300 C. Barus — Use of Compensators. 



2. Lens systems. — If but a single compensator is to be used, 

 i. e. compensation in one of the component beams only, the 

 lens in question must be of a very small focal power; other- 

 wise the adjustment will be impossible, as the two direct 

 images of the slit will be in very different focal plains. More- 

 over the focal power should be variable. All this makes it 

 necessary to use a doublet, preferably consisting of lenses of 

 the same focal power, respectively convex and concave. If 

 these lenses are themselves weak, say one meter in focal dis- 

 tance, both slit images may easily be seen in the telescope and 

 be sufficiently sharp for adjustment. If the lens first struck 

 by light is convex and the second concave, their focal distances 

 f and/!, respectively, and their distances apart D, the focal 

 power of the combination used is 



l/F=V/fJ, = D/r (1) 



&\nc,Qf=f 1 f i . The position of the equivalent lens is cl = 

 DF/f =f, and it lies on the same side of the doublet as the 

 convex lens. 



In the actual experiment, however, the ra,js go through the 

 lens system twice. In this case it is perhaps best to compute 

 the distances directly. Of the two adjustments, the one with 

 the concave lens toward the grating and the convex lens 

 toward the mirror has much the greater range of focus relative 

 to the displacement D. Supposing the mirror appreciably in 

 contact with a convex lens therefore, if b is its principal focal 

 distance measured from the concave lens, b + D = M its princi- 

 pal focal distance from the convex lens or mirror, 



1 = 2//, ~ V(/, + -P) 1 (2) 



b- i -/>(2// a - ]/(/, + jj)) /; 



where f is the (numerical) focal distance of the concave and 

 f that of the convex lens. If we now write 



b= B(l- 2>(2// a - l/(/, + D) (3) 



equation (2) is easily converted into 



so that the usual value of the principal focal distance has been 

 halved relatively to the new position of the equivalent lens. 



If/ =/,=/."' 



f f — 2Z> 5 f 3 J- 2D 3 



Thus if D increases from 2 to 25 cm., If decreases from 2450 

 to 165 cm., 2B from 2500 to 200 cm., d from 49 to 35 cm. As 



