WITHDRAWN FROM THE ACTION OF GRAVITY. 



271 



It is evident that the different values of the length of a division, with a sin- 

 gle exception, are all obviously greater than all those which relate to a cylinder 

 of the same diameter, the surface of which only touches the glass by a si.ngle 

 line, {§ 54.) We must thence conclude that, all other things being the same, 

 the length of the divisions increases with the external resistance; consequently, 

 under the action of the same resistance, this length is necessarily greater than 

 it Avould be if the convex surface of the cylinder had been perfectly free. 



In the above series neither of the results appears to be very regular; but we 



can readily understand that the mean of the values of the third column will 



approach the normal length of the divisions. This is, moreover, confirmed by 



the tables in §§ 54 and 55. If we take in the former the respective means of 



the values of the two series, we find for one 6.77 millimeters, and for the other 



7.17 millimeters, quantities, the first of which is nearly equal to the length 



6.67 millimeters, which may be considered as the normal length, and from 



which the second does not differ much ; and if likewise we take the relative 



mean in the following table, we find 13.15 millimeters, a quantity very near 



the length 13.33 millimeters, which in the case of the second table may also be 



regarded as the normal length. Now, the corresponding mean in the above 



table is 10.81 millimeters ; consequently, in the case of two lines of contact we 



1 SI 

 liave -j-—-- = 10.29 as the approximate value of the proportion of the normal 

 l.Uo 



length of the divisions to the diameter of the cylinder, whilst in the case of a 

 single line of contact we found only 6.35. Hence the proportion between the 

 normal length of the divisions and the diameter of the cylinder increases by 

 the effect of an external resistance. 



59. Let us proceed to the influence of the nature of the liquid. All liquids 

 are more or less viscid ; i. c, their molecules do not enjoy perfect mobility with 

 regard to each other. Now, this gives rise to an internal resistance, which 

 must also render the transformation less easy ; and as external resistances 

 increase the length of the divisions, we can understand that the viscidity will 

 act in the same manner; consequently, all other things being equal, the propor- 

 tion now under consideration will increase with this viscidity. But, on the other 

 hand, with equal curvatures,. the intensities of the forces Avhich produce the 

 transformation vary with the nature of the liquid ; for these intensities depend, 

 in the case of each liquid, upon that of the mutual attraction of the molecules. 

 Now, it is clear that the viscidity will exert so much more influence upon the 

 length of the divisions as the intensities of the forces in question arc less. 

 Thus, leaving external resistances out of the question, the proportions of the 

 normal length of the divisions to the diameters will be greater in proportion to 

 the viscidity of the liquid and the feebleness of the configuring forces. 



