﻿Effect of Variable Head in Viscosity Determinations. 953 



The outstanding difference between solid friction and fluid 

 friction in damped vibrations is that in the one the dissipation 

 per cycle is proportional to the amplitude, whereas in fluid 

 friction the dissipation varies as the square of the amplitude. 

 Since the energy of the motion varies as the amplitude 

 squared, the dissipation per unit time with fluid friction is a 

 constant fraction of the energy of the system, whereas with 

 solid friction the dissipation as a fraction of total energy is 

 inversely as the amplitude. Hence in solid friction the 

 rapid damping of small vibrations until finally the dead 

 region of width 2F/c 2 is reached. Clearly in the two systems 

 the envelopes of the two vibration curves may be tangential, 

 in which event solid friction may be mistaken for fluid 

 friction. As the foregoing analysis indicates, five half 

 vibrations or two complete periods suffice not only to safe- 

 guard against this possibility, but also to apportion the 

 relative magnitudes of the two sets of fractional forces. 



It seems possible that some such analysis as is here 

 outlined may be a useful instrument of investigation in 

 connexion with friction and lubrication, affording at least 

 some sort of criterion in so-called border-line cases. 



LXXXIV. The Full Effect of the Variable Bead in Viscosity 

 Determinations. By Frank M. Lidstone *, 



SIXOE the publication in this Magazine of my paper on 

 the Measurement of Absolute Viscosity (February 1922), 

 it has been pointed out to me by Mr. W. H. Herschel, of the 

 American Bureau of Standards, and by Dr. Guy Barr and 

 Mr. L. F. G. Simmonds, of the National Physical Laboratory, 

 that the logarithmic head correction in the u viscous " term 

 of the equation is, strictly speaking, incomplete, inasmuch as 

 it is based on the assumption that the head varies directly 

 with the velocity. Barr also makes a necessary correction in 

 the final kinetic energy term of the approximate equation, 

 which should read as in equation (2) below. 



As no attempt appears to have been made to find a general 

 equation embracing all these corrections, it is here proposed 

 to try to find the exact expression, however laborious and 

 cumbersome, in order to ascertain to what extent the results 

 obtained by means of the ordinary formula? deviate from the 

 true value. The premises of the whole argument are in- 

 cluded in the generally accepted equation, 



iri A gpth Yp 

 V= ~SVi SvrTT 



* Communicated by the Author. 

 Phil. Mag. S. 6. Vol. 44. No. 263. Nov. 1922. 3 Q 



