WITHDRAWN FROM THE ACTION OF GRAVITY. 293 
Let us pass to the quantity s. We know that the distance between the orifice 
and the contracted section, although not entirely independent of the charge, 
always differs but little from the semi-diameter of the orifice, so that we should 
have very nearly s=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 divi- 
sions of our vein to the diameter / ; 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 number 3; calculation 
will then give for the diameter of the isolated spheres the quantity 1.65.%, and 
for the interval between two consecutive spheres the quantity 1.35.4. Com- 
pleting the operations with these data, in the same manner as above, we obtain 
as the final result 
s—7—0.23.K, 
also a very slight difference. 
Now, as the true value of the difference s~z must be comprised between 
the two limits which we have just found, 2. e, —0.08.K and +0.23. K, and 
as we cannot ascertain either the one or the other, we shall obtain a sufiicient 
approximation to this true value by taking the mean of the two above limits, 
which gives, lastly, 
Let the distance remain D. As this is traversed by a uniform movement during 
the time ? and with the velocity V2gh, we shall first have 
D=0 V 2h. 
Now, as the time @ 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 section of our imaginary vein of mercury were a centimetre, the 
time @ would be considerably more than 2 seconds ; however, in order to place 
ourselves intentionally under unfavorable circumstances, let us suppose that, in 
the above case, the time in question were only equal to 2 seconds. But the 
time 7 is proportionate to the diameter of the contracted section, (preceding 
section ;) if, then, we take the second as the unit of time and the centimetre 
as the unit of length, we shall have for any value & of this diameter 
’ ==): 
and if we replace & by its approximative value 0.8 .K, it will become 
0=1.6.K; 
consequently 
D=1°6.K V2en. 
As we have taken the second and the centimetre as the units of time and length, 
g will be equal to 980.9; and this value being substituted in the above expres- 
sion, it will ‘finally become 
‘ D=70.87 .K vi. 
From this expression, and that of s—z given by the formula (2,) we deduce 
3—7 0.07 f 
D ~ 70.87. Va Vi 
Now, according to the equation (1) this quantity represents the error we com- 
mit in supposing ia 1, or Ld; it is evident that this error is independent 
of the diameter of the orifice, but that it varies with the charge, and that it is 
