Mr. J. Barton on the Inflexion of Light. 267 



computations are performed, referring necessarily to FresnePs 

 Memoir, in the 5th volume of the Memoirs of the National 

 Institute, for further particulars; since it would scarcely be 

 possible to explain the process at length without transcribing 

 a considerable part of that memoir. 

 Assuming the distance of the slit from the opening in the 



shutter = a. 



The distance of the slit from the paper on which the 



raysare received =; b. 



The width of the slit = c. 



The length of an undulation...* = A. 



Then, according to Fresnel, the intensity of the light at the 

 centre of the spectrum varies as 



(f d v cos q v -) 2 + {fdvsmq v 2 ) 2 



q representing the fourth part of a circumference to radius 1, 

 and the integrals being each taken from 



V ~ 2V abX ' t0 * 2V abX ' 



As these expressions do not admit of being integrated directly, 

 the author has given a table of their numerical values for each 

 value of v *. Now we have to find the value of v when the 

 first dark band falls on the centre of the spectrum ; in other 

 words, the smallest value of v at which the intensity of the 

 light becomes a minimum. On reference to the Table, it will be 

 found that this value of v is somewhere between 1*8 and 1*9; 

 and by interpolation, for which purpose the theorem employed 

 by the author f may be conveniently used, the exact value of v 

 sought is 1-875; we have, therefore, 



L JL / *■(*!*? 3) 



2V ab\ ' 



1-875 



* Memoirs of the National Institute, vol. v. p. 408. 



f " Supposing the curve which has for its ordinates the intensity of the 

 light at three nearly adjacent points to coincide within that small space 

 with a curve of the second degree, the position of the least ordinate will 

 be given by the formula 



Z ~ 2('p"z-"p / z'' 

 where z' and z" represent the distances of one of the extreme points from 

 the two others; 'p and "p the differences of their intensities, and z the 

 distance of the same point from the minimum." — P. 435. 



It may be observed that this formula is not analytically exact. The 

 true value of z is 



>p»zi-» p'z>- 1 V "p{! p-"p) 

 2('p»z-"p»e') 

 but when the differences of intensity are not considerable, the last term 

 may be neglected as evanescent. 



2 M 2 



