86 On. dividing Instruments. 



Bird, without doubt, used the radius and its parts in order to 

 secure an exact quadrant ; but Smcaton, treating exactness 

 in the total arc as of little value to astronomv, would, ia 

 order to secure the more essential property of eijualily of di- 

 vision, reject the radius altogether, and proceed entirely 

 upon the simple principle of the computed chord. The 

 means pursued by my brother, to reach the point which 

 terminates the great bisectional arc, is the only part in which 

 it differs fron: liird's method ; and I think it is without 

 prejudice that I give it the preference. It is obvious that it 

 is as well calculated to procure equality of division, as the 

 means sutrgesled by Smealon ; at the same time that it is 

 equal to Bird's in securing the precise measure of the total 

 fire. It proceeds entirely upon the principle of the pro- 

 tracted chord of G0° and its subdivision ; and the uncer- 

 tainty, which is introduced into the work by the sparing use 

 which is made of subdivision by 3 and 5, is, in my opinion, 

 likely to i>e much exceeded bv the errors of a divided scale *, 

 and those of the hand and eye, in taking off the computed 

 chords, and applying ihem to the arc of the instrument to 

 be divided. 



JRamsden's well known method of dividing by the engine 

 unites so much accuracy and facility, that abetter can hardly 

 be wished for ; and I may venture to say that it will never 

 be superseded, in the division of instruments of moderate 

 radii. It was well suited to the time in which it appeared; 

 a time wlien the intprovements made in nautical astronomy, 

 and the growing commerce i>f our country, called for a 

 number of icfiecting instruments, which never coidd have 

 been supplied, 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 Uindley, as described bv Sineaton t. T will 

 venture to predict will never be put in practice fur dividing 

 aslrononnca! instrun)ents, hovi'cver ap|:)licable it might for- 

 merly have been i'^-iv obtaining numbers for cutting cluck- 

 work, for which pi;; pose it was originally intended. It con- 

 sists of a train of violent operations with blunt tools, any 

 one of which is sufficient to s'retch the materials bevond, or 

 press them within their natural state of rest ; and, although 

 the whole is dune 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 coii- 



* That Bird's scalp was not without considerable errors, will be shown tO' 

 wards tiie end of this paper. 

 f rhilosophical Transactions for 1788; 



tact 



