1886.] 



On the Theory of Lubrication. 



197 



used to keep the brass in its place, or by any irregularity in the longi- 

 tudinal section of the journal or brass. Although no direct reference 

 is made to such flanges in Mr. Tower's reports, it is such a common 

 custom to neck the shaft to form the journal that there is great 

 probability of the flanges being used. A coefficient n has therefore 

 been introduced into the theory, which includes both the effect of 

 necking and of irregularity in longitudinal section. Giving n the 

 value 1*25, the calculated results came into accordance with all 

 Mr. Tower's results for olive oil, the difference being such as might 

 well be attributed to experimental inaccuracy, and this both as regards 

 the frictions measured with one brass, No. 1, and the distribution of 

 the pressure round the journal with another, No. 2. 



Not only does the theory thus afford an explanation of the very 

 novel phenomena of the pressure in the oil film, but it also shows, 

 what does not appear in the experiments, how the various circum- 

 stances under which the experiments have been made affect the 

 results. 



Two circumstances in particular which are brought out as principal 

 circumstances by the theory seem to have hitherto entirely escaped 

 notice, even that of Mr. Tower. 



One of these is a, the difference in the radii of the journal and of 

 the brass or bearing. It is well known that the fitting between the 

 journal and its bearing produces a great effect on the carrying power 

 of the journal, but this fitting is supposed to be rather a matter of 

 smoothness of surface than a degree of difference in radii. The 

 radius of the bearing must always be as much larger than that of the 

 journal as is necessary to secure an easy fit, but more than this doea 

 not seem to have been suggested. 



It now appears from this theory that if viscosity were constant the 

 friction would be inversely proportional to the difference in the radii 

 of the bearing and journal, and this although the arc of contact is less 

 than the semi-circumference ; and taking temperature into account 

 it appears from the comparison of the theoretical frictions with the 

 experiment on brass No. 1, that the difference in the radii at 70° F. 

 was 



a=0'00077 (inch), 



and comparing the theoretical pressures with those measured with 

 brass No. 2, 



a=0'00084 (inch), 



or the difference was 9 per cent, greater in the case of brass No. 2. 



These two brasses were probably both bedded to the journal in the 

 same way, and had neither been subjected to any great amount of 

 wear, so that there is nothing surprising in their being so nearly the 



VOL. XL. p 



