ON THE COHESION OF FLUIDS. 



665 



equal weight, these results follow of necessity, which I had already published, in ah essay 

 without any intricacies of calculation what- not (Containing, in its original state, any one 



mathematical symbol, it is obvious that the 



inaccuracy of Newton's reasoning did not 

 depend upon any deficiency in his tnatheilia- 

 tical acquirements. 



" It may be shown by calculation, that the sine of the . 

 inclination of the axis of the cone to the horizon will 

 be veiy nearly equal to the fraction of which the denomi- 

 nator is the distance of the middle of the drop from the 



ever 



" The phenomena exhibited by a drop of a fluid, moving, 

 or suspended in equilibrium, either in a conical capillary 

 lube, or between two planes, inclined in a small angle to 

 each other, are extremely proper to confirm our theory. A 

 small column of water, in a conical tube, open at both 

 ends, and held in a horizontal position, will move towards 

 the vertex of the cone ; and it is obvious, that this must ne- 

 cessarily happen. In fact, the surface of the column is 

 concave at both ends, but the radius of this curvature is summit of the cone, and the numerator the height to 

 smaller at the end nearer the vertex than at the opposite '"^'"^^ «he fluid would rise in a cylindrical tube, of adiame- 

 end ; the action of the fluid upon itself is dierefore less at '"^f^qual to that of the cone at tlie middle of the column. 

 the narrower end, consequently the column must be drawn ^^ *' "^° planes, inclosing a drop of the same fluid, form 

 towards this side. If the fluid employed be mercury, its ^'^^ '^^^^ °'^" *" angle, equal to that which is formed by 

 surface will be convex, and the radius of curvature will still '*'* ^"'^ °f ''^^ '^""^ and its sides, the inclination of a plane, 

 be smaller towards the vertex than towards the base of the b'secting this angle, to the horizon, must be the same as 

 cone ; but, on account of its convexity, the action of the *^' °^ '^^ *"'* °f ^^^ <^0"c> '" °'d" that the drop may re- 

 fluid upon itself will be greater at the narrowerend, and the "*'" '" equilibrium. Hauksbee has hiade, SWth very 

 column must therefore move towards the wider part of the S"^*^" '^^''' *" experiment of this Icind, '♦fhich I have com- 



tube. 



" This action may be counterbalanced by the weight of 

 the column, so as to be held in equilibrium by it, if we in- 

 cline the axis of the tube to the horizon. A veiy simple 



pared with the theorem here laid down ; and the near 

 agreement between the experiment and the theorem is 

 amply sufficient to confirm its truth." 



If the height at which the fluid would 



calculation is sufficient to demonstrate, that if the length of Stand, in a tube of the diameter of the up- 



the column is inconsiderable, the sine of the inclination of per end of the Coluilin, be k ; the distance ot 



this end from the vertex of the cone being it, 

 and the length of the column y, the height 

 corresponding to the remoter end will b6 



■j-^, and the difference of the heights h — 



-r- =-7- 'Which must be the difference of the 



the axis must be inversely proportional to the square of the 

 distance of the middle of the column from the summit 

 of the cone ; and this law is equally applicable to the case 

 of a drop of a fluid placed between two planes, which 

 forma very small angle with each other, their horizontal 

 margins being iij contact. Tlicse results are perfectly con- 

 formable to experiment, as maybe seen in the 3 1st query 

 of Newton's optics. This great geometrician has endea- 

 voured to explain them, but Ms explanation, compared heights of the ends of the drop, in Ordef that 

 with that vfhich has been here advanced, serves only to it maj'remain in equilibrium ; but this heio-ht 

 ihow the advantages of a precise and mathematical invts- j^ to y as A to X+y, consequently the axis 

 ligation." p , , , . 1. 1 t I . 



or tlie tube must be mcliiled to the horizon, 



Mr. Laplace's superior skill in the most re- . , . . ^ , 



c , „ ^u .• 1 • ^- ^- >' • u» in an angle, of which the sine is exactly » 



faned " mathematical investigations might . ° ' J x+y 



perhaps have enabled him to make still more the denominator being the distance of one 



essential improvements, if it had been em- end from the vertex, and the numerator the 



ployed on some other subjects of natural height at which the fluid would stand in a 



philosophy; but his explanation of these tube, of which the diameter is equal to that 



phenomena being exactly the same as that of the column at the other end. 



VOL. n. ^^ 



