[ IGl ] 



XXIX. On Mr. Troughton's Expedient for correcting Errors 

 arising from the Excentricity of the Point round ivhick the 

 Indexes revolve hi Reflecting Circles. By Mr. Edward 

 Riddle, Newcaslle-on-Tyne. 



To Mr, Tilloch. 



Sir, — W HILE the success which has attended the researches 

 of the continental mathematicians in every department of phy- 

 sical astronomy is on all hands allowed to be most splendid and 

 imposing; and while the honour is most cheerfully paid which is 

 due to the meritorious individuals who have devoted themselves 

 to such arduous and important investigations ; it is satisfactory 

 to reflect, that in practical talent the artists and observers of our 

 own age and country are entirely unequalled and without rivals. 

 What artist in any country, but our own, could be put in com- 

 petition with Troughton ? What observer has raised to himself a 

 name so distinguished as thatof Maskelyne, Pond, or Brinkley? 



The skill of the distinguished artist whom I have just named, 

 has succeeded in imparting to comparatively small instruments 

 a degree of accuracy which would scarcely seem compatible with 

 their limited dimensions. Many of the expedients by which this 

 has been effected are very admirable. But there is one which 

 has materially contributed to the well merited esteem in which 

 his instruments are held ; vet the circumstance is curious, that 

 the correction which it is intended to produce is not, in general, 

 theoretically perfect. 



I allude to the expedient which Mr. Troughton has devised to 

 correct, among other errors, that arising from the excentricity of 

 the point round which the indexes may revolve in reflecting cir- 

 cles. 



\n a |)aper on these instruments, by Capt. Mendoza Rios, 

 published in the Philosophical Transactions for 1 801, is the fol- 

 lowing remark : " Two noniuses opposite one another might, 

 however, be advantageous in order to correct the errors of ex- 

 centricity, but in niv opinion a greater number ought uot on any 

 account to be us-ed." 



I know not whether this remark was intended as a hint to 

 Mr. Troughton, who had, for some time previous, made his im- 

 proved circles with three verniers placed at eciual distances from 

 each other on the arc ; but the author of the article " Circle," 

 in Rees's Cijclopcediu, appears to have considered it in that light. 

 He accordingly wrote to Mr. Troughton on the subject, and he 

 has incorporated in the article referred to, a>i extract from Mr. 

 Troughton's reply. Mr. Troughton observes, that " it is plain 

 that two opposite indices will correct this kind of error perfectly, 



Vol..'54. No. 257. S6Y;^ 18U). L and 



