Transmission of Electric Waves along Wires. 377 



7' 



mean of the ratios -j obtained with l 2 f X/8 and l 2 — X/8, and 



F and G may be calculated from (41) as for / 2 simply. 



51. Detection of Phase Change of Reflected Waves. — We 

 have just noticed a method of practically extinguishing H 

 to simplify the determination of A. Now to determine the 

 phase change, a, we must take exactly the opposite course and 

 make H paramount, since this term represents the interference 

 phenomena which alone involve a except in a subordinate 

 degree. 



We therefore choose a number of values of l 2 differing by 

 small amounts and ranging from zero to about two wave- 

 lengths of the interference curve. 



Since in these cases U is very small compared with l x (say 



to 10 metres and 100 metres respectively), the variable 



1 = Z x f l 2 may be put equal to the constant l x without material 

 loss of accuracy. Consequently r is replaced by r\ and D 

 becomes D : . 



52. We thus obtain from (41), under these simplifications, 

 our interference formula, viz. : — 



y=£=F + GH-H, ] 



d 



where 



F= X * 



1-vV 



YY r : 2 sin 2k, 



G=s \ ]TZ^2 - ]^ ( sin 2 * + n 2 sin 2y) 

 and 



H = 2*-* | ™ s0 -« - *L (sin fVa - r? sin + «-2*)' 

 1 — >Y Vl 



y (43) 



J 



H=^ r - 2 {l + n)cos(0-cc + v). . . . (44) 



53. A further simplification is made in the actual calcula- 

 tion and plotting of the theoretical curve, by writing 



2se~ ko 



The small quantities n and v are defined as functions of k, r u 

 and k by the identity of these two expressions for H. Both 

 n and v vanish for k = 0, and assume a simplified value for 

 « = 0. The actual values of n and v in any numerical case 

 can be readily found with sufficient accuracy by the graphical 

 composition of sine and cosine functions, the amplitudes being- 

 represented by the lengths of lines whose inclination denotes 

 the relative phase of the respective vibrations. 



54. Interference by Reflexion from a Resistance. — To obtain 



