388 



HAMILTON'S CHARACTERISTIC FUNCTION 



In certain cases of practical importance the characteristic function may be 

 greatly simplified. For instance, when the axis ray is refracted in one plane 

 through the prisms of a spectroscope, the same positions of the axes of x and y 

 which make / and r vanish, also make c, and c, vanish. The determinant A may 

 now be written as the product of two factors 



, 



+*) (+*)- 



+ 



....(26). 



If we write 



M I= -r- 1 - = 



PA 



v,= 



i ~ - ft ^ ^_ ' * 



7l s'-feA ' g *~ t-\ 



(27), 



the characteristic function becomes 



(28). 



Since in this case the terms of the characteristic function which involv,- 

 x t and x t are separated from those which involve y l and y,, we may consider 



