WITHDRAWN FEOM THE ACTION OF GRAVITY. 



267 



This table sliows, iu the first place, that the diifcrent values obtained for the 

 length of a division are not so far removed from each other as to prevent our 

 perceiving a constant value, the uniformity of which is only altered by the 

 influence of slight accidental causes. In the second place, out of twenty ex- 

 periments, it happened once only that the masses adherent to the bases were 

 both of the small kind. In the third place, both the perfectly regular results 

 have given identically the same value for tlie length of a division; this value, 

 expressed approximatively to two decimal places, is 6.67 millimeters ; but its 

 exact expression is 6§- millimeters ; for the operation to be effected consists, in 

 the case of the first series, in the division of 90 millimeters by 13.5, and, in the 

 case of the second series, in the division of 100 millimeters by 15. As the two 

 lengths given to the cjdinder are considerable in proportion to the diameter, and 

 consequently the numbers of division are tolerably large, this value, 65 milli- 

 meters, ought very nearly, if not exactly, to constitute that of the normal length 

 of the divisions. It is seen, moreover, that to give the divisions this closely 

 approximative or exact value of the normal length, the transformation has 

 chosen, in one case the first, in the other case the second method. 



55. Let us pursue our inquiry into the laws of the phenomenon with which 

 we are engaged ;. we shall soon make an important application of them, and it 

 will then be understood why so extensive a development is given to this part of 

 our work. It might be regarded as evident a priori that two cylinders formed 

 of the same liquid and placed in the same circumstances, but differing in diameter, 

 would tend to become di\'ided in the same manner, i. e., that the respective nor- 

 mal lengths of the divisions would be to each other iu the proportion of the 

 diameters of these cylinders. 



In order to verify this law by experiment, I procured some copper wires, the 

 diameter of which was exactly double that of the first, therefore equal to 2.1 

 millimeters, and 1 made with them a new series of ten experiments, giving the 

 cylinder a length of 100 millimeters. This series also furnished me with only 

 a single perfectly regular result, which I have denoted as before by an * placed 

 opposite the corresponding number of isolated spheres. The following is the 

 table relating to this series : 



Number of 

 isolated 

 spheres. 



Masses adheront to the bases. 



Length 



of a 

 division. 



Two small 



Two laige 



One large and oue small 

 One large aud one small 



Two large 



Two large 



Ouc large and one small 

 Oue laige and one small 



Two small 



One large aud one small 



millijns. 

 13.33 

 13.33 

 14.28 

 1-2..O0 

 13.33 

 13.33 

 14.28 

 11.11 

 11.76 

 14.28 



By stopping at the second decimal place, wc have, as is evident, 13.33 milli- 

 meters for the value of the length of a division corresponding to the perfectly 

 reo'ular result; but as the operation which yields it consists in the division of 

 100 by 7.5, the value when perfectly expressed is 13^ millimeters. This then 

 is very nearly, if not exactly, the normal length of the divisions of this new 

 •cylinder; now this length, 13^ millimeters, is exactly twice the length, C§ 

 millimeters, which belongs to the divisions of the cylinder of the preceding 



