ACCORDING TO THE UNDULATORY THEORY. 4.95 
the m surfaces. All members which are multiplied with r+, or a still 
higher power of 7, must therefore become so small, in comparison with 
those multiplied with 7°, that they may be neglected. Thus the inten- 
sities of the transmitted rays become 
a(1—r)”™ for the retardation 0 
a(l—r)".r2 (m—1) . . by Mer 2b 
a(1—r)” .7? (m—2)(1—7)? meal A 4b 
a(t — r)>..9° (m—S) GQ ryh 7 ee 66 
a(l—r)™. r? (m—4)(1—r)§ foo... 8b 
Be =) aa Ck Ay LS ok ape, 
consequently we have 
u=a(l — ry" sin 2x (¢— x) 
u,=a(1 —r)" r?(m —1) [sine (¢- ) cos 27 22 
_ cos2m(¢— =) sin 2m <] 
r IN 
ug=a(1 —r) r3(m — 2) [ sina = («— 2) cos 2.2429 
—cosan(t— 5) sin? 222] (1 —r)? 
dk pee ee Pe : ed 26 
om a(1—r) r?(m— n) [ sing (« x) SIAL tare 
2 Eee (« _ a) sin 7 . Qn20 a— rae. 
If we reckon from this the resultants of all the retarded systems of 
waves of light, z.e. all those just mentioned, with the exception of the 
first, U', or the velocity which it represents, becomes 
m . 
U'=a(l1—r) re { sin Qn (Ci +) [ —1) cos 2.x 28 
+ (m— 2) (1 — 7)? cos2. an Ze 
2(n—1 
(n cosm. 22? 
+..(m—n)(1—7r) 
— cos2a («- x) [ @™— 1) sin anes 
