240 M. E. Pringsheim on a Measurement of Wave- 



from that employed in determining wave-lengths in the visible 

 spectrum, in which the grating is generally fixed, and the 

 observing telescope can be rotated. 



Let E and E / (fig. 2) be two rays, Fig. 2. 



supposed parallel, incident at and 

 O f upon two neighbouring lines of the 

 grating, and A and A r the two rays, 

 likewise supposed parallel, which re- 

 main at the common interference in 

 T (fig. 1), and whose wave-length is 

 to be measured. Let N and N 7 be 

 the normals erected at and / upon 

 the plane of the grating ; then we 



had, with our arrangement, the case (likewise taken into 

 account in the drawing) that the incident and the observed 

 ray are on the same side of the normal to the grating. If we 

 draw O'P perpendicular to E, O'Q perpendicular to A, and 

 put 00' = d, the angles N0E = N'0'E' = 8, and the angles 

 AOE = A / / E' = S 1 , then the difference of path of the rays A 

 and A! when they arrive at the interference, and consequetly 

 the wave-length X of the rays there remaining of the spectrum 

 of the first order, is 



\=P0+0Q 



= d [sin (PO'O) + sin (QO'O)] 



= eZ[sinS+ sin (8 + 8 )]. 



The complete theory of interference teaches that this for- 

 mula still holds good when, instead of the two rays E and E', 

 a great number of rays are present which are incident upon 

 several apertures of the width d. Since the magnitude of d 

 is known, the measuring of the angles 8 and 8 ± suffices for the 

 determination of X. 



In order to find the incidence-angle 8, first the stand with 

 the grating was placed so that the normal to the grating 

 coincided with the incident ray; and then the number on the 

 scale at which the thread cross of the microscope stood, in 

 this position, was noted. This number we will call a. The 

 grating was then placed so that the direct image of the slit 

 just reached our torsion-apparatus ; let the corresponding 

 position of the thread cross of the microscope be called b. 

 Lastly, by further turning the stand, that orientation was 

 given to the mirror in which the torsion-apparatus was just 

 hit by the extreme rays operative upon it. With this position 

 the thread cross is at the number c ; and since it forms a con- 

 stant angle with the normal to the grating, we can also refer 



