The Reduction of Transit Observations. 



197 



ting the polar stars in arranging the final table of clock corrections. Each 

 star, quick-or slow-moving, should go in, with its proper weight to the 

 clock-correction The method of least squares gives, namely: the most 

 probable values of all the unknowns; and a more probable one than this 

 cannot be obtained in any other way, unless the original system of weights 

 be altered. But this would involve a contradiction; the weight, according 

 to definition, refei's not to the use to be made of the observation, but to the 

 measure of its j)recision. The following example taken from my work on 

 the longitude campaign of 1878 will illustrate several points of this paper. 

 The observer at Fort Bliss (latitude 31° 45') frequently inserted stars 

 subpole in his determinations. As a consequence the weight of the final 

 time determination was less, proportionately, than it otherwise would have 

 been; for a zenith star my formula would give 



1.3 



1 4- 0. z sec'2 31° 45' 



1.415 



= 0.919 



But the group after signals on September 8th contains 11 stars, g'ving a 

 final weight of 6,93; or about that of 8 or 9 stars nearer the zenith; two 

 stars are below pole, and therefore less advantageous. The results of the 

 individual stars (those north of 65° are marked with an asterisk; these are 

 now between 45° and 65°) are as follows: 



Aquarii 



Aquarii 



Aquarii 



Draconis 9 H. sp 

 Groomb. 3834... 



Pegasi 



Pegasi 



Cephei 



BradlevloOSsp. 

 Andromedae . . . 

 Pegasi 



Clock Corr. 



m 



— 1 

 — 1 

 — 1 

 — 1 

 — 1 

 — 1 

 — 1 

 — 1 

 — 1 

 — 1 

 — 1 



s 

 24.79 

 24.89 

 24.82 

 25.28* 

 25.39* 

 24.75 

 24.83 

 25.07* 

 25.37* 

 25.09 

 24.74 



Clamp. 



W 

 W 



w 

 w 

 w 

 w 



E 

 E 

 E 

 E 

 E 



The least square solution gives the mean clock-correction —1' 24". 888, 

 but tliis includes, with their proper weight, the stars marked with an as- 

 terisk. If we omit these, and give all others a weight unity we shall have 

 — 1' 24". 844, or -f-0".044 more. But it is plain from least squai'e solution that 

 some cause affects the observations north of the zenith, probably wear of 

 pivots '; and the mean of the 6 stars south of the zenith gives —1' 24 ".803; 



^ This is conflrmed by theother dates when the same instrument was employed. 



