36 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 51 



dU , , dv , dw , 



u . dx + — . u . dy + — . u . dz — 



dx dx dx 



dtp 

 dx 



<)<p 



dx 



dx 



dM Bl d -f 



dx+A d lL. d y + ^. dz 



dx dx 



a 9 l»(* 



dx 



dip . (d<p 



dx \dx 

 and recall that 



dx+ ydX '.dy+ W 



dy 



dz 



dy \dy I dz v dz I 



dz 



result in a similar manner from the six remaining terms of the right- 

 hand side of the summation, then there results 



-dp = F .dlogp = dV - \d 

 P 



dx J \dy 





? (A) 



= F .d log p -f dF. 



Again, from equation (II), after substituting the values of u, v, w 

 and dividing by p, there results 8 



/ d log p dip d log p dip d log p dip 

 \ dx dx dy dy dz dz 



«V «V «V 



S dx 2 + dy 2 + dz 2 



(B) 



The equation (A) can be more perspicaciously replaced by the 

 following 



d log tp 



•Because p is assumed not to vary with t, therefore — U, and this 



dt 



term drops out. — C. Abbe. 



