WITHDRAWN FROM THE ACTION OF GRAVITY. 665 



those corresponding to two homologous points taken upon both 

 the figures will still be to each other as the configuring forces 

 commencing at these points ; so that in fact the respective re- 

 sultants of the external and internal actions at these two same 

 points will be to each other in the same proportion as the two 

 internal forces alone. Thus the attractions exerted upon the 

 oil by the surrounding alcoholic liquid will certainly diminish 

 the absolute intensities of the configuring forces, but they will 

 not change the relations of these intensities, consequently they 

 may be considered as not exerting any influence upon the dura- 

 tions. But it is clear that this cause will nevertheless greatly 

 increase the absolute values of the latter. For the two reasons 

 which we have explained, the presence of the alcoholic liquid 

 will then increase the absolute values of the two durations to a 

 considerable extent ; but we may admit that it will not alter the 

 relation of these values, so that this proportion will be the same 

 whether the phaenomenon take place in vacuo or in air. We 

 shall therefore consider the law which we deduce from our experi- 

 ments upon short cylinders of oil, as independent of the presence 

 of the surrounding alcoholic liquid, and this will be found to be 

 supported by the nature of the law itself. 



But the exact formation of our short cylinders of oil requires 

 (§ 46) that in these cylinders the proportion between the length 

 and the diameter, or what comes to the same thing, between the 

 sum of the lengths of the constriction and the dilatation and 

 the diameter, exceeds but little the limit of stability. Now in 

 the transformation of cylinders sufficiently long to furnish 

 several spheres, which would be formed in vacuo or in the air, 

 and free upon their entire convex surface, and the divisions of 

 which have their normal length, the proportion of the sums of the 

 lengths of one constriction and one dilatation to the diameter, 

 which proportion is the same as that of the length of one divi- 

 sion to the diameter, would vary with the nature of the liquid 

 (§ 59), and we are ignorant whether the law of the durations is 

 independent of the value of this proportion. The law which we 

 shall obtain in regard to short cylinders of oil can only therefore 

 be legitimately applied to cylinders of sufficient length to furnish 

 several spheres supposed to be in the above conditions, in the 

 case where these latter cylinders are formed of such a liquid that 

 they would give for the proportion in question a value but little 

 greater than that of the limit of stability. 



Now this is the case of mercury (§ 60), and it is also very 



