282 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 



cylinder of oil, the diameter of which is 4 millimeters, the p.artial duration of 

 thini, in virtue of the law which we have found, would be nearly equal to 

 30'' 4- 4 



— — =t: 8". Now, in the nearly cylindrical figure of oil of § 47, Avhich 



lo 



figure is also formed in the alcoholic liquid, the moan diameter was (§ 50) about 

 4 millimeters. In this and the preceding figure, the diameter, tlie liquid, and 

 the external actions then arc tlie same; but in the former, the sum of th(> lengths 

 of the constriction and the dilatation would only be equal to 4 millimeters, 

 + 3.0=: 14.4 millimeters, whilst in the second, this sum, which is equivalent to 

 the length of a division, was {§ 56) approximatively 66.7 millimeters. Now, on 

 observing this latter figure, we recognize easily that the duration of" its trans- 

 formation is much less than 8". In truth, from the nature of the experiment, 

 it is impossible with regard to this same figure to fix upon the commencement 

 of the formation of a given constriction or dilatation, so that the complete dura- 

 tion- should considerably exceed that which would be deduced by the simple 

 i:ispoction of the phenomenon ; but the latter does not amount to one second, 

 and there cannot be any douht that it would be going too far to extend the 

 omplete duration, and a fortiori, the portion Avhicli terminates at the rupture 

 of the lines, to two seconds. Thus in the case w'e have just considered, the sum 

 of the length of a constriction and a dilatation becoming about four and a half 

 times greater, the partial duration becomes at least four times less. 



67. But if, in reckoning the absolute duration in the case of one of our short 

 cylinders of oil, we only obtain with regard to this liquid one upper limit,, and 

 tJiis much too high, the cylinder of mercury in § 55 (which cylinder is formed 

 in the air, and the length of Avhich in proportion to the diameter is sufficient for 

 the divisions to have^assumcd exactly, or very nearly, their normal length) will 

 furnish us, on the contrary, in regard to this latter liquid, with a limit which is 

 probably more approximative and which will be very useful to us. 



First, in the case of this cylinder, the diameter of which, as we have said, 

 was 2.1 millimeters, the transformation does not take place in a sufiicicntly short 

 time for us to estimate with any exactitude the total duration of the phenomenon; 

 I say the total duration, because in so rapid a transformation it would be very 

 difiicult to determine the instant at which the rupture of the lines occurs. To 

 approximate as closely as possible to the value of this total duration, I have had 

 recourse to the following process. 



By successive trials, 1 regulated the beats of a metronome in such a manner, 

 that on rapidly raising, at the exact instant at which a beat occurs, the system 

 of glass strips belonging to the apparatus serving to form the cylhidev, (§ 50 and 

 51,) the succeeding beat appeared to me to coincide with the termination of the 

 transformation ; then having satisfied myself several times that this coincidence 

 appeared very exact, I determined the duration of the interval between two 

 beats, by counting the oscillations made by the instrument during two minutes, 

 and dividing tljis time by the number of oscillations. I thus found the value 

 0".39 for the interval in question. The total duration of the transformation of 

 our cylinder of mercury may therefore- be valued approximatively at 0".39, or 

 more simply, at 0".4. 



But the entire convex surface of this cylinder is not free, and its contact with 

 the plate of glass must exert an influence upon its duration, both directly as 

 well as by the increase which it produces in the length of the divisions! Let 

 us examine the influence in question under tliis double point of view. 



The direct action of the contact with the plate is undoubtedly very slight ; for 

 as soon as the transfoi-raation commences, the liquid must detach itself from the 

 glass at all the intervals b(?tween the dilated parts, so as only to touch the solid 

 plane by a series of very minute surfaces belonging to these dilated parts; 

 consef|uently, if tUc direct action of the contact of the plate were alone eliminated, 

 «. c, if wc could manage so that the euth-e A)nvex surface of the cylinder should 



