OF AIR AND OTHER GASES. 15 



When the oscillations are slow as in these experiments, when the disks 

 are near one another, and when the density is small and the viscosity large, 

 the series on the right-hand side of the equation is rapidly convergent. 



When the time from rest to rest was thirty-six seconds, and the interval 

 between the disks 1 inch, then for air of pressure 29 '9 inches, the successive 

 terms of the series were 



1-0-0-00508 +0-24866 + 0'00072 +0'00386 = 1-24816 ; 

 but when the pressure was reduced to 1'44 inch, the series became 



1-0 - 0-0002448 + -0005768 + '00000008 + '00000002 = 1-0003321. 



The series is also made convergent by diminishing the distance between 

 the disks. When the distance was '1847 inch, the first two terms only were 

 sensible. When the pressure was 29'29, the series was 



1- '000858 +'000278 = 1 -'00058. 

 At smaller pressures the series became sensibly =1. 



The motion of the air between the two disks is represented in fig. 8, 

 where the upper disk is supposed fixed and the lower one oscillates. A row 

 of particles of air which when at rest form a straight line perpendicular to the 

 disks, will when in motion assume in succession the forms of the curves 1, 2, 

 3, 4, 5, 6. If the ratio of the density to the viscosity of the air is very 

 small, or if the time of oscillation is very great, or if the interval between 

 the disks is very small, these curves approach more and more nearly to the 

 form of straight lines. 



The chief mathematical difficulty in treating the case of the moving disks 

 arises from the necessity of determining the motion of the air in the neigh- 

 bourhood of the edge of the disk. If the disk were accompanied in its motion 

 by an indefinite plane ring surrounding it and forming a continuation of its 

 surface, the motion of the air would be the same as if the disk were of 

 indefinite extent ; but if the ring were removed, the motion of the air in the 

 neighbourhood of the edge would be diminished, and therefore the effect of its 

 viscosity on the parts of the disk near the edge would be increased. The 

 actual effect of the air on the disk may be considered equal to that on a disk 

 of greater radius forming part of an infinite plane. 



Since the correction we have to consider is confined to the space imme- 

 diately surrounding the edge of the disk, we may treat the edge as if it were 





