116 Dr Young's theory of Striated Colours. 



becomes 860° for the interval of the two bands, we may always 

 represent the velocity of the oscillations which unite these at 

 any given instant, by the sum of a series of the cosines of the 

 number n of arcs of a circle whose common difference is x ; for 

 example, cos. 4- cos. oc + cos. 2ir . . . + cos. nx, for the in- 

 stant when the velocity of the first oscillation alone is at its 

 maximum ; but it is evident that the entire sum will be a 

 maximum when the mean term is a maximum ; it is easy to 

 see also, that for a considerable number of divisions we may 

 find the sum of the series by representing each term by the 

 narrow space given by the division of a figure of the sine, and 

 the sum of cos. + cos. x + cos. 2x . , . + cos. nx, will be 



nearly n — ^^ = ' ; a quantity whose differential vanishes 



when nx = Tang, nx ; and to find the maxima of light, we 



must take the values for ^ or the half of the lines, and for x 



positive or negative. 



" For the two first maxima beyond the middle, the angular 

 values are 256° 27 =4.4936, and 442° 37 = 7.725, the inter- 

 mediate dark lines being at 180° and 360° of the same scale, 



and for the intensity of the hght, we have — — and — — in 



comparing the squares of the velocities with that of the total 

 velocity of the middle point. 



" This calculation becomes more exact in proportion as the 

 diffractive lines are closer and more numerous, the quantity 



■-— ^ — representing always a finite velocity, though /* becomes in- 

 finite by this multiplication, which happens when we wish to 

 calculate the diffraction of a very narrow pencil of light which 

 enters a dark room by a narrow aperture. But when this 

 pencil is sufficiently long, so that there is a sensible difference 

 between the paths of its different parts with regard to the 

 middle of the card, then the experiment comes under the cir- 

 cumstances of the problems so successfully resolved by M. 

 Fresnel."— -4ww. de Chim. Fexu 1829. 



