374 Dr. Barton and Mr. Lownds on Reflexion and 



42. All the above integrals are included in the following 

 typical form : — 



\ g-2*p(*-0 cos (pt + 8) cos (pf^W a + 8 + e)dt 



= 4kp{i+ky cos ( e ~ e )- k sin (0 + 2S + e ) 



-& 2 (cos0^e + cos0 + 28 + e)f _ - 



And the series to which the columns in (32) and (33) 

 when evaluated give rise are of the type given in equation (24) . 

 The evaluation of (33) then yields 



Up{l + £ 2 )Ed' = F + G + H, .... (35) 

 where 



F = r ^-gr 2 sin2K+ r ^ + |(l-^ C os2«), • (36) 

 G = s 2 { y^ 2 - 4 (sin 2cc + r* sin 2*-2«) 



+ j^2 +^(cos2«-r 2 cos2/c-2a) >, • • (37) 

 tt = 2se-M |^i^ _. A (sin 0+^-r 2 sin + a -2«) 



+ ^-^^ + ^(cos^^-7» 2 cos^+^^)|. (38) 



43. Discussion of Interference Phenomena. — Let us now 

 consider the various features of this result and their physical 

 interpretation. In equations (36) to (38) the values of F, G, 

 and H are arranged in terms commencing with one of the 

 order unity and proceeding by ascending powers of k. The 

 terms involving k are all small as their coefficients are of the 

 order unity, and k is less than O'l in the experimental case 

 under examination. Those involving k? will be omitted 

 finally as their coefficients are likewise of the order unity. 



The presence of the terms in k is due to the fact, already 

 discussed in art. 29, that the electrometer-throw is slightly 

 affected by the phase at the head of a wave-ti*ain of given 

 amplitude, period, and damping. They are therefore but 

 small corrections to the main features of the case which are 

 represented by the first terms only of each of the expressions 

 in (36) to (38) for F, G, and H. The denominators of these 

 terms supply the correction for the successive arrivals at the 

 electrometer of wave-trains which have suffered reflexion at 



