] 52 Notices respecting New Books. 



M-r-d- the apparent intensity of our artificial star at the distance d 

 from the eye." 



In order to prepare the observations for reduction, all the measures 

 of each star taken on the same night must be collected, and the mean 

 taken. The results being then computed according to the formula 

 M-^d*, the influence exercised on the comparisons by the illumina- 

 tion of the general surface of the sky on which the stars are seen 

 projected, becomes at once apparent on comparing the results for the 

 same star obtained from observations on different nights. Taking a 

 Centauri, for example, some of the results were as follows : — 0*443, 

 0-259, 0*156, 0-505, 0*838, &c. " Such enormous differences show 

 clearly, that, as a formula of reduction, the above is utterly inappli- 

 cable. Indeed, at first sight, it would almost appear from this that 

 absolutely no conclusion can be drawn from the observations or the 

 method in question. This, however, is very far from being a correct 

 view of the subject, since, if instead of comparing the results in this 

 manner for a single star, we take any two stars which occur together 

 in more than one series, and compare, not the absolute numbers result- 

 ing from the formula in question, but the ratios of those numbers, 

 we shall find, not, indeed, a precise, but, with a few exceptions (such 

 as might be expected in the first trials of a new method) a reasonably 

 good accordance." — P. 363. 



Each pair of stars occurring in the different series being thus 

 compared, and the mean of the results taken, a set of provisional or 

 temporary values is obtained, expressing the intrinsic light of each 

 star in a scale in which a Centauri is represented by 1. But these 

 numbers, though a process of considerable labour has already been 

 employed in obtaining them, are destined merely to afford a handle 

 for a complete and impartial reduction of the whole, which is accom- 

 plished as follows : — Taking /i-r-d 2 for the expression of the light of 

 the compared star, /u will be a coefficient which may be regarded 

 as constant throughout any single series. The immediate object, 

 then, is to assign for each series such a value of /x as shall give con- 

 sistent results when the individual values of /i-f-rf 2 for any one star 

 deduced from different series are compared together. Now, calling 

 the provisional values obtained as described above S, S', S", &c, 

 and denoting by d, d! , d", &c. the distances of equalization of any 

 number of the stars observed in any series, we ought to have for that 

 series 



fi =Sd*=S'd'2=S"d"z=&c. 



But this being only approximately true, a mean value of jw, is deter- 

 mined for the series in question by taking a mean of all these values, 

 and with the mean value thus obtained the values of <S, S', S", &c. 

 are recomputed by the formula S=[i-i-d % for each star, and for every 

 series in which it occurs. In this manner, as many different values 

 are found for each star as there are series into which it enters, and 

 the means of these values being again taken, the results are finally 

 reduced so as to bring them again to a scale in which * Centauri is 

 (as originally proposed) represented by 1-000. By these successive 



