18 Colorado Colle(;e Studies. 



very favorably because it involves the assumption that the 

 motion is slow. 



The method which I have used is based upon the defini- 

 tion of the coefficient of viscosity and involves no hypothesis 

 save that of continuity of motion, which has been long re- 

 ceived without question. 



The derivation of the ecjuations is much simpler than by 

 former methods, unless an exception is made of the metliod 

 of O. E. Meyer. The equations of Meyer are based upon an 

 assumption which does not satisfactorily explain parts of the 

 terms. (See introduction.) 



The development of the equations of motion by analysis 

 for cylindrical and spherical coordinates enables us to give a 

 definite meaning to each term in the equations, and may aid 

 materially in solving them. 



The metliod definitely determines when the equations 

 hold and when they do not, as is shown in Note III. 



The principal feature of this pa^jer is the relation estab- 

 lished between the motion of a perfect and a viscous liquid. 



Note III. 



The first approximation made in this paper is found on 

 pages 46 and 47, Colo. Col. Studies, Vol. 7, where all terms 

 but the first are neglected in the expression. 



1 /da dii' , dii^ dn^ , , 

 __ f-etc. . 



di\ii u' It' ii' 



This approximation is admissable unless the acceleration in 

 the velocity is very great, which is not usually the case. 



In the second place, we suppose the rate of inflow over 

 the face in a direction perpendicular to the velocity consid- 

 ered uniform along the normal to the face. It is easy to 

 conceive that the inflow might be accelerated. But if it were 

 the acceleration neglected would be of the second order, and 

 might reasonably be neglected. 



If our conclusions are true, the equations hold not only 

 when the motion is slow, but in all cases, except when the 

 motion is rapidly accelerated. 



