OP ARTS AND SCIENCES. 401 



power is concerned, this grating seemed better than the one of 17,296 

 lines per inch, — at least under ordinary conditions of the atmosphere. 

 For the dispersive power * we shall have, according to the formula 

 given by Professor Pickering (vol. xi. (n. s. iii.), p. 273, Pi'oc. Am. 

 Acad.), 



dr _ (340) (3) _ 



Ik— .719 — -^^^y' 



the observations being made upon the third order of spectrum with 

 an angle of reflection of 44°. 



To determine the wave-lengths of the thirty-seven lines given in 

 Plate II., it was only necessary to note the position of each line upon 

 the " ej^epiece scale," and, having found the value of a division of the 

 scale in wave-lengths, to reduce the scale readings to wave-lengths 

 and add them to the wave-length of the line upon which the zero of 

 the scale was set. In this way the absolute wave-lengths were made 

 to depend, practically, upon the wave-length of the initial line, as 



o 



assumed from Angstroms chart. 



It was a matter of no small difficulty to decide upon the positions of 

 some lines, owing to their excessive faintness, and discrepancies in the 

 readings are not to be wondered at. A few preliminary measurements 

 were found to be somewhat discordant, but this was probably due to 

 parallax in the scale, which was discovered a little out of focus. I 

 concluded, therefore, that the most accurate results would be obtained 

 by employing a set of measurements all made on the same day, since 

 relative positions only were required. On May 15, 1880, five inde- 

 pendent sets of readings were made, each set including the whole 

 number of lines to be measured. 



The first line of the scale was set upon the line designated h^, by 

 the aid of a slow motion screw, and the readings of the different lines 

 up to b^ noted by estimation to hundredths of a division. A single 

 reading cannot be relied upon within, perhaps, one-tenth of a division, 

 but in some cases it seemed advantageous to attempt a closer estima- 

 tion. Ten readings of the lines W', b^\ If'^, and h^"^ were made. The 

 probable error of a single reading of ¥'' is ± .014 div., and the 

 probable error of the mean of ten readings ± .005 div. Where but 

 five readings were made, as, for instance, 5^^, the probable error of 

 a single observation is ± .028, and the probable error of the result 

 ± .013 scale divisions, corresponding to 0.011 tenth metres. 



o 



* Angstrom iised dispersive powers of 065 and 798. 

 VOL. XVI. (n. s. VIII.) 26 



