LONGITUDE OF TORONTO ORSERVATORY. 53 



3. The stars usod by the two observers were difFereut, aud as used by the same 

 observer different on different nights. 



4. The personal equation of the observers may fluctuate slightly between different 

 nights about a mean value. 



If we neglect the variations due to the first three causes, and assume that the pro- 

 bable error of the personal equation, on any night, is proportional to the deduced probable 

 error of the time determination, the above solution will still hold ; if, however, we take 

 the variations on different nights in personal equation, as well as that due to other causes, 

 as being independent of the probable error, as obtained from the observations on that night, 

 the probable error of a single determination will be of the form ^x' + (p. e.)-, where x is 

 an unknown quantity and p. e. stands for the probable error of the combined d7's at the 

 two stations. If now x be taken as .04 sec, the resulting weights become 22, 22, 21, 1*7, 

 22, 21, aud 19, showing very little variation in the weight, and the solution of the thus 

 weighted equations gives a probable error of a single equation = 1 sec. and the resulting 

 value of (7^.102 sec. ± .020, and personal equation .130 sec. ± .019. This solution, 

 therefore, while differing little from it, is not so good as the preceding one for represent- 

 ing the original equations ; for this reason we adopt, finally — 



h. m. e. 



Tlie value of the difl'erence of Longitude Montreal and Toronto . . . = 23 10.106 + .019 

 Longitude of Montreal as determined by exchange with Cambridge . . = 4 54 18.543 + .045 



Therefore the Longitude of the Toronto transit =517 34649 ± .049 



