WITHDRAWN FROM THE ACTION OF GRAVITY. 299 
hz the charge which plays the same part with regard to the vein escaping from 
the smallest orifice as that which f, plays with regard to that which escapes 
from the larger one. It must be borne in mind that 3 is less than h,, and let 
us suppose 22 to be comprised between the two latter. With the charges /, 
and fz the vein escaping from the smallest orifice will therefore then still exist 
under the effective conditions of Savart’s first law, whilst, as regards the vein 
which escapes from the larger orifice, these conditions will only commence at 
h,; if, then, we pass from /, to hy, the continuous portion of the first vein will 
decrease in proportion to the square roots of these two charges; but that of the 
latter vein will decrease in a different proportion. Now, with the charge hy 
these two lengths were to each other as the diameters of the corresponding 
orifices; with the charge h2, then, they would exist in another proportion; con- 
sequently the second law of Savart would no longer be satisfied, at least as 
regards the two extreme veins of the series brought into comparison. 
The following new conclusions result from all this: With a sufficiently weak 
common charge, the proportionality of the length of the continuous portion of 
the mercurial column to the diameter of the orifice does not exist throughout 
the entire extent assigned to the Variations of this diameter; but it begins to 
manifest itself when that value is given to the common charge at which the 
vein escaping from the largest of the orifices commences to exist under the 
effective conditions of Savart’s first law. 
Respecting these conclusions, we must repeat what we stated with regard to 
that terminating the preceding section, viz: that they are very probably appli- 
cable, at least to all very slightly viscid liquids, consequently to water. 
Now, we shall see that these same conclusions, as also those of the pre- 
ceding section, are in accordance with the results of Savart’s experiments, 
which results relate to water. 
80. Savart has made two series of observations upon veins of water with- 
drawn from all extraneous influences, one with an orifice 6 millimetres, the 
other with an orifice 3 millimetres in diameter; the successive charges were 
the same in both series. The two following tables represent the results ob- 
tained, 2. e., the lengths of the continuous part corresponding to the successive 
charges ; both the lengths and the charges are expressed in centimetres. I 
have inserted in each table a third column, containing, in regard to each of the 
lengths of the continuous part, the proportion of the latter to the square root 
of the corresponding charge : 
Diameter of the orifice, 6 millimetres. Diameter of the orifice, 3 millimetres. 
Charges. Length of the con- | Proportion to the Charges, Length ofthecon-| Proportion to the 
tinuous portion, square root of tinuous portion. square root of 
the charge. the charge. 
4.5 107 50.4 4,5 24 11.3 
12 126 36. 4 12 39 11.3 
27 143 27.9 27 58 11.2 
47 158 23. 0 47 78 11.4 
Before discussing these tables, we may remark here that all the lengths of 
the continuous portions are expressed in whole numbers; which shows that 
Savart has taken for each of them the nearest approximative whole number in 
centimetres, disregarding the fraction ; hence it follows that the lengths given 
in these tables cannot, in general, be perfectly exact. 
