767 



Neglecting in these and tlie two otlier equations any terms of 

 the second order we get 



dw dw dw 



"d^ • • • 



dy 



(14) 



and so 



da; Oy Oz 



(14a) 



We now may everywhere replace in the terms of the second 

 order in the complete equations the quantities .c,i/,z and vv by the 

 values taken from (14) and (Ha). We then find 



(. dw -da- .0*. 

 0.B dy dz 



■ /■ dw - dw ■ di. , 



' + '\'d:. + '^d., + 'd-^) = ''d. 



(15) 



These are the equations of motion required. From them we can 

 deduce the equation of energy by muhiplying the first by x, the 

 second by y, and the tiiird by z, and then adding them. So we get 



d dw 



dw dw 



ê c' w — . 



dt dt 



In connection with (14«) we write the second term in the form 



^ dw 2v^v d / V* \ 

 dt~~^'~dt\2^) 



and this gives us 

 d 

 dt 



On the other side we find from (13) 

 d 

 dt 

 or 



d 

 dt 



■ C' w ~\- 4- c' w' 



2c' * 



. dP . dP . dP 



oiB dy dz 







(16) 



i w= + i v-w + — r — <•'«' + I 



oC' 



This agrees with (16) because the difference 

 d (v' \ 



is equal to 



lc^«.= j 



0. 



(lüa) 



