The 
‘Advantages ™¢ans pursued by my brother, to reach the point which 
of ae Jan terminates the great bisectional are, is the only part in 
Troughton’s Which it differs from Bird’s method ; and I think it is 
method. without prejudice that I give it the preference. It is 
obvious, that it is as well calculated to procure equali- 
ty of division as the means suggested by Smeaton, at 
the same time that it is equal to Bird’s in securing the 
precise measure of the total arc. It proceeds entirely 
upon the principle of the protracted chord of 60° and its 
subdivision; and the uncertainty which is introduced 
into the work, by the sparing use which is made of sub- 
division by 3. and 5, is, in my opinion, likely to be 
much exceeded by the errors of a divided scale, * and 
those of the hand and eye in taking off the computed 
chords, and applying them to the arc of the instrument 
to be divided. 
Ramsden’s well known method of dividing by the 
engine unites so much aecuracy and facility, that-a bet- 
ter can hardly be wished for; and I may venture to 
say, that it will never be superseded in the divisions of 
instruments of moderate radit. It was well suited’ to 
the time in which it appeared ; a time, when the im- 
provements made in nautical astronomy, and the grow- 
ing commerce of our country, called for a number of re- 
flecting instruments, which never could have been su 
pee had it been necessary to have divided them by 
hand ; however, as it only applies to small instruments, 
it hardly comes within the subject of this paper. 
The method of Hindley, as described by Smeaton, t 
I will venture to predict, will never be put in practice 
for dividing astronomical instruments, however applica- 
ble it might formerly have been for obtaining numbers 
for cutting clockwork, for which purpose it was origi- 
nally intended. It consists of a train of violent opera- 
tions with blunt tools, any one of which is sufficient to 
stretch the materials beyond, or press them within 
their natural state of rest ; and, although the whole is 
done by contact, the nature of this contact is such, as 
I think ought rather to have been contrasted with, than 
represented as being similar to, the nature of the con- 
tact used in Smeaton’s Pyrometer, which latter is per- 
formed by the most delicate touch ; and is represented, 
I believe justly, to be sensible to the 5,355 part of an 
inch. Smeaton has, however, acquitted himself well, in 
describing and improving the method of his friend ; and 
the world is particularly obliged to him for the histori- 
cal part of his paper, as it contains valuable information, 
which perhaps no one else could have written. 
The only method of dividing large instruments now 
ere in London, that I know of beside my own, 
as not yet, I believe, been made public. It consists in 
dividing by hand with beam compasses and spring divi- 
Original 
‘Graduation. 
Ramsden’s 
method by 
the engine. 
Hindley’s 
wethod. 
London 
practice of 
dividing 
large instru- 
ments. 
GRADUATION. 
ders, in the usual way ; with the addition of examining 
the work by microscopes, and correcting it, as it pro. 6? 
ceeds, by pressing forwards or backwards by hand, with 
a fine conical point, those dots which appear erroneous ; 
and thus adjusting them to their proper places. The 
method admits of considerable accuracy, provided’ the Its def 
operator has a steady hand and good eye ; but his work 
will ever be i and ine t. He must have a 
circular line ing through the middle of his dots, to 
enable him to make and keep them at an equal distance 
from the centre. The bisectional ares also, which cut 
them across, deform them much; and what is w: the 
dots which require correction (about two-thirds per 
of the whole) will become larger than the rest, and un-— 
equally so in i ee to the number of’ attempts, 
which have been found necessary to adjust them. In 
the course of which operation, some of them grow in- 
sufferably too large, and it becomes neces to reduce 
them to an equality with their neighbours. This is done 
with the burnisher, and causes a hollow in the surface, 
which has a very disagreeable appearance. Moreover, 
dots which have been burnished up are always ill defi- 
ned, and of a_bad figure. Sir George Shuckburg Eve- 
lyn, in his paper on the Equatorial, } denominates these 
‘doubtful or bad points ;’ and (considering the few 
places: which he examines) they bear no inconsider- 
able proportion to the whole. In my opinion, it 
woth: be a great improvement of this method, to divide 
the whole by hand at once, and afterward to correct the 
whole ; for a dot forced to its place as above, will sel- 
dom allow the compass-point to rest in the centre of its 
apparent area; therefore other dots made from these 
will scarcely ever be found in their true places. This im- 
provement also prevents the corrected dots from being 
injured or moved by the future application of the com- 
passes, no such:application being necessary. 
I will now dismiss this method of dividing, with ob- 
serving, that it is tedious in the extreme; and did I not 
know the contrary beyond a doubt, I should have sup- 
posed it to have surpassed the utmost limit of human 
patience. § When sd natetle my first essay at subdividing 
with the roller, I used this method, according to the 
improvement suggested above, of correcting a few pri- 
mitive points ; but even this was too slow for one who 
had too much to do. Perhaps, however, had my in- 
struments been divided for me by an assistant, I might 
not have grudged to havepaid him for the labour of going 
through the whole work by the method of adjustment ; 
nor have felt the necessity of contriving a better way. 
I might now extend the account of my method of divi- 
ding toa great length, by relating the alterations which 3 
the apparatus has undergone during a long course of Troue 
Its ted 
years, || and the various manner of its application, before ™™ 
I brought it to its present state of improvement; but I 
think I may save myself this trouble, for truly I donot 
see its use. I will, therefore, proceed immediately to a 
disclosure of the method, as practised on a late occasion, 
in the dividing of a four feet meridian circle, now the” 
property of Stephen Groombridge, Esq. of Blackheath. 
* That Bird’s scale was not without considerable errors, will be shewn towards the end of this paper. 
+ Phil. Trans. for 1788. 
t+ Phil. Trans. for 1793- 
§ At the time alluded to, the double microscopic micrometer was unknown to me, and I did not learn its use, for these purposes, till the 
year 1790, from General Roy’s description of the large theodolite. Previous to that time, I had used a frame, which carried a single wire 
very near the surface to be divided. T 
lower end of a tube, 
structing the apparatus is, that the wire, 
in cases where any doubt is 
|| The full conception of the method had occu 
linquish branch of the business to me in which 
his wire was moyeable by a fine micrometer screw, ‘and was viewed by a single lens inserted in the 
which, for the purpose of taking off the parallax, was four inches long. The greatest objection to this mode of con- 
being necessarily exposed, is apt to gather up the dust ; yet it is preferable to the one now in use, 
entertained of the accuracy of the plane which is to receive the divisions. ~ 
pied my mind in the year 1778 but, as my brother could not be readily persuaded to re- 
uish he himself excelled, it was not until September 1785 that I produced my first specimen 
by dividing an astronomical quadrant of two feet radius. ie ’ ( 
1 
\ 
