S86 Oil ilie Divisions of a$tronoiniccd Instruments, 



against the whole circle, or against the muliiple of it, which 

 appn^achcs nearest to the circle, and from thence to deduce 

 its value in ihc manner explained above, and we shall either 

 have entirely excluded tlie error which we apprehended, or 

 have rendered it too snudl to bo of any importance. Sup- 

 pose, for instance, that the arc determined by the observa- 

 tion was 4 8"^; then by measuring it against the whole cir- 

 cumference increased by an arc of 24-, we shall obtain a 

 result free from any greater error of unequal temperature, 

 than one eighth of the increase or decrease of this arc of 

 24^ beyond a due proportion to that of the circle itself. 



This expedient gives us all the advantages of the French 

 circle of repetition, without the inconvenience arising from 

 being obliged to turn the instrument, and move the tele- 

 scope, so many times in the course of the observation. 

 Nay, r am p;rsuaded that the result may be made more 

 accurate in this way than by the French method, because 

 not only can the object be more frequently observed, but 

 the contacts or bisections, it may be presumed, will be 

 more exact when the observer is not disturbed by the hurry 

 attendant upon the use of the repeating circle ; and with 

 respect to any error in the instrument, from whatever cause 

 it may arise, it will be as effectually excluded by the process 

 which I recommend, as by moving the telescope round the 

 circle. Besides, this method is applicable either to the 

 azimuth or altitude circle, or iudeed to any circle which 

 turns upon its own axis ; whejeas the French method can 

 never be applied to the azimuth circle, nor to any other 

 circle which does not turn both upon its own axis and 

 upon one which is perpendicular to it. 



After all, however, it is possible that the process which 

 I have been explaining to you may be no new discovery, 

 and that you may be already acquainted with it. If this 

 should be the case, you will be kind enough to inform me. 

 At any rate, indeed, I should esteem myself greatly obliged, 

 if vou would favour me with your sentiments upon the 

 subject, as soon as you can do it with perfect convenience 

 to yourself. 



I am, dear sir, yours, 8cc. 



William Lax. 



XLVIL Or, 



