OF AIR AND OTHER GASES. 13 



Hence the value given by Meyer is 1'8 times greater than that adopted in 

 this paper. 



M. Meyer, however, has a different method of taking account of the dis- 

 turbance of the air near the edge of the disk from that given in this paper. 

 He supposes that when the disk is very thin the effect due to the edge is 

 proportional to the thickness, and he has given in Crelle's Journal a vindication 

 of this supposition. I have not been able to obtain a mathematical solution 

 of the case of a disk oscillating in a large extent of fluid, but it can easily 

 be shewn that there will be a finite increase of friction near the edge of the 

 disk due to the want of continuity, even if the disk were infinitely thin. I 

 think therefore that the difference between M. Meyer's result and mine is to 

 be accounted for, at least in part, by his having under-estimated the effect of 

 the edge of the disk. The effect of the edge will be much less in water than 

 in air, so that any deficiency in the correction will have less influence on the 

 results for liquids which are given in M. Meyer's very valuable paper. 



Mathematical Theory of the Experiment. 



A. disk oscillates in its own plane about a vertical axis between two fixed 

 horizontal disks, the amplitude of oscillation diminishing in geometrical pro- 

 gression, to find what part of the retardation is due to the viscosity of the 

 air between it and the fixed disks. 



That part of the surface of the disk which is not near the edge may be 

 treated as part of an infinite disk, and we may assume that each horizontal 

 stratum of the fluid oscillates as a whole. In fact, if the motion of every 

 part of each stratum can be accounted for by the actions of the strata above 

 and below it, there will be no mutual action between the parts of the stratum, 

 and therefore no relative motion between its parts. 



Let 6 be the angle which defines the angular position of the stratum which 

 is at the distance y from the fixed disk, and let r be the distance of a point 



jn 



of that stratum from the axis, then its velocity will be r-r-, and the tangential 

 force on its lower surface arising from viscosity will be on unit of surface 



(P0 /..V 



