1886.] 



On the Theory of Lubrication. 



191 



It seems best therefore in this, as well as other cases, to omit the 

 terms involving cosines of odd multiples of 6. 



3. As regards the observations with the artificial surface in water, 

 the coefficients of the cosines in the expression for the azimuths and 

 of the sines in the expression for the polarising angles are insensibly 

 small, indicating no introduction of asymmetry with respect to the 

 principal plane arising from the process of polishing. The coefficients 

 of the cosines of odd multiples of 6 in the second expression are also 

 insensible. The constant term in the first expression, representing 

 (on the assumption of symmetry with respect to the principal plane) 

 the index error of the circle carrying the Nicol, agrees almost exactly 

 with those obtained for the cleavage surfaces in air and water. 



It would seem best then to omit those terms which we have reason 

 to think are really nil, and which the observations show to be at any 

 rate extremely small, and to exhibit the final result accordingly. 



February 11, 1886. 



Professor STOKES, D.C.L., President, in the Chair. 



The Presents received were laid on the table, and thanks ordered 

 for them. 



The following Papers were read : — 



I. "On the Theory of Lubrication and its Application to 

 Mr. Beauchamp Tower's Experiments, including an Expe- 

 rimental Determination of the Viscosity of Olive Oil." By 

 Professor Osborne Reynolds, LL.D., F.R.S. Received 

 December 29, 1885. 



(Abstract.) 



Lubrication, or the action of oils and other viscous fluids to 

 diminish friction and wear between solid surfaces, does not appear to 

 have hitherto formed a subject for theoretical treatment. Such 

 treatment may have been prevented by the obscurity of the physical 

 actions involved, which belong to a class as yet but little known, 

 namely, the boundary or surface actions of fluids ; but the absence of 

 such treatment has also been owing to the want of any general laws 

 revealed by experiment. 



The subject is of such fundamental importance in practical 

 mechanics, and the opportunities of observation so frequent, that it 



