528 HENRY A. ROWLAND 



CASE I. SIMPLE PERIODIC RULING 



Let the surface be divided up into equal parts in each of which one 

 or more lines or grooves are ruled parallel to the axis of z. 



The integration over the surface will then resolve itself into an 

 integration over one space and a summation with respect to the num- 

 ber of spaces. For in this case we can replace y by na -\- y where a is 

 the width of a space and the displacement becomes 



g-il)(R-Vt) v e + ibnan I I e +ib (Ax + Ml/) ds , 



but ~bnit. 



n-i - smw 



v 0+ibpan 



sin ba;i 

 Bin -- 



Multiplying the disturbance by itself with i in place of -j- i we have 

 for the light intensity 



I C e-n l * x + /> ds \ I /(.+ ib < Ax + *v) ds\ 



sm - 

 The first term indicates spectral lines in positions given by the equation 



with intensities given by the last integral. The intensity of the spec- 

 tral lines then depends on the form of the groove as given by the equa- 

 tion x = f(y) and upon the angles of incidence and diffraction. The 

 first factor has been often discussed and it is only necessary to call 

 attention to a few of its properties. 



When bafjt*=%7rN, N being any whole number, the expression be- 

 comes n 2 . On either side of this value the intensity decreases until 

 ribdfj! '=2xN, wheniit becomes 0. 



The spectral line then has a width represented by// / M"=T 2^ nearly; 

 on either side of this line smaller maxima exist too faintly to be ob- 

 served. When two spectral lines are nearer together than half their 

 width, they blend and form one line. The defining power of the spec- 

 troscope 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, 



3 An expression of Lord Rayleigh's. 



