ASTRONOMICAL CIRCLE. 207 



of the circle, bat only insures a similarity of position in the in- the miscro- 



dex, for each position of the instrument; and, provided that the ^?"^^^' '^^"''^^ 



phimb-lime apparatus was free from all danger of derangement, and each obser- 



this. would be sufficient. This verification may be rendered vation is made 



perhaps more intellieible, by considering that a circular instru- '^'^"'.^ corres- 

 r r b ' J o _ ponding one, 



ment, in whatever manner its vertical axis be placed, indicates afier leversing 



by a double observation, the angle v/hich the objectmakes with. ^'^^ instrumt. 



Ill ^ziniiilitt 

 the axis, round which the whole instrument has revolved in 



passing from one position to the other. For let P/j be the axis, 

 Tx the telescope x in one position; it is evident, that in turn- 

 ing the instrument half round, iy will then be the position t of 

 the telescope; Vx being equal to Py. The arc xy, which the 

 telescope passes through to regain i'jfi former position^ is the 

 quantity really given by the instrument; and if the axis Pp be 

 vertical, half this quantity is the true zenith distance of the 

 object. Now the intention of Mr. Troughton's verification is 

 to insure a vertical position to the axis ?p. 



For instruments which rest on moveable pillars, and turn Objection, that 

 freely in azimuth, this method is much to be preferred; but it ^'"'^ corres- 



-1)1 r r n ^ ponding ODSCr- 



is not without a considerable defect: for, if by any derange- A-ation cannot 



ment in the plumb-line apparatus, the error in collimation be ^^ ''^^ ^^ ^''® 



, , . , , , 1 •,. - • r ' plumb-line 



changed, it cannot be restored with certainty to its former po- should be de-. 



sition; so that sometimes a very valuable series of observations ranged. 

 may be lost, for want, of a corresponding one to compaio- with 

 it. The mode which I propose to adopt to remedy these in- 

 conveniences, will enable us to combine all the advantages of 

 the two methods above described: it is extremely simple in its 

 principle, and easy of execution, for it merely consists in unit- 

 ji)g on the same plumb-line the two principles already explained, 

 t .Two very fine holes should be made in the farther limb of Union of both 

 the circle, and two lenses firmly fixed opposite to them, jn "methods m one 

 the other., which should each form an optical image of its 

 corresponding dot or hole, in the tube through which the 

 plumb-line passes.* It will be best, if these dots are made 



exactly 



* As these transparent dots are int-ended to be bisected by the 

 plumb-hne, they must be capable of the necessary adjustmentSj both 

 for distinct vision, and for pb.cing them in an exact diameter. 



It may be found more convenient in practice to arrange the whole 

 apparatus in sliding tubes, but in whatever way the contrivance be 

 executed, the points should ultimately be fixed as firmly as the divi- 

 sio;^$ of the instruments. 



