Electromagnetic Wave-surface. 411 
_ By differentiation, o being variable, and therefore 8, also, 
—0=2(douc)(B,e“'8,) + 2(ou0)(dByc—'8,) —2m(dBw-"3,). (55) 
Also, differentiating (53), 
do =2(dopo)c~'B, + (ono )de—'!B; —mdpB, ; 
land, multiplying this by 26,, gives 
2B,do =4 (doc) Bic 18, + 2(ouo)(dB,c~!8,) —2m(dB,w-'B;). (56) 
Subtract (55) from (56) and halve the result ; thus obtaining 
Bido= (dopo) (Pyc~'B:), 
—(Pyeo Bi uo do=0e,...), rhe (DO) 
In the last five equations it will be understood that do and 
d®, are differential vectors, and that doo is the scalar product 
of do and wo, &c.; also in getting (56) from the preceding 
equation we have Byde~"B; =B,c~'d8, = dByc~"By, &c. Equation 
(57) is the expression of the result of differentiating (50), 
d(oB,)=dop; + «dp, =0, 
with d6, eliminated. 
Now (57) shows that the vector in the {} is perpendicular 
to do the variation of c. But by (51) we also have, on dif- 
ferentiation, 
4 
: 
| BOC Reka he, (0S he ea ate ta OO) 
| 
or 
Hence p and the {} vector in (57) must be parallel. This 
| gives 
Hae B (GC By) MG, 892.0 eee OD) 
where h isa scalar. If we multiply this by c—18, and use 
| ° 
( (52), we obtain 
| Pee Sinrehu entrée edhe s (60) 
vor, by (49), giving 4, in terms of cH, 
| pi= 0; ° ° e ° 5 ° e ° (61) 
va very important landmark. The ray is perpendicular to the 
selectric force. 
| Similarly, if we had started from, (instead of (49), (50), 
ov (52)), the Bien ke H equations, viz., 
| ce Ne 
| aaa 2 (ceo)! —ne-"” 
“=,  couif,=1, 
; 
with of course the same equation (51) connecting p and o, we 
| 
