44 PROFESSOR STOKES, ON THE DYNAMICAL THEORY OF DIFFRACTION. 



ment 6 was liable to changes to at least that extent in consequence of the changes in the 

 direction of the light. The same remark applies to i, the angle of incidence, in experiments 

 11 and 12. In these experiments the three principal images already described were observed 

 separately. The angle of diffraction is measured from the direction of the regularly reflected 

 ray, so that i is the angle of incidence, and i + 9 the angle of reflection, or, in the case of the 

 images which suffered one internal reflection, the angle of emergence. 



The eleven experiments which are not found in the following tables consist of five on 

 diffraction by reflection, which did not appear worth giving on account of the superposition of 

 different images; one on diffraction by refraction, to which the same remark applies, the 

 grating having been placed at a considerable distance from the polarizer, so that the spot 

 illuminated was too large to allow of the separate observation of different images ; one on 

 diffraction by reflection, in which the grating was placed perpendicularly to the incident light, 

 with the grooved face turned from the polarizer, but the errors of observation, though much 

 smaller than the whole quantity to be observed, were so large on account of the large angle of 

 diffraction, (about 75°,) with which the observations were attempted, that the details are not 

 worth giving; one on diffraction by refraction, in which the different observations were so 

 inconsistent that the experiment seemed not worth reducing; one which was only just begun ; 

 and two qualitative experiments, the results of which have been already given. I mention this 

 that I may not appear to have been biassed by any particular theory in selecting the experi- 

 ments of which the numerical results are given. 



The following remarks relate to the particular experiments : 



No. 1. In this experiment each value of a was determined by six observations, of which 

 the mean error* ranged from about 15' to 55'. So far the experiment was very satisfactory, 

 but it was vitiated by changes in the direction of the light, sufficient care not having been 

 taken in the adjustment of the mirror. 



No. 2. a determined by single observations. 



No. 13. a determined by two observations at least, of which the mean error ranged from 

 about 10' to nearly 1°, but was usually decidedly less than 1°. At and about the octants, that 

 is to say, when ■& was nearly equal to 45°, or an odd multiple of 45°, the light was but very 

 imperfectly polarized in one plane. 



No. 14. a determined by two observations. Marked in note book as " a very satisfactory 

 experiment." The mean of the mean errors was only ll'. 



No. 15. a determined by three observations at least. The light was very imperfectly 

 polarized, except near the standard points, that is to say when ■&■ was equal to 0° or 90°, or a 



* The difference between each individual observation and 

 the mean of the six is regarded as the error of that observa- 

 tion, and the mean of these differences taken positively is 

 what is here called the mean error. When two observations 

 only are taken, the mean error is the same thing as the semi- 

 difference between the observations. Since, for a given position 

 of the pointer of the polarizer, the readings of the analyzer 

 were usually taken one immediately after another, the mean 



error furnishes no criterion by which to judge of the errors 

 produced by the small changes in the direction of the light 

 incident on the grating, but only of those which arise from the 

 vagueness of the object observed. The reader will be much 

 better able to judge of the amount of probable error from all 

 causes after examining the reduction of the experiments given 

 in the next section. 



