CAPILLARY ATTRACTION. 



ment, which tins t><"-n constructed and tried with suc- 

 cess, wo can employ solids of all kinds, and asct > 

 tin ir action upon fluids, under circumstances which 

 i-miM not be obtained with capillary tubes. This me- 

 thod has another great advantage, as it is extremely 

 easy to remove from the outsides of the solidi all that 

 grease and foreign matter which it is BO difficult to 

 remove in tubes of glass. In another part of our 

 work, we hope to be able to give a complete draw- 

 ing of this instrument, and a table of results for va- 

 rious bodies. See Dr Brewster's Treatise on New 

 Philosophical Instruments, for various purposes in 

 the Arts and Sciences, Book vi. Edin. 1812. 



Theory of Capillary Attraction. 



Dr Hooke, who was one of the earliest writers on ca- 

 pillary attraction, ascribed the ascent of fluids, in capil- 

 lary tubes, to the unequal pressure of the atmosphere, 

 arising from a diminution of the pressure of the air 

 in consequence of its friction in the tube. This opi- 

 nion was maintained till the experiment was tried in 

 the receiver of an air pump, and when the fluid was 

 found to rise as high in vacuo as in the open air, a 

 new cause was sought for the phenomenon. Sir 

 Isaac Newton and Mr Hauksbee were of opinion, that 

 the attraction of the tube was insensible at sensible 

 distances. Dr Jurin ascribed the suspension of the fluid 

 to the attraction of the ring of glass to which the 

 upper surface of the water is contiguous, and adheres. 

 Dr Hamilton and Dr Matthew Young maintained, 

 that the fluid was elevated by the lower ring of glass 

 contiguous to the bottom of the tube, and that this 

 ring raises the portions of fluid immediately below 

 it, and then the other portions in succession, till the 

 column thus elevated was in equilibrium with the at- 

 traction of the ring. 



Clairaut had the honour of being the first mathe- 

 matician who gave any thing like a theory of capilla- 

 ry attraction. After pointing out the insufficiency 

 of preceding theories, he enters into an analysis of 

 all the forces by which the fluid is suspended in the 

 tube, of which we shall endeavour to give our read- 

 ers a brief account. Let ABCDEFGH be the 

 section of a capillary tube, MNP the surface of the 

 water in the vessel, I i the height of its ascent, VIZ 

 the concave surface of the fluid column, and IKLM 

 an indefinitely small column of fluid reaching to the 

 surface at M. Now the column ML is solicited by 

 the force of gravity which acts through the whole 

 extent of the column, and by the reciprocal attrac- 

 tion of the molecule, which, though they act the 

 same in all the points of the column, only exhibit their 

 effects towards the extremity M. If any particle e 

 is taken at a less distance from the surface than the 

 distance at which the attraction of the liquid gener- 

 ally terminates, and if m n is a plane parallel to MN, 

 and at the same distance from the particle e, then this 

 particle will be equally attracted by the water be- 

 tween the planes MN, mil. The water, however, 

 below 77i, will attract the particle downwards, and 

 this effect will take place as far as the distance where 

 the attraction ceases. 



The column IK, on the other hand, which is in a 

 state of equilibrium with ML, is acted upon by the 

 force of gravity through the whole extent of the co- 

 tymn, also by other forces at the upper and lower 



extremities of the tube. The forces exerted at the ' 

 upper part of the column, arc the attraction of the Auractk 

 tube upon the particles of water, and the reciprocal w *~" 

 attraction of these particles ; but as every particle ic 

 as much drawn upwards as downwards by the first of 

 these forces, the consideration of it may be dropped. 

 In order to estimate the other force, let a horizontal 

 plane VX touch the concavity at I, a particle/), si- 

 tuated infinitely near to I, ie attracted by all the par- 

 ticles above VX, and by all below it whose sphere 

 of activity comprehends that particle ; and as the 

 particles above p art fewer than those below it, the re- 

 sult of these forces must be a force acting downwards. 



In order to estimate the value of the forces which 

 act at the lower end O of the tube, let us suppose 

 that the tube has a prolongation to the bottom of the 

 vessel, formed of matter of the same density as the 

 water. Let a particle R be situated a little above 

 the extremity of the tube, and another Q as much be- 

 low that extremity, they will be equally acted upon by 

 the water above that place, and by the water between 

 the fictitious prolongation of the tube, and therefore 

 these forces will destroy one another. By applying 

 to the case of the particle R the same reasoning that 

 was used for the particle e, it will appear, that the 

 result of its attraction by the tube is an attraction 

 upwards. The particle R is likewise attracted down- 

 wards by the supposed prolongation of the tube, 

 and the difference between these is the real effect. 

 Theother particle Q is also drawn upwards by the tube 

 with the same force as R, since, by the hypothesis, 

 it is as far distant from the points D, G, as the par- 

 ticle R is from the points d, g, where, with respect to 

 it, the real attraction of the tube commences. The 

 particle Q is attracted also downwards, by the sup- 

 posed prolongation of the tube, and the difference of 

 these actions is the real effect. Hence the double of 

 this force is the sum of all the forces that act at the 

 lower part of the tube. These forces, when com- 

 bined with those exerted at the top of the tube, and 

 with the force of gravity, give the total expression, 

 which should be combined with that of the forces 

 with which the column ML is actuated. 



Clairaut then observes, that there is an infinitude 

 of possible laws of attraction which will give a sensi- 

 ble quantity for the elevation of the fluid above the 

 level MN when the diameter of the tube is very 

 small, and a quantity next to nothing when the dia- 

 meter is considerable ; and he remarks, that we may 

 select the law which gives the inverse ratio between 

 the diameter of the tube and the height of the li- 

 quid, conformable to Exp. 4>. 



It follows from the expression obtained by Clai- p rx 

 raut, that if any solid, AB, possesses half the at- Fi^lo. 

 tracting power of the fluid CD, the surface of the 

 fluid will remain horizontal ; for the attraction being 

 represented by DA, DE, and DC ; DA and DE 

 may be combined into DB, and DB and DC into 

 DE, which is vertical. The water will, therefore, 

 not be raised, since the surface of a fluid at rest must 

 be perpendicular to the resulting direction of all the 

 forces which act upon it. 



When the attracting power of the solid is more p;_ jj 

 than half as great, the resultant of the forces will be 

 GF in Fig. 11, and therefore the fluid must rise to- 

 wards the solid, in order to be perpendicular to GF. 

 When the attractive power of the solid is less than 



