362 
Original 
Graduation. 
+ 
thought their works sufficiently correct for the purpose; 
or, as the ancient astronomers praduated ‘their own. in= 
struments,—might not the magistrates'of old make their 
own standard measures? La yeewe grktaeal 
Hevelius, ‘and ‘the astronomers who preceded -him, 
‘made their observations without ‘the’ assistance ‘of’ tele- 
Hook’s me- - 
thod of gra« 
duation, 
Scopes, and the result of the’ ‘well-known controversy 
between Hevelius and Dr ‘Hook speaks highly in fa- 
vour of the division of his sector; for’ men ‘of science 
decided the dispute in favour of the Dantzig’ astrono- 
mer, from the superior ‘accuracy of his’ observations ; 
‘whereas, had the instruments of Hook been equal in 
other respects, the ‘téleseupic ‘sights, as is row well 
known; must have'given him the advantage. >? 
Dr Hook, in his animadversions tipon the Machina 
Ceelestis of Hevelius, published in 1674 the first method 
‘of graduation ‘that has been described. ‘It consisted of 
indenting the edge of an arc by the rotation: of 'a‘screw 
about its axis, in the manner that’has'since been practised 
with success in the dividing engine ; the indentations 
themselves stood for the divisions of the instrument, 
the angular value of which ‘were tobe found by other 
means. “A scréw similar to that which cut the teeth, 
‘was connected with the telescope; ‘and the number of 
teeth, and parts of a tooth, as shewn upon the’ micro- 
meter head of the screw, gave the observed angle. 
‘As the inventor of this method describes no means 
for correcting’ distant divisions, it may fairly be conclu- 
ded, that he did not forésee the necessity of any.’ And 
‘his own words bear out this supposition. Dr Hook 
entitles it, An explication of the new way of dividing’: 
and says, that the perfection of his instrument is in the 
“way of making the division ; that 7 excels all the comnion 
ways of division ; and that it does not at all depend upon 
the care and diligence of the insirument-maker, in dividing, 
graving, or numbering the divisions, for the same screw 
makes it from end to end. é 
With such screws as may be supposed to have “been 
in use-at that time, their want of truth could have had 
no good effect upon the run from end to’ end of the are ; 
yet as the same error would recur at every complete re- 
volution, no material mischief might arise. “But it is 
evident that the parts of a revolution would be affected 
‘by the whole amount of such error. The method was 
put in practice by ‘ompion, Sharp, ‘Rowley, the’ Duc 
de’ Chaulnes, and perhaps many‘others; but: in every 
recorded instance it completely failed ; and such instru- 
ments as bore this-graduation, before they could be de- 
pended on to any useful ‘degree, were furnished ‘with 
hand dividing. 
Mr Smeaton ‘seems to ascribe ‘the failure of Hook’s 
method to the different resistance which the different 
hardness in-parts of the metal presented to the action 
of the'serew ; and undoubtedly this afforded one source 
of error.» But wevare of opinion, that much greater er- 
rors arose from the screw not being’so sharp at the end 
of the are, as it was'at the beginning ; and that notch- 
ing the screw, ‘in order to produce the full tooth, made 
it cut sharper with the preceding edge of the threads in 
some parts, andthe following edge in others; a fact 
which is mentioned by Troughton as having embarrass- 
‘ed him ‘in racking his engine. ; 
Both Hook and Hevelius, in their controversy, pre- 
tended, in measuring an angle, to come at the exact- 
ness of a single second ; but as they flourished upon 
the verge of anage when most: things relative: to: sci- 
ence were taken upon credit, perhaps their works should 
not be too severely criticised by those who live at a 
time when every thing is tried be the test of experi- 
‘ment. 
GRADUATION 
/ Lhe polar sector of Mlamstead, made by Tompion; 
“eith which he made «so many neat 1676 ° 
to 1689, bore the screw division ; but its gross ‘errors ,) 
obliged Mr Flamstead himself to perform an original yo 
diagonal Leeper its limb.. -It..was about the tor. 
latter ‘date 'thatia -are was:completed. Bue) 
observatory, which, under the direction of Flamstead, 
was altogether constructed (by his assistant: Mr Sharp. 
This:also had ‘the’ division of Hook, but it ‘does «not 
appear to have succeeded better than thatiexecuted by 
Tompion: however, Sharp’s instrument ‘was at first 
furnished: with *a di ‘graduation more accurate — 
than'any that had precededit!.) 0 0) a 
The celebrated astronomer of Denmark, Olaus Roes Ro 
mer, about the year 1715, finished a muraliare.. Pro. ™"" 
— kacamgren the oe the screwmethod in _ 
England, ‘he performed his:graduation ina very ‘differ- 
eaqinrayy r archoaten in the paper before alluded to, 
a Mee account of Roemer's method withthe fol- © 
lowing remark : “ Th itis'a very si 
a eres 
right line into any number of’ parts ‘required ; yet it is 
‘still a‘much more simple thing to set off uponagiven = 
tight ‘line, from api radi eciaisigliiacahecctot tad : 
‘parts ired, where the’ total length is not exactly li- 
mited ; is amounts to nothing more than assum-~ 
ing‘a convenient opening “of the poe ee and be- 
ginning at the ‘given point, ito ‘set off the opening of 
the compasses as ‘many times in succession, as there 
-are “equal required ; which ‘process is ,asap- 
plicable to the arch of a circle, as it is to a right line. 
Of ert principle Roemer endeavoured ‘to avail 
-himself.”) To this end he took two finely pointed pieces 
of steel, and bound ‘them firmly»together at a distance 
which, as‘nearly as he could re psy would give him 
divisions nhis are of 10’ peau This pane: 
was to avoid the spring of long-le: compasses, | 
was, for the cienpasertnedadiock eal better than the 
best spring-dividers of the present day. With this dis- 
tance between the points of the tool, set off in succes- 
sion 450 times, Roemer divided his are of 75°. This 
way of dividing has appropriately been denominated — 
stepping, and k’s can be considered: in no other 
li Me Neither of them could give exactness in the to- 
are, even within moderate limits ; but this defect, 
great as itis; would have been amply com for, — 
had they secured the d desideratum tig? wees 
Smeaton is of opinion, that of those two methods, Hook’s 
is the best, because the screw, in making the teeth, has 
hold of several at a time; and, as far as neig i 
divisions:are concerned, it-certainly is so: but with re- 
spect to distant ones, as well as accuracy, we 
feel inclined to:give the preference. to Roemer’s. The 
astronomer of Uraniburg was the first who read off the Tycho 
angles observed with instruments, by means of a dou- 5*ie 
ble microscope ; not indeed/by a-wire put in motion by 4... 
a micrometer screw; as is now done. Instead of this, 9 dou 
10 equidistant parallel lines of single silk were stretch- crosec 
ed across the field of view, and bemg adjusted so as to 
fill the space between two. of his dots, gave him single 
minutes: the seconds were obtained only by estima-— 
tion, a 
Soon after the death of Flamstead, the royal obser- 
vatory was unfurnished. It has been said, that his ex- 
_ecutors demanded a higher price for. the instruments 
than government thought it right to pay. Thiswas 
the more excusable in thedatter, as it is probable that — 
it was in contemplation to procure new ones, in, which 
case the old. ones were intrinsically of no more val 
than the materials of which they were composed ; yet it 
