SOLAR ECLIPSE, MAY 6, 1883, 109 



We see at once that 



A_a 



for if this is not so, either some portions of the image lens can never send liglit to any portion 



of the collimating lens, or some parts of the latter never receive liglit from the image lens; in 



snch cases either A or a ceases to be the effective aperture. 



The quantity of light (Q) falling on a minute square of slit, measured from the image lens, is 



evidently, 



Q=i^A'^5. 



To find the quantity falling on a unit surface of the slit we must divide Q by the value of a minute 

 square expressed in area. If we denote this quantity by Q/ we may write 



The function of the collimating lens is to form a distant vertical image of the slit. The bright- 

 ness of this image may be expressed in the same way as that which we have chosen to exi)ress the 

 brightness of the source, namely, by the quantity of light from a minute square of its area falling 

 upon a unit surface. Let us denote this quantity, which is a measure of the brightness of the 

 image, by q'. Now, we have already obtained an expression for the total quantity of light, Q', 

 falling upon the whole of the collimating lens from a unit area of the slit. To find q', then, 

 we have only to divide Q' by the area of the collimating lens and by the value of a unit area 



of the slit expressed in minutes square. The first of these divisions is \ -«'-, the second is ^r^, whence 



O' A'' f- 



that is to say, the brightness of the image is the same as that of the source, and this perfectly 

 independently of the apertures of the system used. 



We may arrive at the same couclusion, by a process of reduciio ad ahsurdum, very briefly, thus: 

 Suppose q' less than q, then, since there are no limitations as to the values of F and /, we may 

 make them infinite without change of angular apertures. In this case we have reduced the quan- 

 tity of light by introducing media which are assumed to have no action on light, which is absurd. 

 Again, suppose q' greater than q, then we have simply to regard the image as the source of light 

 in a similar apparatus in which the image will be brighter than </'. Thus, by successive repeti- 

 tions, we may increase the brightness indefinitely — an evident absurdity. 



Hitherto we have not regarded the portions of the spectroscope which follow the collimator. 

 Of these the system of prisms or the grating forms a virtual spectrum of the slit at the same dis- 

 tance {i. e., infinite distance) from the collimating lens as the image itself, since only plane surfaces 

 are concerned in the action. In order to determine the brightness of the spectrum we have here 

 to distinguish between two cases. We assume, as we have tacitly done heretofore, that there is 

 no loss either bj' reflection or absorption. Then, if the light is strictly monochromatic, or is com- 

 ])osed of determinate wavelengths, the brightness of the spectrum dejiends solely ujion the bright- 

 ness of the image of the slit. In the second case the light is such as to yield a continuous spectrum. 

 Then its brightness is proportional to the brightness of the slit-image and to the width of the slit, 

 and inverselj' proportional to the angular dispersion of the prism or its substitute. 



The function of the telescope is simply to aid in observing the virtual spectrum, and the laws 

 governing the apparent brightness as seen through the telescope are the familiar laws of telescopic 



