ON THE COHESION OF FLUIDS. 



669 



3. Central depression .09. 



Diameter. Observed central True central True marginal 

 depression. depression. depression. 



By continuing the calculations of the 

 figure of some of these curves to an arc of 

 90% I have adapted them to the surface of 

 water contained in a cylindrical tube; but 

 in this case, the scale must be supposed to 

 be augmented in the proportion of 1 to i/2. 

 The additional numbers stand thus in ab- 

 stract. 



1. Central depression .025. 



2. Central depression .05. 



Hence, for water, we have the central ele- 

 vation .035355, .07071, and .12728, and the 

 marginal elevation .17258, .19050, and 

 .22495, in tubes of which the diameters are 

 .49964, .36354, and .2490 respectively. The 

 difference of the elevations is expressed 



neary bv n=: ; — rr. r.N> which is cor- 



■' •' V8+10{</+100(/')' 



rect in the extreme cases on both sides, and 

 becomes, when d is .25, and .5, .O98, and 

 .136 respectively, instead of .0977 and .137; 

 and when <i=:l, /«=:.141. 



" Clairaut," says Mr. Laplace, " has made this singu- 

 lar remark ; that if ihe law of the attraction of the matter 

 of tlie tube, for the fluid, differs only in its intensity from 

 that of the attraction of the particles of the fluid among 

 themselves, the fluid will be elevated above the level, as 

 long as the intensity of the first of these forces exceeds 

 half that of the second. If it be exactly half as great, it 

 may easily be shown, that the surface of the fluid in the 

 tube will be horizontal, and that it will not be raised above 

 the level. If the two forces be equal, the surface of the 

 fluid will be concive and hemispherical, and it will be ele- 

 vated within the tube. If the intensity of the attraction pf 

 the tube be wholly wanting or insensible, the surface of 

 the fluid will be hemispherical, but it will be convex and 

 depressed. Between these two limits, the surface will be 

 that of a segment of a sphere, and it will be cither concave 

 or convex, accordingly as the intensity of the attraction of 

 the matter of the tube for the fluid is greater or less, than 

 half of that of the mutual attraction of the particles of the 

 fluid." 

 These conclusions are in all probability nearly 



conect with respect to very small tubes ; but 

 it is remarkable that they are not fairly dedu- 

 cible from Mr. Laplace's principles, nor from 



