ASTRONOMICAL CIRCLE. , 209 



ced from different stars. This method is founded upon the 

 supposition that halt the difference of the two extreme quan- 

 tities is the greatest error of division, which has in this case 

 influenced each result in an opposite direction. For instance, 

 let us suppose the errors of division never to exceed 2", but 

 occasionally to amount to that quantity, on several parts of the 

 circle; it will then sometimes occur that each index will give 

 2" too much in one position of the instrument, and 2" too 

 little in the other; there will then appear a difference of 

 4'' in the error of collimation ; but the observations in these 

 extreme cases will not on that account be the less to be de- 

 pended on ; on the contrary, the probability is in favour of 

 their superior accuracy. 



Nor, on the other hand, will those observations which give 

 the mean error of collimation- deserve greater confidence than 

 the rest^ since it is evident that some of them may be, and 

 most probably are, affected with the greatest possible error; 

 for we suppose the mos't erroneous observation to arise from 

 the greatest error of division occurring on each of the four arcs 

 4n the same sense, that is all plus or all tninus; nevertheless, 

 the observation thus erroneous, will give the mean error of 

 collimation. 



By an attentive consideration of these circumstances, correc- The great ac- 

 tions might perhaps be obtained which would somewhat dimi- curacy of ob- 



• 1 ,1 11 -I- r r, ■ ■ 1 • • 1 r .1 serving by cir- 



rush the probabihty or error, but it is to the principle ot the (.^,13^ instru- 



revolving microscopes, that in the future construction of in- '"ntnt is to be 



struments we should look for perfection. , In the French circle the'^revolvhi'g* 



of repetition, too great a sacrifice is made to the supposed rnicroscopes. 



advantage of reading off'a great number of observations at once. 



Our best instruments are too well constructed to stand in need 



of this contrivance, as the divisions on a two-feet circle are 



read off with precision to a single second. The errors of simple The method of 



division alone are those which continued observations have no no^ correct "he 



tendency to diminish ; these, by making the microscopes errors of divi- 



revolve, maybe completely done away. An instrument thus "°"' 



constructed would be well adapted to detect small motions in 



the fixed stars which hitherto have escaped notice, or such as 



are but imperfectly known , for we cannot reasonably conclude 



that what is termed the proper motion of a star, is so uniform 



and constant, that being once determined, it will remain 



always the same. 



VoL.XVL— March, 1807. U X 



