56 PROFESSOR STOKES, ON THE DYNAMICAL THEORY OF DIFFRACTION. 



A comparison of the two tables will leave no reasonable doubt that the experiments are 

 decisive in favour of Fresners hypothesis, if the theory be considered well founded. In con- 

 sidering the conclusiveness of the experiments, it is to be remembered that on either the first or 

 second supposition respecting the place of diffraction, (and the third certainly cannot apply to 

 the case in which the grooved face is turned towards the incident light,) the planes of polar- 

 ization of the diffracted light are crowded by refraction towards the perpendicular to the plane 

 of diffraction, and therefore the observed crowding towards the plane of diffraction does not 

 represent the whole effect of the cause, be it what it may, of crowding in that direction. 



If /3 be the value of a - nr for ■zsr = 45°, /3 = 1° when log to = .015, nearly; and when 

 log m is not large, /3 is nearly proportional to log to. In this case /3 is nearly the maximum 

 value of a - w. Hence the greatest value of a — w, expressed in degrees, may be obtained 

 approximately from Table IV, and, within the range of observation, from Table III, by 

 regarding the decimals as integers and dividing by 15. Thus, for logm= - .388 the real 

 maximum is 24°.8, and the approximate rule gives 25°.9, so that this rule is abundantly sufficient 

 to allow us to judge of the magnitude of the quantity by which the two theories differ. For 

 6 = 60°, the two columns in Table III headed " I", as well as those headed "III", differ by .602, 

 and those headed "II", differ by .169, so that the values assigned to /3by the two theories differ 

 by about 40° or 11°, according as we suppose the diffraction to take place in air or in glass. For 

 = 40°, the corresponding differences are 15° and 6°, nearly. These differences, even those which 

 belong to diffraction within the glass plate, are large compared with the errors of observation ; 

 for the probable cause of the large errors in experiment No 15, has been already mentioned. 



In the following figure the abscissas of the curves represent the angle of diffraction, and the 

 ordinates the values of log to calculated from theory. The numerals refer to the three supposi- 

 tions respecting the place of diffraction, and the letters E, A, (the first vowels in the words 

 perpendicular and parallel,) to the two hypotheses respecting the direction of vibration. 

 The dots represent the results of the experiments in which the grooved face of the glass plate 

 was turned towards the polarizer, and the crosses those of the experiments in which it was 



turned in the contrary direction. 



III. E. 



• I. E. 



II. E. 



II. A. 



III. A. 



I. A. 



The smallness of log to in experiment No. 23, to which the 5th dot belongs, is probably due 



