HOGG. — VISCOSITY OF AIR. 615 



/I/' j-ra-\-3-i h ,, ., .. -, 



^^P- '«=• ^^^^- = jTZ^^ ■ I i 1 I ^• 



1 + — + ir^^ 



1/ a 2 v"' «■' 



"Where /x' = -, /j. is the coefficient of viscosity and p the density, 31K'^ 

 p 



is tlie moment of inertia of tlie peiululum, a is the radius of the sphere, 



7'tlie time of a single swing of the pendulum, M' the mass of the fluid 



displaced by the S2)here, and 



^ = 'i^,^=i^. 



IT p 



•2p! T ^ 2/x7" 



The decrement here considered is, of course, that due to the resistance 

 of the fluid on the sphere alone. 



General Method. 



The constancy of the elasticity of quartz fibres commended the use of 

 one of them as a suspension. Since the sphere had to be provided with 

 a stiff wire support to which to fasten. the fibre, and on which to support 

 a small mirror to be used in reading the arc of swing, it was necessary 

 to devise a plan by which the friction of the air on the mirror, wire, and 

 fibre, and also the friction in the fibre itself, might be eliminated. The 

 following plan was used. First, a sphere was made of suitable size. 

 The size was accurately measured, and the density of the material of 

 which it was composed determined. Another material was then chosen 

 whose density was two or three times that of the sphere. Two disks 

 of the same dimensions were then made, one of the heavy material and 

 the other of the same material as that of wliich the sphere was made. 

 The dimensions of the disks were determined by two relations. First, the 

 moment of inertia of the heavy disk about its axis had to be the sum of 

 the moment of inertia of the sphere about a diameter and of the light 

 disk about its axis; and second, the weight of the heavy disk had to 

 be that of the sphere and light disk. Thus, a pendulum formed of the 

 sphere and light disk fixed on a wire passing along the axis of the disk 

 and a diameter of the sphere would have the same period of swing as 

 that of a pendulum consisting of the heavy disk alone mounted as the 

 light disk was. The tension of the supporting fibre would also be the 

 same in the two cases. Two experiments were then performed, one to 

 get the decrement when the vibrator consisted of the sphere and light 

 disk, supported as described on the wire, and the other to get the decre- 



