EguATiuNs OF ^Motion or a \ isiors LigiiD. '.U 



He be.Lfins his investigation after some preliminary con- 

 siderations with the following statement: "The internal fric- 

 tion of a tlnid takes place between the different strata of the 

 same tluid, and is proportional to the differential coefficient 

 of the velocity along the normal to the plane separating the 

 strata." But this hypothesis explains only six of his nine 

 initial expressions. For instance, if we take the three initial 

 expressions for the retarding forces parallel to the x axis, viz., 



cln , , 

 —n —- dy dz, 

 ax 



— n — dz dx, 

 dy 



du , , 

 —n — dx ay, 

 dz 



the second and third readily follow from the hypothesis, but 

 the first has no definite meaning, unless we extend his hy- 

 pothesis, as W. M. Hicks has interpreted it in the British 

 Association Report for 18S1, so that it reads: " The friction 

 on a small plane in a given direction in the plane is propor- 

 tional to the rate of variation perpendicular to the plane of 

 the component of the velocity in the given direction, whilst 

 there is a normal part proportional to the rate of variation 

 perpendicular to the plane of the component perpendicular 

 to this plane." 



The subject has been investigated by Stefan (1802), and 

 later by Maxwell, Levy, Klutz, and Butcher, without adding 

 materially to what had been done already. 



However, the work of Maxwell resulted in the determina- 

 tion of the constant called the coefficient of viscosity. Fol- 

 lowing Maxwell, numerous experiments have been made for 

 the purpose of determining the value of the coefficient 

 of viscosity. Helmholtz, Piotrowski, Maxwell, Meyer, and 

 Poissenille may be named as having made the most elaborate 

 series of experiments. 



Lamb, in his Trediisc on Fluids (1879), derives the equa- 

 tions of motion for a viscous fluid by a method based on 

 those of St. Venant and Stokes. Basset, in 1888, published 



