IIYDR O DYNAMICS. 



475 



ry adhering to the lent, in the same manner as the depres- 

 oa s i on u produced on the surface of alcohol, hy a drop of 

 alcohol rolling over it, a* shewn in Fig. 5, or by some 

 other repulsive force with which we are unacquainted. 



, m f a The transference of the focus from F to/, may be 



LATE occasioned by the optical contact of the glass and water 



I- taking place at a greater distance from the lens than the 



"" * dittaiM 1 ? at which the capillary attraction commence*. 



For if the surface* / /, m n, at a certain distance, act upon 



the rays of light as if they were one surface, then it is 



manifest that a dark spot ought to appear at /f, if this 



distance is less than that at which capillary attraction 



begin*. 



6. Account of La Placet Theory of Capillary 

 Attraction. 



L, Pbc*'i I" the fir** supplement published by M. le Comte 

 La Place, his method of considering the phenomena 

 was founded on the form of the surface of the fluid in 

 capillary spaces, and on the conditions of equilibrium 

 of this fluid in an infinitely narrow canal, resting by 

 one of its extremities upon this surface, and by the 

 other on the horizontal surfaces of an indefinite fluid, 

 in which the capillary tube was immersed. In his se- 

 cond supplement, be has examined the subject in a 

 much more popular point of view, by considering di- 

 rectly the forces which elevate and depress the fluid in 

 this space. By this means, he is conducted easily to 

 several general results, which it would have been dif- 

 ficult ta oUain directly by hi* foraer method. Of this 

 method we shall endeavour to give a* dear a view a* 

 possible. 



Let AB, Fig. 7- be a vertical tube whose side* are per- 

 pendicular to its base, and which is immersed in a fluid 

 that rises in the interior of the tube above its natu- 

 ral level. A thin film of fluid is first raised by the ac- 

 tion of the side* of the tube ; this film raises a second 



** 7 - film, and this second film a third film, till the weight 

 of the volume of fluid raised exactly balances all the 

 forces by which it is actuated. Hence it is obvious, 

 that the elevation of the column is produced by the at- 

 traction of the tube upon the fluid, and the attraction 

 of the fluid for itself. Let us suppose that the inner 

 surface of the tune AB is prolonged to E, and after 

 bending itself horixmtally i the direction ED, that it 

 assume* a vertical direction DC ; and let us suppese 

 the sides of thi tube to be so extremely thin, or to 

 be formed of a film of ice, so a* to have no action on the 

 fluid which k contain*, awl not to prevent the recipro- 

 cal action which takes place between the particle* of 

 the first tube AB and the particle* of the fluid. Now, 

 since the fluid in the tubes A F., CD is in equilibrium, 

 obvious that the excess of preMure of the fluiil in 

 AE is destroyed by the vertical attraction of the tube 

 and of the fluid upon the fluid contained in AB. In 

 "?' t** different attraction*, M. Ijt FTace eon- 

 sid*n KM those which take p'are under the robe AB. 

 The ftaid eeJamn BE is attracted, 1. by itself; 2. by 

 the fluid MiTDimdang the tube BE. But these two at- 

 tractions are destroyed by the similar attractions expe- 

 rienced hy the Arid contained in the branch DC, so 

 that they may be entirely nrglected. The fhmt in BE 

 is also attracted vertically by the fluid in AB ; bat this 

 attraction is destroyed by the attraction which it exer- 

 OM m the oppoaite direction upon the flMd in BE, so 

 that thmfcatjneed attractions may likewjea be neglect- 

 ed. The fluid in BE is likewise attracted vertically 

 upwards by the tube AB, with a force whkh we shall call 



An.Jyti.of 

 I * farce* by 

 which the \hat 



Q, and which contributes to destroy the excess *f pres- OnCapillary 

 sure exerted upon it by the column BF raised in the Attraction 

 tube above its natural level Coition "of 



Now, the fluid in the lower part of the round tube Fluids. 

 AB is attracted, 1. By itself; but as the reciprocal at- VV-M' 

 tractions of a body do not communicate to it any mo- Analysis of 

 tion if it is solid, we may, without disturbing the equi- t ^ 1 f. f ? rc ? bir 

 librium, conceive the fluid in AB frozen. 2. The *.fi 

 fluid in the lower part of AB is attracted by the inte- ,.,;.!. 

 nor fluid of the tube BE, but as the latter is attracted PLATE 

 upwards by the same force, these two actions may be CCCXVI. 

 neglected as balancing each other. 3. The fluid in r ''iS- 7> 

 the lower part of BE, is attracted by the fluid which 

 surrounds the ideal tube BE, and the result of this 

 attraction is a vertical force acting downwards, which 

 we may call Q', the contrary sign being applied, as 

 the force is here opposite to the other force Q. A* 

 it is highly probable that the attractive forces exercised 

 by the glass and the water vary according to the same 

 function of the distance, so as to differ only in their in- 

 tensities, we may employ the constant co-efficients j, ^ 

 as measures of their intensity, so that the forces Q and 



' will be proportional to j, / ; for the interior surface 

 of the fluid which surrounds the tube BE, is the same 

 as the interior surface of the tube AB. Consequently, 

 the two masses, viz. the glass in AB, and the fluid 

 round BE, differ only in their thickness ; but as the 

 attraction of both these masses is insensible at sensible 

 distances, the difference of their thicknesses, provided 

 their thicknesses are sensible, will produce no differ- 

 ence in the attraction*. 4. The fluid in the tnbe AB 

 is also acted upon by another force, namely, by the 

 aides of the tube AB in which it is inclosed. If we 

 Conceive the column FB divided into an infinite number 

 of elementary vertical columns, and if at the upper ex- 

 tremity of one of these column* we draw a horizontal 

 plane, the portion of the tube comprehended be- 

 the plane and the level surface BC of the fluid, will not 

 produce any vertical force upon the column ; conse- 

 quently, the only native vertical force is that which it 

 produced by the ring of the tube immediately above the 

 LorizonU) plane. Now, the vertical attraction of thai 

 part of the tube upon BE, will be equal to that of (he 

 entire tube upon the column BE, which is equal in 

 diameter, and similarly placed. This new force will 

 therefore be represented by + Q. In combining these 

 different forces, it is man lest that the fluid column BF 

 is attracted upwards by Uie two forces 4. Q, -f Q, snd 

 downwards by the forte Q* : cnnsrqurntly the fere* 

 with which it is raised upward* will be tQQ'. II 

 we represent by V the volume ef the column BE, I> 

 it* density, and g the force of gravity, then g DV will 

 HSynstlU the weight of the elevated coluwn ; but a* 

 this weight is hi equilihrie> with tlie force* by which 

 it is elevated, we hare the fellow ing equation* 



If the force 2 Q is less than Q 7 . then V will be nega* 

 tive, and the fluid will sink in the tube; but a* long a* 

 8 Q is greater than Q', V will be positive, and the 

 fluid will rre above it* natural level ; a* was long be* 

 fore shewn by M. Clairsut. 



Since the attractive force*, both of the gnu* and tie 

 fluid, are imensible at sensible distances, the surface of 

 the tube AB wiU act sensibly only on the column of 

 fluid immediately in contact with it. We may there- 

 fore neglect the consideration of the curvature, and 

 consider the inner surface a* developed upon a plane. 

 The force Q will therefore be proportional to the 





