88 Colorado College Studies. 



A Trecdise on Hydrodynamics, in which he uses Stokes' 

 method. Both authors accept the second hypothesis of Stokes, 

 so that we have no assurance that their equations hold, except 

 in the case of slow motion. Both fully realize this, and re- 

 stricted the application of their results accordingly. Of all 

 methods so far, that of Stokes has received the most general 

 approval. 



In the following paper we have derived the equations for 

 the motion of a perfect fluid in order that we might extend 

 the same methods as far as possible in obtaining the equa- 

 tions for a viscous liquid (the discussion is limited to an 

 incompressible fluid, or liquid). The second section is 

 devoted to the consideration of a viscous liquid. The dis- 

 cussion is based upon the definition of the coefficient of vis- 

 cosity as agreed upon by experimental physicists. Then by 

 comparing the motion of a viscous liquid with that of a perfect 

 liquid we are enabled to give a definite meaning to all nine 

 of the initial expressions obtained by Meyer. To obtain the 

 equations referred to cylindrical and spherical coordinates we 

 have not used the method of transformation, but have derived 

 them by analysis similar to that used in determining the 

 equations when referred to rectangular coordinates. By this 

 method a definite meaning attaches to each term in the result- 

 ing equations. This part of the subject is given in Sections 

 3 and 4, and will appear in a later issue of the Colorado Col- 

 lege Studies. The essential features of Sections 1 and 2 

 were completed before April 1, 1895 ; of Sections 3 and 4 before 

 June 1, 1896. The notes at the end of Section 4 were added 

 during the spring of 1897. 



Works consulted in preparing this historical sketch: 

 Encycloptedia Britannica, ninth edition: subject, Hydromechanics. 

 British Association Reports. Report on the Recent Researches in Hy- 

 drodynamics, by Stokes, 18ib: by Hicks, 1881. 

 Works on Hydrodynamics, by Lamb and by Basset. 

 Pamphlets on Internal Friction of Fluids, by O. E. Meyer. 

 Stokes' Papers. 

 Newton's Principia. 



Penny Encycloptedia; subject, Hydrodynamics. 

 Cajori's History of Mathematics. 

 Lagrange's Mechanique Analitique. 



