Prof, J. Perry on Liquid Friction, 455 



Above the critical speed, which is possibly below ft ==17, 

 the law is probably y oc ?i 1-32 . 



It is not worth while to publish any of the observations 

 which we have made upon other liquids, nor to publish the 

 curves we have drawn for sperm-oil, although we exhibit 

 them before the Society. Errors of one degree in obser- 

 ving temperature were quite possible, and errors of half a 

 degree in the deflexion of our pointer were also possible. 

 Small fluctuations in speed were continually taking place, so 

 that the pointer was never quite still, the motion of the fluid 

 was therefore not truly steady. Jt is our determination to 

 repeat the whole work with improved apparatus. In the 

 meantime, however, it will be observed from Table III. that 

 there is fair agreement in the law connecting [x with tem- 

 perature, from all the sets of observations. There is, on the 

 whole, a very fair agreement with what we venture to call 

 Prof. Keynokls's rule, 



y = ciF 2 ~' c n\ 



where k has the value 1*33 or 1 according as n is above or 

 below the critical speed*. The sheet of squared paper on which 

 we have plotted all our values of logy and log n for the various 

 constant temperatures shows that the errors of observation are 

 too great for the establishment of this value of k ; but it is the 

 probable value. It shows, however, in the allineation of the 

 points of discontinuity, with sufficient accuracy that y c oc n c 2 , 

 if the rule is taken to be generally true; and although there 

 is some little vagueness always in one's observations just about 

 the critical speed, we may take ?/ c =0 , 009n/ without very 

 great error. Indeed, we are satisfied with the substantial 

 agreement of all our observations with the formula 



=a (*mJ 



* Prof. Reynolds, in criticizing- a proof of this paper, lias been kind 

 enough to point out that his rule for pipes does not necessarily apply to 

 the fluid in our apparatus. We had not seen the reprint of his Royal 

 Institution lecture, else we should have known that the condition of the 

 liquid in circular flow is inherently stable or unstable according as r is 

 greater or less than the radius of the fixed cylindric surface. As he 

 points out, the liquid in the outer space is inherently stable for velocities 

 far exceeding the critical velocity (if there is one) for plane surfaces, 

 whereas the liquid in the inner space is unstable from the first. 



We directed the attention of the meeting to the fact that Tables IV., 

 V., VI., and VIII. give unmistakable evidence of the truth o( what 

 we have called Prof. Reynolds's Rule, however difficult we may Bud it in 

 explanation. 



