278 PROFESSOR AIRY ON THE LATITUDE 



and reduced with the assumed co-latitude 37° . 47' . 6,"83 : those de- 

 termined from the lower transits of the star have the negative sign. 

 For refraction, Bessel's tables are used. The fourth column contains 

 the seconds only, as corrected for the errors above described ; this 

 has been done by taking the number of observations in each position 

 of the telescope on the circle, and finding the mean correction, 

 supposing that to each observation the correction proper to that 

 position was applied. The negative sign has still been retained for 

 the lower observations. The fifth column contains the whole number 

 of observations in each position of the star : and the sixth contains 

 the mean N.P. D. for each position, as inferred from the combina- 

 tion of direct and reflected observations. The seventh contains the 

 whole number of observations for both positions. The eighth contains 

 the algebraic sum of the two determinations of N.P.D., as the star 

 is above or below the pole. If the assumed co-latitude were correct, 

 this sum would = ; if the assumed co-latitude be increased by x, 

 this sum would be increased by ^x, and therefore to make it now 

 = 0, X must be taken = — i x sum in 8th column. The results, as 

 might be expected, are however different for different stars, though 

 the difference is much smaller than I could almost have hoped ; the 

 extreme difference in the correction of latitude being 1,"3, and this 

 being the difference between two results from stars nearly in the 

 same parallel (shewing that it does not arise from error in the cor- 

 rections above described), and which had been not much observed. 

 It now becomes necessary to determine how the relative importance 

 of these results shall be estimated. It would not be right to give 

 a value proportionate to the number of observations, because part of 

 the discordance may be produced by errors of division and other 

 causes which, in the observations of a single star, produce constant 

 errors. The ninth column contains the immbers by which (from my 

 estimation of the comparative influence of constant and variable errors) 

 I suppose the value of each result to be estimated. The tenth con- 

 tains the product of the corresponding numbers in columns 8 and 9- 

 The sum of the numbers in column 10 being divided by the sum of 

 those in column 9, gives + 2",82 for the double correction, or + 1",41 



