322 Hydrostatics. 



Of the Equilibrium of Floating Bodies. 



437. In order that a heavy body may be in equilibrium on 

 the surface of a tranquil fluid, it is necessary that its weight 

 should be less than that of an equal bulk of the fluid. There 

 is an exception to this rule, however, in the case of very small 

 bodies, the particles of which are of a nature not to exert any 

 attraction upon the particles of the fluid, or whose attraction is 

 much less than that of the particles of fluid for each other. In 

 this case the fluid is depressed below its level, forming a little 

 hollow about the floating body, which may be regarded as mak- 

 ing a part of the bulk of the body ; and on account of this aug- 

 mentation, it is evident that the body may float, although its spe- 

 cific gravity should be greater than that of the fluid. It is on 

 this account that a needle smeared with tallow may be made to 

 float on water. Small globules of mercury also are supported in 

 a similar manner. To render this effect of no avail, we have 

 only to suppose the floating bodies so large, that the void space 

 which may be formed about them (and which is always very 

 small) may be neglected when taken in connection with a bulk 

 so much greater. 



438. The weight of a body being smaller than that of an 

 equal bulk of the fluid, the body will sink till the weight of the 

 fluid displaced becomes equal to that of the body ; and when 

 these two weights are thus equal, the body will be in equilibri- 

 um, if its centre of gravity and that of the fluid displaced, or 

 the centre of buoyancy, are situated in the same vertical. With 

 respect to homogeneous bodies, the centre of buoyancy coincides 

 with that of the immersed part of the body ; and that the weight 

 of the fluid displaced may be equal to that of the body, it is nec- 

 essary that the densities should be in the inverse ratio of the 



Calling these tenths of an inch, we have, by dividing by 10 and by 12, 

 10800 feet for the absolute length of the circumference ; whence, 



2;r or 6,2832 : 1 :: 10800 : 1719. 



In the best spirit levels, the requisite curvature is effected and rend- 

 ered true by grinding with emery. 



