258 THE FIGURES OP EQUILIBEIITM OF A LIQUID MASS 



respectively adlieront to the two opposite solid surfaces. The limit of the 

 stability of the cylinder, therefore, really lies between 3 and 4. 



The experiments which we have just related are very delicate, and i-equire 

 some skill. In this, as in all other cases of measurements, the oil must be 

 allowed to remain in the alcoholic mixture for two or three days, then the pel- 

 licle must be removed from it, (note to p. 254;) afterAvards, when the mass, 

 after having been again introduced into the vessel, has been attached to the two 

 solid disks, some time must be allowed to elapse in order that the two liquids 

 may be exactly at the same temperature ; moreover, it must be understood that 

 the experiments should be made in an apartment the temperature of which 

 remains as constant as possible. Lastly, it is scarcely necessary to add, that 

 when the alcoholic liquid is mixed, after having added small quantities of pure 

 alcohol or alcohol at 16°, the movements of the spatula should be very slow, so 

 as to avoid the communication of too much agitation to the mass of oil ; we are 

 even sometimes compelled momentarily to depress the upper disk, so as to give 

 greater stability to the mass, and thus to prevent the movements in question from 

 producing the disunion. 



4G. It might be asked whether the want of symmetry, which -3 constantly 

 seen in the spontaneous modification of the above unstable figures, is the result 

 of a laAv which governs these figures ; or whether it simply arises, as we should 

 be led to believe at first sight, from imperceptible differences still existing be- 

 tween the densities of the two liquids, which differences acting upon unstable figures 

 might produce this want of symmetry, notwithstanding their extreme minuteness 

 After having concluded the preceding experiments, I imagined that to solve 

 the question in point, all that would be requisite would be to arrange matters so 

 that the axis of the figure, instead of being vertical, as in the above experiments, 

 should have a horizontal direction. In ftict, in the latter case, the slightest 

 difference between the densities ought to haA'e the effect of slightly curving the 

 figure, but evidently cannot give the liquid any tendency to move in greater 

 quantity tOAvards one extremity of the figure than the other ; whence it folloAvs, 

 that if the spontaneous alteration of the figure still occurs unsymmetrically, 

 this can only be OAving to a peculiar law. 



On the other hand, if the figure really tends of itself to change its form un- 

 symmetrically, it is clear that, in the case of the vertical position of the axis, 

 the effect of a trace of difference betAveen the densities ought to concur with that 

 of the instability, and thus to accelerate the moment at which the figure com- 

 mences to alter spontaneously. Consequently, on avoiding this extraneous 

 cause by the horizontal direction of the axis of the figure, we may hope to 

 approximate more nearly to the cylindrical form, or even to attain it exactly; 

 we can, moreover, understand that the difficulty in the operations will be found 

 to be considerably diminished. 



I therefore constructed a solid system, presenting two vertical disks of the 



same diameter, placed parallel Avith each 

 other, at the same height, and opposite 

 each other. Each of these disks is sup- 

 ported by an iron wire fixed normally 

 to its centre, then bent A^ertically doAvn- 

 "wards, and the lower extremities of 

 these two Avires are attached to a hori- 

 zontal axis furnished Avith four small 

 feet. This system is represented in 

 perspective in Fig. 27. The diameter 

 of the disks is 30 millimeters, but the 

 distance Avhich separates them is not 

 four times this diameter. I thought that 

 by approximating the figure more to the limit of stability, the operations 



