ON THE REPEATING REFLECTING CIRCLE. 101 



have pointed out in my former communication to the Society, 

 on ascertaining time. I have also invariably observed alternate- 

 ly the upper and lower limb of the sun during the repetitions, 

 both for the time and latitude ; by which means the true alti- 

 tude of the centre is obtained, independent of the application 

 of the semidiameter. 



Two examples completely worked out accompany this me- 

 moir, which it is hoped will render it clear and explicit. 



In the communication I had the honour to submit to the 

 Royal Society of Edinburgh on the subject of ascertaining time 

 with accuracy, and which was read on the 2d February 1818, I 

 intimated my intention, if that was deemed worthy of a 

 place in the Transactions, to transmit a memoir on the repeat- 

 ing circle, which I now beg leave to lay before them, as I feel 

 confident that the more practical astronomers work with that in- 

 strument, so as to understand it perfectly, the more they will 

 be satisfied with the results obtained from it, which I have al- 

 most uniformly found to be highly satisfactory. Even a small 

 one of five inches radius, executed for me at Paris by Messrs 

 Jakers, has afibrded me additional proofs of the value of this 

 instrument, and the justness of its principle. 



There are one or two remarks that I should wish to make 

 on the subject of the adjustments of the instrument, which I 

 have learnt from some years constant practice in observino- 

 with it, and which I think may not be deemed unworthy of 

 detailing. 



Although the general nature and principle of the adjust- 

 ments are similar to those of the sextant, there are others 

 which differ. In the first place, in order to ascertain whether 

 the great and small mirrors are parallel, I place the index at 

 zero ^, and then bring the sun seen direct and reflected in 



contact, 



