58 EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 



to atmospheric pressure, may be admitted. Suppose, therefore, that at 

 any time, y and V are constant relatively to r, and integrate the equation. 

 Then the pressure excess at r is 



( ) - 2 ^( I Jj 



P ~~ : iry 2 \r " ~R 



If R is the radius of the disks, p = o at r = R, and the equation may be con- 

 sidered to hold short of r = o. Thus the thrust P becomes 



-r- 



<J n 



2 -jrrdr 'P = 2T)R V/y 2 



d_ 

 dt 



(3) 1 



But 



(4) V = 



whence 



(5) 



or, on second integration, 



(6) 



\y yo, 



But for the horizontal pendulum the force P is proportional to yy', which 

 may be written 



so that (5) becomes 



This, on again integrating, becomes finally 



(9) 





arn^r // y' \ i-y'/y \ 



Pa/ 1 \"\y " y*)' *-?/*) 



natural logarithms being in question. Since yy' = AN/2, equation (7) cor- 

 responds in case of the large disks to P=F^ = 2X65.2AA^/2. Hence, P = 

 2X65.2. Furthermore, in case of this apparatus and in the present experi- 

 ments, the following data may be entered : P = 2X65. 2; y = i / 1 5 or y'/yo = 

 2/3; -R=io.2 cm.; yo = o.io cm.; ij = igoXio~ 6 , so that roughly 



(10) ta'ig[[- -} log (3 ) 



V ViS^ 3/ 3 \ $yJ 



Table 3 contains some corresponding values of y and P computed in this way. 

 TABLE 3. Motion of movable brass disk retarded by viscosity of air film. 



