PROFESSOR STOKES, ON THE DYNAMICAL THEORY OF DIFFRACTION. 53 



The reader will please to remark that in order to follow the observed values of a — 73- 

 beginning with sr = 0°, and going in the positive direction, it will be necessary to begin at the 

 top of the table and go downwards, taking the upper number in each bracket. In order 

 to go in the negative direction from sr = 0°, it would be necessary to begin at the top 

 and go downwards, taking the under number in each bracket. A nearly constant error 

 appearing in the table of differences would indicate merely that the value of e used in the 

 reduction was slightly erroneous. A slight error in e, it is to be remembered, produces no 

 sensible error in log m, whenever the observations are balanced with respect to one of the 

 standard points. 



In the first two experiments entered in the table, the crowding of the planes of polarization 

 is so small that it is masked by errors of observation, and it is only by combining all the ob- 

 servations that a slight crowding towards the plane of diffraction can be made out. In all the 

 other experiments, however, a glance at the numbers in the second column is sufficient to shew 

 in what direction the crowding takes place. From an inspection of the numbers found in the 

 columns headed "diff." it seems pretty evident that if the formula (49) be not exact the error 

 cannot be made out without more accurate observations. In the case of experiment No. 15, 

 the errors are unusually large, and moreover appear to follow something of a regular law. In 

 this experiment the observations were extremely uncertain on account of the large angle of dif- 

 fraction and the great defect of polarization of the light observed, but besides this there appears 

 to have been some confusion in the entry of the values of ■&. This confusion affecting one or two 

 angles, or else some unrecorded change of adjustment, was probably the cause of the apparent 

 break in the second column between the third and fourth numbers. Since the value of log m 

 is deduced from all the observations combined, there seems no occasion to reject the experiment, 

 since even a large error affecting one angle would not produce a large error in the value of 

 log m resulting from the whole series. In the entry of experiment No. 12 the signs of "or have 

 been changed, to allow for the reversion produced by reflection. This change of sign was 

 unnecessary in No. 11, because in that experiment the polarizer was actually reversed. The 

 results of experiment No. 12 would be best satisfied by using slightly different values of the 

 index error of the analyzer for the three images, adding to the assumed index error about 

 — 1^°, + 1 J n , + 2°, for the first, second, and third images respectively. The largest error in the 

 third columns, 2.7°, is for ■ar = + 25°, third image. The three readings by which a was 

 determined in this case were - 1.5°, - 13°30', - 12° ? Hence the error + 2.7°, even if no part of 

 it were due to an index error, would hardly be too large to be attributed to errors of 

 observation. 



Since the formula (49), even if it be not strictly true, represents the experiments with 

 sufficient accuracy, we may consider the value of log m which results from the combination of 

 all the observations belonging to one experiment as itself the result of direct observation, and 

 proceed to discuss its magnitude. Let us consider first the experiments on diffraction at 

 refraction, in which the light was incident perpendicularly on the grating. 



Although the theory of this paper does not meet the case in which diffraction takes place at 

 the confines of air and glass, it leads to a definite result on each of the three following supposi- 

 tions : 



