^52 Capillary tube#. 



Laplace's theo- the spherical segments will be evident, if we consider that thfi 

 tionand de-^^' <^istance where the action of the tube ceases to be sensible, is 

 piession of imperceptible ; so that if, by means of a very powerful micro- 

 efiect of attrac- ^^^P^j ^^'^ could succeed in rendering it sensible to the amount 

 tion which is of one millimetre (or one twenty-fifth of an inch English), it is 

 lary. probable that the same amplifying power would give to the 



diameter of the tube an apparent magnitude of several metres. 

 The surface of the tube may therefore be considered as being 

 veiy nearly plain in a radius equal to that distance; the fluid 

 in that interval will therefore fall or rise as to that surface very 

 nearly as if it were plain : beyond that space, the fluid being 

 ho longer subjected as to sense to any power but that of weight 

 and its own action upon itself, its surface will be extremely^ 

 near to that of a spherical segment, of which the extreme sides, 

 being those of the surface at the limits of the sphere of sensi- 

 ble activity of the tube, will be very nearly alike inclined to thft 

 horizon in the different tubes ; whence it follows that all these 

 segments will be very nearly similar. 



The near coincidence of these results gives the true cause of 

 the ascent or depression of fluids in capillary tubes in the in- 

 verse ratio of their diameters. If inrough the axis of a tube of 

 glass, we imagine a canal infinitely narrow, which being recurv- 

 ed a little below the tube, shall proceed tp terminate at the 

 plane and horizontal surface of the water of a vessel in which 

 the lower extremity of the tube is plunged, the action of the 

 water of the tube on this canal will be less, on account of the 

 concavity of its surface, than the action of the water of the 

 vessel on the the same canal ; the fluid must therefore rise in 

 the tube to compensate this difference ; and as this is froni 

 what has been shewn in the inverse ratio of the diameter of 

 the tube, the elevation of the tube above its level must follovi?' 

 the same ratio. 



If the fluid be mercury, its surface within a capillary tube 

 of glass is convex ; its action on the canal is therefore stronger 

 than that of the mercury of the vessel, and the fluid must be 

 depressed in the tube on account of this difference, and con- 

 sequently in the inverse ratio of the diameter of the tube. 



The attraction of capillary tubes has not, therefore, any in- 

 fluence on the elevation or depression of the fluids which they 

 include, except by determining the inclination ofthefirst planes 



of 



