in a Magneto-static Field. 401 
the contraction of the liquid under the equal hydrosiatic 
pressure on Mr. Walker’s system. 
Under this internal force per unit area which we may 
call pp, the walls will bulge outwards, and we may consider 
them as thin elastic plates clamped at the edge. 

Taking O as origin, the equation for the displacement » 
parallel to OZ is 
3 poll—p*) » 
:: ea 
ome oo gh? g 
where y is Poisson’s ratio, 
g is Young’s modulus, 
and / is the thickness of the plate ; 
assuming symmetry about OZ. 
The solution is 
PS pl pe) Sy st 
Bmore: pays gals? 
where ¢ is the distance from O and a is the radius of the disk. 
Thus the increase of volume due to bulging is 
f, a 
Arr | ordr 
“0 
Ad ag (i=) 
32° Po ox he” 
The radius of the bulb was 1-75 cm. and the length “4 cm. 
I do not suppose the walls were more than 4 mm. thick, so 
that we have 
a=1°75 cm., (=-4 cm., 2h="05 cm. ; 
 a=4Al, haa. 
For glass we may take g=6 x 10" and p=¢. 
* Rayleigh, ‘ Theory of Sound,’ vol. i. p. 356, 
