The Beduction of Transit Observations. 



195 



It will be noticed that I have introduced no stars at lower culmination. 

 The reason for this is, that unless they are very near the pole, the azimutli 

 CO efficient which they furnish is positive in sign, and the stars which bal- 

 ance them as to the sign of this co-efficient do not as to the form of the 

 pivots. In other words, a combination of stars below and above pole would 

 give the clock correction with a large probable error and with a danger of 

 constant error, while a combination of stars below pole with those at cor- 

 responding south zenith distances would be far less advantageous, owing 

 to the identity of sign in the azimuth co-efficient, and its greater magni- 

 tude for the southern stars, than a combination of stars above pole on the 

 nortli side with the ordinary northern time-stars. 



When the least square reduction is made, the theoretical test of a good 

 combination is obtained by Jacobi's theorem, which I quote below; the- 

 practical test by the quotient. 



Weight of clock-correction. 

 Number of transits 



which should approach the weight of one transit of a zenith star: Practi- 

 cally I usually employ the following formula for the weight or of one com- 

 plete transit (on 5 or more wires, or 7 or more, according to the way the 

 diaijhragm is arranged). 



1.3 



w = 



1 + 0.3 Sec.-<5 



For latitude 42° 42' 5, this gives the weight of a zenith star equal to 

 0.836; in general it is easy so to arrange the groups that the weight of the 

 clock correction from 10 stars shall.be 7 at least; but wlitre lower culmina- 

 tions and southern stars are freely employed this number frequently is re- 

 duced to 5 or less. That is to say, 10 stars well arranged give as good a 

 clock coiTection as 14 ill an-anged; and waste of time spent in computation 

 is thus avoided. The few extra minutes lost in observations are usually of 

 less account; and are pcrhai)s compensated by the greater pains necessary 

 beforehand. In order to modify the weight-formula to advantage more 



