4 Mr. Ivory on the Theory of Capillary Action, and 



4|3 9 being a quantity to be found by experiment in tubes of 

 any given matter. 



In the glass tubes of which barometers are made, 4 /3 2 is 

 very nearly equal to 496, and j3 to 7 ; and the value of z at the 

 surface of such tubes, or the sine of the inclination of the mer- 

 cury to the horizon, may be taken equal to 0*735. These 

 numbers, which are very convenient, accord nearly with the 

 results of the best experiments, or at least approach to them 

 within the limits of the errors to which all such experimental 

 determinations are liable. 



Instead of the curve surface actually formed in the tube, I 

 shall now consider another similar surface, of which the linear 

 dimensions are increased fourteen times, or in the proportion 

 of 2/3 to 1. If ?/ represent the vertical ordinate of this new 

 curve, and y stand for 2/3r, we shall have these equations, viz. 



dz z 



dy z_ 



Exterminate y, and put t = -^- = /3r; then 



, ddz dz z 4* 



~dF~ + Tdt """ ~F ~ ^73^" 



It may be proper to observe here, that the depression is the 

 value of the vertical ordinate, when % and x vanish together, 



in which case also — = -r-. Hence the depression is equal 

 to — or — ,— , that is, to ■»-■ or -^-, when z and t are both 



x dx t dt' 



evanescent. 



Next assume, z = qt cf a d \ 



c being the base of Napier's logarithms, and q a constant 

 quantity, which is no other than the depression. Substitute 

 the values of z and its fluxions in the last equation, leaving 

 untouched the radical on the right-hand side ; then, 



dt 



dt V 1 - z* 



In the foregoing operations z and co are considered as func- 

 tions of t : but I shall now suppose that z is a function of /, 

 and co a function of the independent variables z and t. In the 



last equation we must therefore write -£ + ~ • -^ for 



at 



