tlie Pressure of Radiation. 151) 



second term the reflected wave with a change of phase 8, and 

 (9) represents the transmitted wave. 



The conditions at x = are continuity of y and ^\ these 



•here 



A + Bcos S=Ccos 8' 



BsinS = Csiny 

 A-B cosS = CX«^^in 8^ + /3^cos h') 



Bsin8 = C(a'cos8'-^^sin8') 



K/3')-^^(-.,5). 



(10) 



a' 



These equations lead to 



tang= j^_^,a_^,, , ; tanS' = y^^, . . (11) 

 /BV a-^ + ff^ + l-2/j- 



Now we require the total extra force on the part of the 

 string from to co . Y ^ is continuous, and we integrate 

 from a point just to the left of the origin up to a point at an 

 infinite distance to the right ; at the latter limit Y.^ vanishes, 

 hence the total force is given by the mean density at ^^' = 

 of the potential energy of the vibrations given by (8). We 

 have 



Mean density of V at x = \^N . Mean /||Y 

 = iW . K, . Mean [a sin p('/5 - Q - B sin {y/^+ ^j + 3 } T 



= iW.^rA2 + B^-2ABcos(^2^^ + 8^J. . . . (18) 

 Thus 



Mean density of V at 0=:iW^ (A^ + B^^-2AB cos 6). (U) 



Also the mean density of V along the string, that is, with 

 respect to x from -co to 0, is from (13) equal to 



-.2 



I 



^ a 



W^,(A2 + B2); 



and this is equal to ^E, where E is the mean density of the 

 total energy, potential and kinetic. 



