ON OPTICAL THEORIES. 159 
These give— 
sin 79’ tan x 
cos 9’ sin (¢ + ¢’) 
= — co Djetem 6! f(a 
tan 0, cos (¢ + ¢’) tan ops" din (= 9’) 
tan 6 = cos (@ — 9’) tan 6! + 
(1) 
__ The theory is applied to Iceland spar, and agrees with experiments of 
Brewster and Seebeck. 
_ $4. The same problem is considered by Neumann! ina long paper 
ead in 1835 before the Berlin Academy, and in a second memoir pub- 
lished separately in Berlin 2 in 1837, and the same results deduced from 
similar hypotheses. 
§ 5. In 1839 MacCullagh attempted to found his theory on a dyna- 
ical basis by finding an expression for the potential energy of the ether 
hen strained by the passage of the waves of light, and applying to the 
tpressions thus obtained Laplace’s principle of virtual velocities, 
‘This leads to a volume integral which holds throughout the space 
cupied by the medium, and a surface integral to be taken over the 
_ The surface integral taken in connection with the principle of the 
eontinuity of the displacement gives the conditions at the surface, and 
Pee are shown to be identical with the conditions found in the previous 
ie 
= Be tnfoscor Stokes, in the Report on Double Refraction, has pointed out 
“the error in the fundamental expression assumed by MacCullagh for the 
‘energy, and this error of course affects the theory of reflexion. 
if 
Chapter II.—Greern. 
 §1. Tue correct expression for the energy, and the correct laws of re- 
‘Hexion and refraction on a strict elastic solid theory, had at the date of 
MacCullagh’s paper been given by George Green ‘ in a memoir read before 
he Cambridge Philosophical Society in December 1837. 
_ The potential energy of the medium is shown to be a function (¢) 
of the three principal elongations s,, sj, s3, and the three principal 
shearing strains a, (3, y. 
_* Neumann, ‘ Theoretische Untersuchung der Gesetze nach welchen das Licht an 
der Griinze zweier vollkommenen durchsichtigen Medien reflectirt und gebrochen wird.’ 
cumann, “Ueber den Einfluss der Krystallfliichen bei der Reflexion und tiber 
die Intensitat des gewéhnlichen und ungewOhnlichen Strahls.’ See also ‘ Vorlesungen 
liber theoretische Optik,’ von Dr. F. Neumann, edited by Dr. E. Dorn. Leipzig: 1885. 
_ * MacCullagh, ‘An Essay towards a Dynamical Theory of Crystalline Reflexion 
| and Refraction,’ Zrans. of Royal Trish Academy, vol. xxi. 
* Geo. Green, ‘On the Laws of Reflexion and Refraction of Light at the Common 
| Surface of two Non-crystallised Media,’ Camb. Phil. Trans. 1838, and Papers of the 
| late Geo. Green, p. 243. 
