Wave-lengths in the Invisible Prismatic Spectrum. 211 



Lay off upon a line, AB (fig. 4), any convenient distance, and divide 

 it into equal spaces to represent the normal wave-length scale, and upon 

 a hue CD, at right angles to the first, lay off the same distance and divide 

 it into the same number of parts, spaced according to the law of disper- 

 sion of the prism, as in the wave-length scale marked on the bottom of 

 the prismatic chart (plate iii. this Journal, vol. xv.). Erect ordinates 



Fig. 4. 



at the points of division, and mark them with the proper wave-lengths, 

 beginning on both lines at the ends which lie nearest to each other, as in 

 the figure, where five ordinates are shown ; through the intersection of 

 corresponding ordinates draw the curve EF, and upon CD draw the curve 

 of distribution of energy in the prismatic spectrum. 



Let a, fig. 3, be a very small wave-length interval on the prismatic 

 scale ; c the same interval on the normal scale, and b and d the average 

 heights of the energy-curves over the two intervals respectively ; the 

 shaded part of the figure representing therefore the portion of the 

 total area included between these limits, e/is a portion of the curve EF, 

 Hg. 4. Then, according to the condition of transformation, 



whence 



cd=ab, 

 b :d::c:a. 



From geometrical considerations, 



c : a • : 1 : tan 0, 



where is the angle which the chord EF, joining the intersections of the 

 two pairs of ordinates, makes with AB ; consequently 



b : d : : 1 : tan 0, 



from which d== b tan <p, 



P2 



