450 Prof. J. Perry on Liquid Friction. 



Prof. Osborne Reynolds *. As his ingenious theory has been 

 completely verified by experiments made upon the very 

 smallest and largest pipes with flowing water, and as it is 

 simple we had adopted it for the reduction of our experiments. 



According to his theory, -j — - or, as we shall call it, y, 



ought to be proportional to n until n exceeds a certain value; 

 this value being a function of /n/p, where p is the density of 

 the fluid. Now the alteration of p with temperature in such 

 a liquid as sperm-oil is so small that the error in neglecting 

 it is small in comparison with our errors of experiment. 



Neglecting, then, the alterations in p, the theory of Prof. 

 Reynolds leads to 



y = aF 2 -W, (8) 



where F is a function of the temperature, n the number of 

 revolutions per minute ; where /c = l until the critical speed 

 n c is reached, n c being proportional to F, and k having a 

 higher value than 1 for all speeds above the critical ; a is a 

 constant. This is on the assumption that Prof. Reynolds's 

 theory would lead to the same result in our case as in his 

 pipes. 



Now, in the first place, it seemed absurd that the temperatures 

 for which the speeds 9 and 40 were the critical speeds should 

 be so near to one another as 40° 0. and 45° C. But a much 

 more serious consideration was this. According to any rea- 

 sonable application of the theory to our case, at constant 

 speed, if y$ m is constant when the speed is less than the 

 critical speed, and if y<j> s is constant when the speed is 

 above the critical speed, then s ought to be less than m, 

 whereas 1*349 is about twice 0*686. We came to the con- 

 clusion that the point of discontinuity has nothing whatever 

 to do with the critical speed ; indeed, we subsequently found 

 it probable that n = 9 does not become the critical speed until 

 the highest temperature of Table III. is reached. 



Using the deflexions in Table III. to determine /j, according 

 to (7), we have the results given in column 5 of the Tables. 

 The numbers in column 5 of Table I. are calculated for tem- 

 peratures lower than 2Q° C, which is about the temperature 

 at which 40 is the critical speed. In some of the following 

 tables, giving the results of experiments made at various 

 constant temperatures, we have also given values of fi. There 



* " An Experimental Investigation of the Circumstances which deter- 

 mine whether the Motion of Water shall be Direct or Sinuous, and of the 

 Law of Resistance in Parallel Channels," by Osborne Reynolds. F.R.S., 

 Phil. Trans, pt. iii. (1883). 



