le to what I have heard, &c.’? Sir George’s 
examination of his own equatorial furnishes. me with 
—> the means. of a -ineas smapeEsae SB his account of 
;. the declination circle, we find an error +2”.35, and 
ants be sak A RE Se Ova: Aessaate 
in i , which Sir George also admits, 
wre aba then have a di ey of 4.85; but, as the 
errors of reading off are not errors of division, let them 
be di from both, and the errors will then stand 
for the quadrant 2”, and for the circle 3”.85. As the 
radius of the former, however, is four times greater than 
that of the latter, it, will appear, by this mode of trial, 
that the equatorial is rather more than twice as accu- 
rately divided as the quadrant, In doing justice to Bird 
in this instance, I have only done as I would be done 
by: for, should any future writer set me back a centu- 
ry on the chronological scale of progressive improve- 
ment, I hope some one will be found to restore me to 
my proper niche. I now subjoin a restatement of the 
t error of each of the instruments that are brought 
into comparison by Sir George, after having reduced 
them all by one rule, viz. allowing each of the two 
points which bound the most erroneous extent, to di- 
vide the. apparent error equally between them. They 
are expressed in parts of an inch, and follow each other 
in the order of their accuracy. : 
Sir G Shuck ’s 5 feet standard . . . .000165 
Getieral Roy's scale 42 inches ....... . .000240 
Sir George’s equatorial, 2 feet radius . . + . by 
The Greenwich quadrant, 8 feet radius ... 
Mr Aubert’s-standard, 5 feet long ... 000700 
*The Royal Society's standard, 92 inches long .000795 
For the justness of the paves statement, I consider my 
name as ple ; requesti e permission to say, that 
if, on the result of each pe Seve examination, vA here 
presented, there could have been more than one opi- 
nion, it would not have here. I am farther 
prompted to add, that the above comparative view pre- 
sents one circumstance to our notice, which cannot do 
less than gratify every individual, who is at all conver- 
sant in. matters; I mean, the high rank which 
General Roy’s scale takes in the list ; that scale having 
been made the agent in measuring the base line of our 
must 20 return, finally, to the dividing of circles; I must 
Htaken, to State, as matter of precaution, that great care should be 
. taken during the turning of the outer edge, to have the 
Jeofs circle of the same temperature ; for one part may be 
seenre &XP2nded by heat, or contracted by cold, so much more 
je turn- than another, as to cause the numbers in the tables of 
i the out- errors to be inconveniently large. A night is not more 
than sufficient for allowing the whole to take the same 
tem: , after having been handled by the work- 
j men ; and the finishing touch should be given within a 
4 short of time. But, if the effects of temperature 
i are to be regarded in turning a circle, it is of tenfold 
more importanee to attend to this circumstance, while 
the examination of the larger arcs of the instrument is 
carried.on; for it is absolutely n , that, during 
this time, the whole circle should be of the same heat 
more They generally su the expansion of metals to be a 
trifle, which neat tar Wa in practice ; and 
sup- Wonder how the parts of a circle can ‘be differently 
heated, without taking pains to make it so. One de- 
executors. 
GRADUATION. 
- within that quantity: Yet so ne 
,estimate of the time, which the different 
exactly. Few workmen are sufficiently aware of this. - 
379 
gree of Fahrenheit’s thermometer indicates so small Original 
a portion of heat, that, in such places as workmen are Graduation. 
usually obliged to do their business in, it is not very easy 
to have three thermometers attached to different parts of 
a large instrument, showing an equality of temperature 
is correctness 
in this respect, that if'a circle has the vertex one degree 
warmer than its opposite, and if this difference of tem- 
perature be regularly distributed from top to bottom, 
the upper semicircle will actually exceed the lower b 
2”; And, if such should happen to be the case while 
the examination of the first ae of the third quadrant 
is made, the regularity of the whole operation would 
thereby be destroyed. . 
It may not be improperto remark, that'dividing by The appara- 
the eye does not require a more expensive apparatus ‘s not ex- 
than the operation of dividing by hand ; and, indeed, P&*¥e 
less so when the scale of inches is deemed necessary. 
The method by adjustment is still more expensive, re- 
quiring whatever tools Bird’s method requires, and, in 
addition to these, a frame and microscopes, somewhat 
similar to those for dividing by the eye. 
It is somewhat more difficult to give a comparative yfuch time 
ods of saved by it? 
dividing require. I know, that'13 days of eight hours 
each, are well employed in dividing sucha circle by 
my method; about 52 days would be consumed in 
doing the same thing by Bird’s method ; and I think I_ 
cannot err much, when I state the method by adjust« 
ment, su ing every dot to be tried, and that two 
thirds of been want adjusting, to require about 150 of 
such days. 
The economy of time, (setting aside the decided 
means of accuracy,) which the above estimate of its ap- 
plication offers to view, will, I think, be considered of 
no little moment. By the rising artist, who may aspire 
to excellence, it will at least, and I should hope with - 
gratitude, be felt in the abbreviation of his labours. To 
me, indeed, the means of effecting this became indis« 
pensible ; and it has not been without a sufficient sense 
of its necessity, that I have been urged to the progres- 
sive im ement and completion of: these means, as - 
now described. It is but little that a man can perform 
with his own hands alone; nor is it om all -occasions, 
even in frames of firmer texture than my own, that he 
can decisively command their adequate, unerring use. 
‘And I must confess, that I never could reconcile it to 
what I hold as due to myself, as well as to~a solicitous . 
regard for the most accurate cultivation of the science 
of astronomy, to commit to others an jon requi- 
ring such various and delicateattentions, as the division. 
of my instruments. 
That my attentions on this head have not failed to 
procure for me the notice and patronage of men, whose 
approbation makes, with me, no inconsiderable part of 
my reward, I have to-reflect on with gratitude and plea- 
sure: and as-I look with confidence to the continuance 
of that patron so long as the-powers of execution 
shall give me the.inelination +o solicit it, I cannot en- 
tertain a motive,»which might-go to extinguish the 
more liberal wish. of:pointing out to future ingenuity a 
shorter road to:eminence; sufficiently gratified by the 
idea of having, in the present communication, contri- 
buted to facilitate the operations, and toaid the Seq 
of art, (as far.as the limited powers of vision will ad- 
mit,) toward the point of perfection.” 
® This isthe same which Mr Bird used in dividing his eight feet murl quadrants, and was presented_to the Royal Society by Binl’s 
