28* Mr. Nixon's New Method of Levelling 



are required, being so very simple, and the calculation being 

 more than sufficiently accurate if conducted with five decimal 

 places, the time required for the calculation is not very con- 

 siderable. If cases should occur in which observations only 

 for which x exceeds 90° could be combined, one might either 

 directly calculate the formula, or use this form : 



It appears to be most convenient to begin with trials of 

 assumed values of a. We have agreeably to the above-given 

 notation : 



« = i(E,-E3)-i(E,-E,). 



It will easily be decided whether a is to be taken negative 

 or positive, whenever it diifers considerably from 0. If there 

 is no semi-revolution between any two successive observations, 

 a will always be < 45°. The quantities /3 + «, y + /3, being 

 by their nature always positive, and at the same time < 180°, 

 if the period of the observations does not embrace a whole 

 revolution the quadrants in which ^ and y are to be taken, are 

 consequently fully determined. 



As soon as a, /3, y and then likewise a b have been deter- 

 mined, only two of the equations (4) are required for deter- 

 mining a, 6, and 5, and for obtaining, consequently, the pro- 

 jected ellipsis in magnitude and position with regard to the 

 star at rest. If, however, we have been at the trouble, which 

 cannot well be dispensed with, of adapting all four observa- 

 tions to the same ellipsis, we may obtain these data more 

 easily by a symmetrical combination of the same. 



[To be continued.] 



XXXVII. New Method of Levelling the Axis of a Transit 

 Instrument. By J. Nixon, Esq.* 



TN the subjoined figure, A is an achromatic object-glass, 

 -*■ firmly secured within one of the pivots of the hollow axis of 

 the transit instrument, a is a stop furnished with adjustable 

 cross lines placed within the other pivot exactly at the sidereal 

 focus of the object-glass A. 



B is another object-glass fixed within the opposite pivot 

 having its corresponding stop and cross lines situate at b. 



D and E are two upright columns, each carrying a hori- 

 zontal bar to which a pair of Ys is fastened. These columns 

 might be attached to the Ys of the transit, but it would be 

 more prudent to fix them independent of it. 



* Communicated by the Author. 



Cis 



