Rays of Great Wave-length in Rock-salt, Si/lvite, Sfc. 39 



latter curve might have been observed directly, had the 

 distance between the plates enclosing the reflecting layer of 

 air been sufficiently increased. This curve R ==/(«), which 

 represents the distribution of energy when no interference is 

 present, can be constructed, however, with sufficient accuracy, 

 when at each point an ordinate is erected equal to the mean 

 of the ordinates of the corresponding points of the enveloper, 

 P and Q. If the curve G=/(«) is intersected at any point 

 by the curve B, =/(«), then the amplitude for the abscissa of 

 this point must have the same magnitude which it would have 

 attained had a superposition of the energy of the two beams 

 taken place without interference. 



The vibratory motion of the two beams whose amplitude 

 and period are A and T respectively, may be represented by 

 the equations 



. . _ ft cc\ 



?/ 1 = Asm27r^ 7 j- 1 



?/ 2 ^A sill27T ( 7n 



-r-r X 



tf + K-f- 



They unite to form the ray 



/ T ^ \\ K X 



V OA '( + *> ■ 9 (* ,r+ 2 + i \ 



Y = 2Acos sin 2?r ( r p ) 



K X 



ttK . . /* X+ 2 + 4 



= 2 A sm — — sm zir 



ft- 



X ~~— \T X /' 



It follows from what has been said above that, for the 

 abscissa of the point of intersection of the two curves R and 



ttK 



G, the amplitude of the beam Y, viz. 2 A sin -r— , must equal 



+ A */2. X is accordingly determined from the equation 

 sm y = +|\/^ 



TrK 7T 07T 57T (2?2+l)7T 



T~~I T T'" 4 ' 



where w is any whole number. The wave-length, therefore, 

 of each point of intersection is given by the equation 



2n+r 



A knowledge of the order of the adjacent maxima and 

 minima gives at once an interpretation to the quantity n. If 



