1886.] 



On the Theory of Lubrication. 



199 



result, with such slight amounts of using as those in Mr. Tower's 

 experiments before reversal, seems doubtful, but supposing the brass 

 Dew, and the surface more or less unequal, the wear for some time 

 would be considerable, even after the initial tendency to heat had 

 disappeared. Hence it is not surprising that the effect should have 

 eventually seemed to disappear. 



The circumstances which determine the greatest load which a bear- 

 ing will carry with complete lubrication, i.e., with the oil film con- 

 tinuous between brass aud journal throughout the entire arc, are defi- 

 nitely shown in the theory, so long as the brass has a circular section. 



As the ratio of the load to velocity increases JI or c increases, and 

 the point H approaches 0, when c reaches the value 0*5, which makes 

 GH = a(l — c)=05a, the pressure of the oil in the film is every- 

 where greater than at A and B, the pressure in the bath, but for a 

 further increase in the load the pressure falls near A on the off side, 

 the fall will cause the pressure to become less than that of the atmo- 

 sphere, or if sufficient to become absolutely negative, until discon- 

 tinuity or rupture of the oil film occurs. The film will then only 

 extend between brass and journal over a portion of the whole arc, 

 and a smaller portion as the load 'ncreases or velocity diminishes, i.e., 

 as c increases. Thus since the amount of negative pressure which 

 the oil will bear depends on circumstances which are uncertain, the 

 limit of the safe load for complete lubrication is that which causes 

 the least separating distance to be half the difference in radii of the 

 brass and journal. 



The rupture of the oil does not take place at the point of nearest 

 approach, but on the offside of this, and will only extend up to a point 

 P 2 definitely shown in this theory, which is at the same distance on the 

 off side of H as Pi is on the on side. Hence after this rupture the brass 

 may still be in equilibrium, entirely separated from the journal, and 

 the question as to whether it will carry a greater load without descend- 

 ing on to the journal will depend on the relative values of — and on 



H' 



the smallness of the velocity. The condition then becomes the same 

 as that for imperfect lubrication, and except in the case of a being- 

 very small, theory shows that the ultimate limit to the load will be the 

 same with the oil-bath and with partial lubrication as Mr. Tower 

 found it to be. 



This much may be inferred without effecting the integrations for 

 imperfect lubrications ; could these be effected, the theory would be as 

 applicable to partial lubrication as it has been to complete lubrication, 

 i.e., a sufficient supply of oil. And as it is, sufficient may be seen to 

 show that with any supply of oil, however insufficient for complete 

 lubrication, the brass will still be completely separated from the 

 journal, although the supporting film of oil will not touch the brass 



p 2 



