Transmission of Electric Waves along Wires. 371 



Now all the above integrals fall under the type 



Further, the series, to which (22) when integrated gives 

 rise, are represented by- 



sin <ft + r' 2 sin (p + ty ■+ r 4 sin <ft + 2^ + 



= sin <ft— r 2 sin ft — ifr _ _ _ ^4.) 



1 — 2/' 2 cos i/r + r 

 Hence (22) is easily transformed to 

 4fy>(l+£ 2 )EdV<^ 



f 1 £ 



= B 2 J 1^7 ~ B ( sin 2 ^- ? ' 2 sin 2/S-2«) 



z-2 ^.2 ] 



+ j— ^ + D (cos2/3-r 2 cos2/3-2«) ; . (25) 



where D = 1 — 2r 2 cos 2/c + r 4 . 



34. Now in the experimental case under consideration k is 

 less than O'l; we may therefore, for the order of accuracy 

 aimed at, simplify by neglect of k s . Then dividing (25) by 

 (20) gives 



d'' n J 1 k a 1 



y= Ti = B J TZ-,3 ~ D ( sin 2/3-r 2 sin 20-2*) | ; . (26) 



which is the working formula for comparison with the 

 experimental results. 



35. Regarding this expression physically, we may note 

 that its essence is the factor B 2 , the square of the amplitude 

 transmitted. The denominator 1 — r 2 of the first term in the 

 brackets is due to the repeated coursings of the waves to 

 and fro between the condenser and oscillator. Finally, the 

 second term, which vanishes with k, or with /3 and k, is a 

 small correction whose existence is due to the fact that with 

 a damped wave-train the electrometer-throw varies slightly 

 with the phase at the head, as shown in Art. 29. 



36. Stationary Waves at Electrometer. — Now suppose the 

 electrometer to be at a point on the line distant l^ cm. from 

 its beginning at the oscillator, and let the condenser be at 

 l x + l z = l cm. from the beginning, i. e. l 2 cm. beyond the 

 electrometer. This disposition is exhibited in fig. 1. Let 

 the absorbing bridge be at the end of the line as before. 

 Take the origin of coordinates at the electrometer, and let the 



