00000028_2.htm

l] BOUNDARY-CONDITIONS 21

that tho derivatives of M are finite or behave IE such a way
that an application of Green's theorem is justifiable. Now
let M bo the discontinuity of M_t i.e. the difference in the values

of M at two neighbouring points on opposite sides of the wave-
boundary. Them when tho two faces of the disc coincide wo
find that a certain surface-integral over one face of the disc is
zero. The Bur face-integral in of tho sumo type as (21) except

that M is written in place of M. Since the face of the disc can
bo ehoHon arbitrarily tho integrand must vanish and HO wo
obtain three equations of the typo*

-0 ............ (22).

These equations give

m A a

Jf^a«0 and

\dy/

Hence the wave-front advances with the velocity of light
and the difference between the two electromagnetic fields at
the wave-boundary behaves as a aolf-conjugato field in which
Poyuting'H vector is along tho normal to tho moving
boundary,

If tho equation of the wave-boundary be expressed in tho

form

JF(a*>y,s₉t)mQ₉

we find on calculating tho values of

tit t)t U

that,

Thin in the differential equation of tho charactonBtica, it

exproHHos that tho moving boundary movon normally to iteolf
with tho velocity of light, According to tho theory of i

wjulvalwifc to ihtniti lire obtained in a ditforont itiaimur
0, Hiiiwirtldii, Klwtrlwt PapM*, Vol. *2» |>» 405 j A. 1, It. "Lov**, l^jw<
ATfK/i. Ntw. Hw. *J_f Vol. 1 (l(K)8)» p. »7 ; lj. HUbttfutoin, Ann. (L Phi/M, VoL tt6
(19U«), IK 7«i ; J*. Duiwtm, (;«w/>«r« Jf^rfiw, t. m (1900), p* U71.

t Pmi. tktmth Mitt, *S'<>(?. (IHHil) ; Mmctmter Mtm<$r$ (IH97) ; A/<a/i« «ndt
_f Vol. 4,



	l] BOUNDARY-CONDITIONS 21 that tho derivatives of M are finite or behave IE such a way that an application of Green's theorem is justifiable. Now let M bo the discontinuity of M_t i.e. the difference in the values of M at two neighbouring points on opposite sides of the wave- boundary. Them when tho two faces of the disc coincide wo find that a certain surface-integral over one face of the disc is zero. The Bur face-integral in of tho sumo type as (21) except that M is written in place of M. Since the face of the disc can bo ehoHon arbitrarily tho integrand must vanish and HO wo obtain three equations of the typo*

		-0 ............ (22). These equations give m A a Jf^a«0 and
	\dy/ Hence the wave-front advances with the velocity of light and the difference between the two electromagnetic fields at the wave-boundary behaves as a aolf-conjugato field in which Poyuting'H vector is along tho normal to tho moving boundary, If tho equation of the wave-boundary be expressed in tho form **JF(a>y,s₉t)mQ₉*** we find on calculating tho values of tit t)t U

	that, Thin in the differential equation of tho charactonBtica, it exproHHos that tho moving boundary movon normally to iteolf with tho velocity of light, According to tho theory of i

	wjulvalwifc to ihtniti lire obtained in a ditforont itiaimur 0, Hiiiwirtldii, Klwtrlwt PapM,* Vol. 2» \|>» 405 j A. 1, It. "Lov, l^jw< ATfK/i. Ntw.* Hw. J_f Vol. 1 (l(K)8)» p. »7 ; lj. HUbttfutoin, Ann. (L Phi/M,* VoL tt6 (19U«), IK 7«i ; J. Duiwtm, (;«w/>«r« Jf^rfiw, t. m (1900), p U71. t Pmi. tktmth Mitt, S'<>(?. (IHHil) ; Mmctmter Mtm<$r$* (IH97) ; A/<a/i« «ndt _f Vol. 4,