672 PLATEAU OX THE PMiENOMENA OF A FREE LIQUID MASS 



produces in the length of the divisions. Let us examine the 

 influence in question under this double point of view. 



The direct action of the contact with the plate is undoubtedly- 

 very slight ; for as soon as the transformation commences, the 

 liquid must detach itself from the glass at all the intervals be- 

 tween the dilated parts, so as only to touch the solid plane by a 

 series of very minute surfaces belonging to these dilated parts ; 

 consequently, if the direct action of the contact of the plate were 

 alone eliminated, i. e. if we could manage so that the entire con- 

 vex surface of the cylinder should be free, but that the divisions 

 formed in it should acquire the same length as before, the total 

 duration would scarcely be at all diminished. 



There still remains the effect of the elongation of the divisions. 

 The length of the divisions of our cylinder is equal to 6'35 times 

 the diameter (§ 56), whilst, according to the hypothesis of the 

 complete freedom of the convex surface, this length would very 

 probably be less than four times the diameter (§ 60) ; now in virtue 

 of the principle established in the preceding section, this in- 

 crease in the length of the divisions necessarily entails a dimi- 

 nution in the duration, which diminution is more considerable 

 in proportion as it occurs in the vicinity of the limit of stability ; 

 consequently, if it could be managed so that the elongation in 

 question should not exist, the total duration would be very consi- 

 derably increased. Thus the suppression of the direct action of 

 the contact of the plate would only produce a very slight dimi- 

 nution of the total duration ; and the annihilation of the elonga- 

 tion of the divisions would produce, on the other hand, a very 

 considerable increase in this same duration ; if then these two 

 influences were simultaneously eliminated, or in other words, if 

 the entire convex surface of our cylinder were free, the total du- 

 ration of our transformation would be very considerably greater 

 than the direct result of observation. 



Wow the quantity which we have to consider, is the partial 

 and not the total duration ; but under the same circumstances, 

 the first must be but little less than the second ; for when the 

 lines are about to break, the masses between which they extend 

 even then approximate to the spherical form ; consequently, in 

 accordance with the conclusion obtained above, we must admit 

 that the partial duration under our present consideration, i. e. 

 that referring to the case of the complete freedom of the convex 



