204 REPORT—1885. 
In any case we shall have 
tana=m tana. ‘ : . . (85) 
where 7 is a function of the angle of diffraction and the refractive index, 
which can be calculated on either of the above hypotheses. 
The results were reduced by plotting from the experiments a curve 
with log m as ordinates and 6, the angle of diffraction, as abscisse. The 
curves given by the two theories on either of the above assumptions 
as to the relation between diffraction and refraction were also drawn, and 
a comparison of the two results ‘leaves no reasonable doubt that the 
experiments are decisive in favour of Fresnel’s hypothesis, if the theory be 
considered as well founded.’ And, moreover, the comparison shows us 
that we must suppose the diffraction to take place before the refraction. 
Thus, when the grooved face is towards the incident light we must sup- 
pose the wave to be broken up in the air and then to be obliquely 
refracted through the glass, while when the grooved face is away from 
the light the wave must be treated as if it were diffracted in the glass 
and then obliquely refracted out, and Professor Stokes shows that it is 
& priori more probable from physical reasons that this is what takes 
lace. 
, § 3. In the results of the experiments a certain amount of irregularity 
is produced by the want of symmetry of the grooves of the grating, and 
Holtzmann,! who in 1856 repeated Stokes’s experiments, failed to obtain 
consistent results with glass gratings, and had recourse in consequence to 
a Schwerd’s lamp-black grating; with this he obtained results more in 
accordance with the theory of Neumann and MacCullagh than with that 
of Fresnel. 
Holtzmann thought that Stokes had neglected to consider the effect of 
the longitudinal waves, ‘and to this neglect he attributes the error of 
Mr. Stokes;’ and Hisenlohr,? who ‘had not read the great paper of 
Prof. Stokes,’ attributes to him the same neglect, and endeavours to 
give a theoretical account of the question from Cauchy’s standpoint. 
Of course both these authors were quite wrong in their estimate of 
Stokes’s work, and Lorenz * showed, from some decisive experiments of his 
own, that Holtzmann’s results were due to an error of his method. Lorenz 
gave a fresh demonstration of Stokes’s theorem, and arrived at the same 
results. Lorenz appears to consider his method as more general than 
that of Stokes, but this is due to a misconception on his part. The 
results of his experiments agree with Fresnel’s theory. 
§ 4, The matter has since been experimentally investigated by 
Quincke,’ who showed that the method of forming the grooves on the 
grating was of the utmost importance, and whose experiments led to no 
decisive results, and more recently by Frohlich.’ Fréhlich investigated 
the polarisation of the light reflected from a glass grating, but did not 
compare his results with theory. A few experiments of the same kind 
were made by Stokes in 1852, but he also omitted the comparison with 
theory. 
1 Holtzmann, Pogg. Ann. t. xcix. p. 446. 
2 Hisenlohr, Pogg. Ann. t. civ. p. 337. 
8 L. Lorenz, Pogg. Ann. t. cxi. p. 315. 
4 Quincke, ‘ Experimentelle optische Untersuchungen,’ Pogg. Ann. t. cxlix. p. 73. 
4 Frohlich, Wiedemann, t. i. 
