[smith] depression OF DISC UNDER PRESSURE 219 



mirror Q, of focal length about 50 cms., was attached to X" so that its 

 pole was on the axis of rotation of K and its principal axis set per- 

 pendicular to the axis of K. A carbon filament lamp was placed in 

 front of Q at such a distance from it as to project an image of a selected 

 horizontal portion of the filament on to a scale situated 275 cms. from 

 the mirror. 



In figure 3 -P is the pole of the mirror, PNo, the principal axis, S is 

 a point source of light on the filament and So' is its image on the scale 

 before the centre of the disc is depressed. PSo' was arranged to be 

 perpendicular to the scale, the lever L being in this case perpendicular 

 to^, i.e., perpendicular to the direction of the subsequent depression. 



Denote the initial angle of incidence of the ray SP by do. Then 



angle NqPSo' is also equal to ^o- Now suppose the centre of the disc 



is depressed a distance w cms. The mirror is rotated about P through 



w 

 an angle 6 such that sin 6 = — -, a being the length of the lever arm 



tv 



L in centimetres. 



The angle of incidence of SP is increased to 6-{-doa.nd the reflected 



ray strikes the screen at S' making angle So'PS' = 26. 



s 

 If 5 is the scale deflection in centimetres then tan 26 =~ where 







b is the distance of the scale from p. 



s w a 



For small angles of deflection 26 = — and 6 = — hence w = — • s. 



b a 2b 



In the experiments a= .88 cms.; b = 275 cms. 

 hence w= .0016 5. 

 or .9 = 625 w. 

 Thus the arrangement multiplies the depression by the factor 

 625. This, together with the fact that the friction effects are very 

 small, enables the depression at the centre to be measured with a 

 high degree of accuracy. In evaluating the values of w from the 

 observations the relation w= .0016.? was used for scale deflections 

 below 40 cms. but for larger deflections than this 6 was first obtained 



from tan 20= — and the value of w calculated from 'w = asin 6. The 

 b 



first observations as mentioned above were carried out with a circular 



portion of the disc of di?meter 4 cms. exposed to the pressure difference 



p, this circle being concentric with the disc itself. Thé diameter, d, 



of the exposed area was then increased successively to 4.27, 4.5, 



4 . 65, 4.8, 5, 5.3, 5.5 cms. and the depressions measured for a number 



of values of p from zero to about 700 mms. of mercury. In each case 



