WITHDRAWN FROM THE ACTION OF GRAVITY. 689 



the semi-diameter of the orifice, so that we should have very 

 nearly *=0'50 . K, and therefore 



s—i=0-50 . K-0-58 . K= -0-08 . K, 

 evidently a very slight difference. 



We have assumed 4 as the value of the proportion of the 

 length of the divisions of our vein to the diameter k ; this value 

 is undoubtedly too great ; but as the exact value must necessarily 

 exceed the limit of stability, which is itself more than 3, we 

 may admit that this exact value is considerably more than the 

 latter number. Suppose it, however, to be equal to this num- 

 ber 3 ; calculation will then give for the diameter of the isolated 

 spheres the quantity 1"65 . k, and for the interval between two 

 consecutive spheres the quantity 1*35 . k. Completing the opera- 

 tions with these data in the same manner as above, we obtain 

 as the final result 



s—i = 0-23.K, 



also a very slight difference. 



Now as the true value of the difference s — i must be comprised 

 between the two limits which we have just found, i. e. — 0*08 . K 

 and +0*23 . K, and as we cannot ascertain either the one or the 

 other, we shall obtain a sufficient approximation to this true 

 value by taking the mean of the two above limits, which gives, 

 lastly, 



s-i=0-07.K (2.) 



Let the distance remain D. As this is traversed by a uniform 

 movement during the time and with the velocity */ 2yh^ we 

 shall first have 



D = ^\/2p. 



Now as the time Q is equal (preceding section) to the partial 

 duration of the transformation of a cylinder of the same diameter 

 and of the same liquid as the vein, and which would be formed 

 under the conditions of the results summed up in § 68, it follows 

 from one of the latter, that if the diameter of the contracted sec- 

 tion of our imaginary vein of mercury were a centimetre, the 

 time 6 would be considerably more than 2 seconds ; however, in 

 order to place ourselves intentionally under unfavourable circum- 

 stances, let us suppose that, in the above case, the time in ques- 

 tion were only equal to 2 seconds. But the time 6 is propor- 

 tionate to the diameter of the contracted section (preceding sec- 

 tion) ; if then we take the second as the unit of time and the 



