14 



oliscrvatiuns, especially in tlie cas^e of one or two lines in the measurement, of 

 wiiicli great care had been taken, it proved to he a correction whicli would not 

 correct. .It therefore became uecepsary to make a redetermination of this con- 

 stant. It was found upon trial to he ]iossihle to raise the temperature of the 

 room ill which the spectrometer was mounted, as high as 18° or "20° C, when 

 the temperature outside was much lower and to keep it nearly constant for a 

 considerable length of time. A series of measurements was therefore made 

 upon a fine line, near to ?/|, wliile the temperature of the room was low and 

 tlien afterwards it was raised to about 18° and another series made upon the 

 same line. Tliis plan avoided the principal difliculties met w'itli in the preceding 

 and Ihe result is, without doubt, much more reliable. The lower temperature 

 was nearly 4°, the results being reduced to that, and the upper differed little 

 fnmi 18°, to wliich the measurements at the high temperature were reduced. 

 Thus tliere was a range of 14° whiuh is grcatc-r thim that of the previous deter- 

 minal inn. 



From these observations the following was obtained ; — 



db = 3".89 rh 0."03 



h = 44° 56' .TO" 



and for tlu; coefficient of expansion 



e = .0000189 



the pndiable error of whicli is less tlian one percent of the \\liole. The result 

 of the first determination was, — e = .0000202 and without doubt there existed 

 some source of constant error wliich was not detected. 



'J'he direct method of applying this correction would lie, of course, to 

 determine the value of the grating space for such degree of temperature at wliich 

 an angular measurement was made. It has been found to be much more conve- 

 nient, however, to apply it directly to tJie angular measurement itself, li b and 

 bi be the angles for the two lines we shall have, since c is constant, — 



cot bdh = cot //| (//>i 



cot b 



or dhi = r-. db 



cot (<| 



Thus having determined the value for one line, by observations at difi'erent tem- 

 peratures, that for any other line can be easily computed. 



In this \vay all of the angular measurements ha\-e been reduced to a common 

 temperature of 18°, which is also the tmupcraturc a.ssumed ftu' the grating space. 



COKKECTION FOR BAROiMETRIC VARIATION. 



The observations may be assumed to have been made, in general, under a 

 standard pressure of 700 mm. With a single excc])tion, it has happened that 



