WITHDRAWN FROM THE ACTION OF GRAVITY. 281 



We may, tlierefore, I think, legitimately generalize the above law iu accord- 

 ance with the whole of the remarks made in the preceding .^ection, and deduce 

 the following conclusions : 



1. If we conceive a cylinder of mercury formed in vactio or in air, of sufficient 

 length to furnish several spheres, its convex surface being entirely free, and its 

 length such that the divisions assume exactly their normal length, the time 

 which will elapse from the origin of the transformation to the instant of the 

 rupture of the lines will be exactly or apjxa-rently projjortional to the diameter 

 of this cylinder. 



2. The same very probably applies to a cylinder formed of any other very 

 slightly viscid liquid, as water, alcohol, &c., and supposed to exist under the 

 same circumstances. 



3. It i.s possible tliat this law is completely general, i. e., applicable to a cyl- 

 inder formed, always under the same circumstances, of any kind of licjuid what- 

 ever; but our experiments leave us in doubt on this point. 



66. Let us now enter upon the consideration of the absolute value of the time 

 in question for a given diameter, the cylinder always being supposed to be pro- 

 duced ill vacuo or iu air, of sufficient length to furnish several spheres, its entire 

 convex surface free, and its length such that its divisions assume their normal 

 length. It is clear that this absolute value must vary according to the nature 

 of the liquid; for it evidently depends upon the density of the latter, upon the 

 intensity of its configuring forces, and, lastly, upon its viscidity. The experi- 

 ments which we have detailed give with regard to oil a very remote superior 

 limit ; this results, first, from the two causes which we have mentioned in § 64, 

 and which are due to the presence of the alcoholic liquid ; but with these two 

 causes is connected a third, which we must make known. If we imagine a cyl- 

 inder of oil formed under the above conditions, the simi of the lengths of a 

 constriction and a dilatation will necessarily be much greater in regard to this 

 cylinder than in regard to one of our short cylinders of oil of the same diameter; 

 for in the former this sum is equivalent to the length of a division ; and in con- 

 sequence of the great viscidity of the oil, this latter quantity must greatly 

 exceed the length corresponding to the limit of stability. Now, it may be laid 

 down as a principle, that, all other things being equal, an increase iu the sum 

 of the lengths of a constriction and a dilatation- tends to render the transfiirmation 

 more rapid, and consequently to abbreviate the total and partial durations of 

 the phenomenon. In fact, for a given diameter, the more the sum in question 

 difi'ers from the length corresponding to the limit of stability, the more the forces 

 which produce the transformation must act with energy ; moreover, as the trans- 

 formation ceases to take place immediately above the limit of stability, the 

 duration ef the phenomenon may then be considered as infinite, whence it fol- 

 lows that when this limit is exceeded, the duration passes from an infinite to a 

 finite value, consequently it must decrease rapidly as it deviates 'from this limit; 

 lastly, this is also confirmed by the results of observation, as we shall slow 

 hereafter. Thus, even if it wefe possible to form in ractio or in air one of our 

 very short cylinders of oil, consequently to eliminate the two causes of retarda- 

 tion due to the presence of the alcoholic liquid, ^the duration relative to the 

 cylinder would still exceed that which would relate to a cylinder of oil of the 

 same diameter formed under the conditions we have supposed. 



I have said that the principle above established is confirmed by experiment, 

 i. c, for the same diameter, the same liquid, and the same external actions, if 

 any exist ; when, from any cause, the sum of the lengths of a constriction and a 

 dilatation augments, the total and partial durations of the transformation become 

 less. We shall proceed to make this evident. In the experiments of the pre- 

 ceding section, the partial duration relating to the cylinder, the diameter of 

 which was 15 millimeters, was, for instance, about 30 seconds, iJic mean, as shown 

 by the table. Consequently, if we \tere to form iu the alcoholic liquid a similar 



