2 Mr. E. F. J. Love on a Method of Discriminating 



in which approximate equality obtains between a great number 

 of lines in two spectra, one or both of which is so crowded 

 with lines that the question arises, What difference of wave- 

 length between the lines is admissible as a coincidence? 

 This difficulty especially meets us when we are dealing with 

 certain parts of the solar spectrum — especially those obtained 

 from portions of the sun's surface near to, or including, a 

 spot; and Schuster's method gives us no hint towards its 

 solution. 



While engaged in preparing a report on Griinwald's* recent 

 investigations into the relation between wave-length and 

 specific volume, the present writer was led to a simple method 

 of comparison, based on the Law of Error. In accordance 

 with this law, the errors of observation of a single quantity 

 group themselves about the mean value of the quantity in 

 such a way that the number of observations in which the 

 errors are less than some small quantity x is greater than the 

 number in which the}' lie between x and 2.?-, this again is 

 greater than the number between 2x and 3.r, and so on ; the 

 equation between the number of observations and magnitude 

 of error being, as is well known, of the form 

 y = ae- cix \ 



Now since the various spectrum-lines of a substance in a 

 given physical condition are connected by an invariable 

 relation, it seems allowable to assume that observations of 

 the several lines in one spectrum maj r be regarded as different 

 observations of one phenomenon, viz., that spectrum ; as a 

 consequence it is here assumed that, if the differences of 

 the wave-lengths of corresponding lines in spectra really due 

 to the same substance, but determined by different observers, 

 and under different conditions (e.g., the substance as examined 

 by one observer being on the earth; and as examined by the 

 other, on the sun) be compared, they will accord with the 

 Law of Error. The method thence derived is as follows : — 

 The differences between the wave-lengths of the lines com- 

 pared are arranged in groups, each group containing those 

 observations the errors of which lie within certain narrow 

 limits. The number of observations in each group is then 

 plotted as an ordinate of a curve, the average error of the 

 group being the abscissa. If this curve be then compared 

 with the curve given by the Law of Error, any serious diver- 

 gence from the form of the latter curve is at once made 

 manifest. It should, however, be borne in mind that the Law 

 of Error admits the possibility of errors of every conceivable 

 * Astr. Nachr. Bd. 117 ; Phil. Mag. [5] xxiv. p. 354, 1887. 



