On Figures of Equilibrium of a Liquid Mass. 61 



of every other crop, the rest of the land being defrauded of 

 its due share of nourishment to supply the increasing demands 

 of the hop-garden : and further, that in this cultivation there is 

 no relief by alternating crops or fallows, unless the occasional 

 failures from blight and other causes may be so termed. The 

 quantity of alkali thus removed every year exceeds that of a 

 very heavy crop of grain, while the phosphoric acid amounts to 

 more than half that of the latter. It is probable also that the 

 quantities of phosphoric and sulphuric acids present in the 

 ash do not indicate the total quantities of sulphur and phos- 

 phorus removed from the soil, inasmuch as portions of these 

 elements may exist in the plants as pi'oteine-compovinds. 



IX. Experimental B.esearchcs on Figures of Eqidlibritim of 

 a Liquid Mass "withdraivn from the Action of Gravity : 

 Second Series. By M. Plateau*. 



'T^HE theory of capillary action, as established by the 

 -■■ labours of Laplace, Poisson, &c., is not limited to the ex- 

 planation of the cause of the ascension or the depression 

 of liquids in narrow spaces, and the determination of the 

 laws which regulate this phsenomenon ; it also permits, as is 

 well known, of our arriving at the differential equation which 

 represents the free surface of a liquid, in circumstances where 

 the form of that surface is influenced by molecular attraction, 

 as for example at the summit of the raised or depressed column 

 in a capillary tube, along the sides of a solid body in part 

 immersed, &c. But this equation cannot be integrated but 

 by approximation, so that it is impossible to determine strictly 

 the forms of the surface in question. On the other hand, on 

 account of the preponderating action of gravit}', the influence 

 of molecular attraction can only become observable on sur- 

 faces, or portions of surfaces, which present but a small ex- 

 tent either in all directions or at least in one direction, such 

 as the surface which terminates a capillary column, that of a 

 liquid drop placed on a solid plane which it cannot moisten, 

 the portion of the surface of a liquid raised along the sides of 

 the vessel which contains it, &c. It would consequently be 

 very difficult to verify by accurate admeasurements this im- 

 portant part of the theory; and it has hitherto remained 

 almost without any other confirmation than that deduced 

 from the simple aspect of the phajnomena. 



Now it will be remembered that in his preceding memoir 



• From an abstract by M. Quetelet, published in the Bulletin dc I'AcU' 

 demie Koi/a'e de Belgifjue. The First Series of these interesting investiga- 

 tions aiipeiircd in the I3tii Part of tlie Scicntifii; Memoirs. 



