135 



In the second place, it seems probable that some cause remains in 

 action during a whole night, modifying the result, whose origin and 

 law remain to be discovered, but which seems tolerably constant in 

 its operation. 



The observations of my Catalogue of double stars are drawing to a 

 close, and it became extremely desirable that if there were any fault 

 in the reductions or method of computing hitherto employed it 

 should be speedily remedied, and the necessary corrections made ; I 

 therefore applied to the Astronomer Royal, stating the embarrass- 

 ments arising from the above-mentioned causes, and requesting his 

 opinion as to the best mode of proceeding. The Astronomer Royal 

 exhibited on this, as on all other occasions, where his aid has been 

 solicited, the greatest readiness to give me the benefit of his extensive 

 knowledge of all that appertains to Astronomical science. 



Mr. Airy observed that if there were a constant cause of error on 

 any night, no multiplication of observations on that night would tend 

 to remove it, and in that case he knew of no mode of proceeding 

 which would quite meet the difficulty but the adoption of the follow- 

 ing formulae. 



Assuming that all the observations are equally good, or can be 

 made so by grouping discordant measures, let f be the probable error 

 of a single observation, and e the probable value of the error of each 

 night. Let S 15 S 2 , S 3 , &c. represent the sums of the squares of the 

 errors obtained in the usual manner from the observations on the 

 first, second, third, &c. nights respectively, and put n lt n 2 , &c. for 

 the number of observations obtained on each of those nights ; then 

 the observations of the first night give, 



-4549x8,; 

 those of the second, 



( W2 -l)/ 2 =-4549xS 2 , 



and so on: and from the sum of all these equations /may be accu- 

 rately determined. 



Then to find e, compare the mean result obtained from the obser- 

 vations on all the nights, i. e. the mean of all the means, with the 

 separate means for separate evenings ; then putting S for the sum of 



L2 



