in Theory and Practice. 401 



given by the equation x=f(y) and upon the angles of inci- 

 dence and diffraction. The first factor has been often discussed, 

 and it is only necessary to call attention to a few of its pro- 

 perties. 



When ba/j, = 27r~N, N being any whole number, the expres- 

 sion becomes n 2 . On either side of this value the intensity 

 decreases until nba/jb'=27rl$, when it becomes 0. 



The spectral line then has a width represented by ///—//," = 2 - 



nearly ; on either side of this line smaller maxima exist too 

 faintly to be observed. "When two spectral lines are nearer 

 together than half their width they blend and form one line. 

 The defining power of the spectroscope can be expressed in 

 terms of the quotient of the wave-length by the difference of 

 wave-length of two lines that can just be seen as divided. 

 The defining power is then 



nN* = na p. 



Now na is the width of the grating. Hence, using a 

 grating at a given angle, the defining power is independent 

 of the number of lines to the inch and only depends on the 

 width of the grating and the wave-length. According to this, 

 the only object of ruling many lines to the inch in a grating 

 is to separate the spectra so that, with a given angle, the 

 order of spectrum shall be less. 



Practically the gratings with few lines to the inch are 

 much better than those with many, and hence have better 

 definition at a given angle than the latter except that the 

 spectra are more mixed up and more difficult to see. 



It is also to be observed that the defining power increases 

 with shorter wave-lengths, so that it is three times as great in 

 the ultra-violet as in the red of the spectrum. This is of 

 course the same with all optical instruments such as telescopes 

 and microscopes. 



The second term which determines the strength of the 

 spectral lines will, however, give us much that is new. 



First let us study the effect of the shape of the groove on 

 the brightness. If N is the order of the spectrum and a the 

 grating-space, we have 



/A = i(sin0 + sin y) = — », 



. bafi A 

 since sin —~ =0, 



* An expression of Lord Rayleigh's. 



