258 Theory of Transit Corrections. 



Art. XXI. — Theory of Transit Corrections ; by Enoch F. Burr. 



An accurate determination of the element of time is so essen- 

 tial to the purposes of astronomy, that whatever may serve to 

 to simplify or illustrate the modes of obtaining it, may justly 

 be deemed of importance. 



In expounding the theory of the transit instrument, the reason- 

 ing necessarily partakes much of a metaphysical character. From 

 this causey combined with limited space, a specific object or the 

 necessities of a popular exhibition, arise certain assumed prin- 

 ciples and partial demonstrations in our ablest treatises on the sub- 

 ject. This fact gives occasion for a few supplementary reason- 

 ings on the principles of the transit corrections. 



There are four prominent corrections to be made in the appli- 

 cations of the transit instrument. These are for errors of obser- 

 vation, inequality of the intervals between the wires, the time 

 of passing over these intervals, error of collimation and deviation 

 of the optical axis from the plane of the meridian. A few sug- 

 gestions will be made with reference to these corrections in their 

 order. 



An observer is liable to error in estimating the instant at which 

 a star transits the wire which indicates the plane of the meridian. 

 To correct for this error, and reduce its probable amount, other 

 wires are introduced into the focus of the instrument, and a 

 mean taken of the times of the transits over them all ; and the 

 reduction is proportional to the number of wires introduced. 



Let e— error of one observation and -= the mean of a number 



n 



ef 



of observations. Then - is probably less than e. There is no 



probability that e is less than - when all the errors denoted by e' 



are of the same sign, and one expression in this case has no advan- 

 tage over the other. But these errors probably have not all the 



same sisrn : but. snm*> am nooati™ ~.t.;i_ ~+u~_„ „«^ ^citiw and 



cancel 



nd 

 advantage 



ujiho tcim iu cancel eacn otner. This constitutes an aavauw^ 

 of the latter expression and renders it probably less than the first- 

 The diminution of error by takine a mean, is probably in pr°" 



e 



portion to the number of observations. Let - = the mean error 



n 



of a number of observations, and —r% - the mean error v> hen 

 the number of observations is increased by unity. Then jTi 



