376 PKOFESSOR C. PIAZZI SMYTH ON THE 



more proper in the present case, and respectful from myself to older observers, 

 seeing that double-star measuring is one of the most refined and diflBcult branches 

 of practical astronomy, where few persons succeed without much longer expe- 

 rience of it than has fallen to my share ; and in which, from the nicety of the 

 micrometrical apparatus employed, it is always possible to read off an observa- 

 tion, and record it on paper to very many more decimal places than it can really 

 be trusted to. 



A. — 5. Prohahle Error of Observation. 



Now these errors in my work at Elchies I believed were always large, not 

 only for the reasons given above, but also because the number of nights that any 

 object was observed was seldom more than two or three, and sometimes only 

 one ; and because, too, the definition of the atmosphere was almost invariably, 

 on every occasion that I looked through the telescope, so extraordinarily bad, 

 that every star, instead of appearing like a proper typical stellar point, was 

 blurred into a more or less, and often exceedingly large, and therefore corre- 

 spondingly faint, nebulous patch or wisp of light. — (See Royal Astronomical 

 Society's Monthly Notices for November 1862, p. 3, and p. 13.) 



Whereas, therefore, most observers assign to their best measures a Aveight of 

 10, and to their worst a weight of 1 only ; I, while keeping to their upper limit 

 for an ideal best, have often in practice found it expedient to go lower still than 

 their lowest, and to divide their 1 into tenths. 



These numbers will accordingly be found set down against every Elchies 

 observed quantity ; and it is expected that any astronomer who hereafter may 

 use the quantities for purposes of his own, will duly refer to the numerical weight 

 attributed by their ol3server. Yet the numbers, after all, indicate only an 

 opinion or marked impression, which may be biased either way ; and the number 

 of observations of each object is too small to allow of estimating the degree of 

 probable error on any rigid mathematical basis, with a logical prospect of prac- 

 tical success ; something else therefore, and more suitable to the case, is absolutely 

 required ; and with the view of attempting to furnish such a desideratum, I 

 have compared my Elchies observations, in each of the four features above 

 enumerated, with the mean determinations brought up from the " Cycle," and 

 other standard authorities; i.e., whenever the stars concerned appeared to be 

 relatively fixed and constant, or very nearly so, in order to avoid being misled by 

 any large change, depending on time. 



The results of this comparison are given in the two tables below, whereof the 

 first refers to " Magnitude" and " Colour," which are mere matters of approxi- 

 mate estimation; and the second to " Position" and " Distance," which, being 

 affairs of micrometric measurement with all available accuracy, have had more 

 care bestowed upon them. 



