EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 59 



These values are reproduced in fig. 35, which with table 3 shows that the 

 position of equilibrium is reached to AN=io~*, the smallest quantity easily 

 measurable, in about 25 seconds. 



XL 



0! 

 -06 



05 



041 



0* 



4 6 



8 10 

 FIG. 35. 



The fluid has been treated as incompressible. If this is not done, the results 

 apparently become unavailable. A further step may, however, be made: 

 Poiseuille's equation (i) if the condition VP=Vo PO is introduced, leads on 

 integration to the form 



(u) p l -p\ = 



R 



where P is the pressure and Vo the volume issuing at the edge, per second at 

 the normal pressure po. In endeavoring to use (n) directly, I have not 

 succeeded in producing a practical form of equation. 



Equation (9) may be put in a different form suitable for computing in the 

 ultimate times of very close approach to equilibrium. For this purpose, let 



y'/yo a and yy' b 



where b is to be very small, so that y = ayo+b. Equation (9) then reduces 

 nearly to 



( 



\ 

 I 



b \ 



~a -- ) 

 ayo/ 



b/ayo \ 



log- -*- > 



i a j 



Usually b/ay may be neglected compared with i a. Thus if 6 = io~ 4 cm., 

 t= n. i sec., with the other constants as above, yo = o.i cm.; = 2/3. For the 

 same case, 6 = io~ 4 cm., if ^0 = 0.05 cm., = 2/3, ^ = 38.3 sec., are needed to 

 approach within io~ 4 cm. of the position of equilibrium, etc. In case of repul- 

 sion, a> i and b is negative. Thus for = 3/2 cm., b = io~ 4 cm., y =i/i$ cm., 

 2 = 6.53 sec. For ^0 = 2/45 cm., y'=i/i$ cm., 2=13.8 sec., etc. The intervals 

 so computed are small as compared with the times actually observed, where 

 many minutes have to elapse before equilibrium is obtained. It seems diffi- 



