WITHDRAWN FROM THE ACTION OF GRAVITY. 305 
Now, to obtain, by means of this formula,*the numerical value of the propor- 
aE: : : : : 
tion = relative to a determined charge and orifice, we have only to ascertain, 
k 
by experiment, the number of vibrations per second corresponding to this 
charge and this orifice; for then the value of 4 will be given, that of & may 
be deduced from the diameter of the orifice employed; we shall find that of x 
by taking (see preceding section) half the number of vibrations found; and, 
lastly, that of g is known. It is unnecessary to remark that the values of h, 
k, and g must be reduced to the same unit of length. Now, Savart’s observa- 
tions relative to the first law give us, for an orifice of 3 millimetres, the num- 
ber of vibrations per second corresponding respectively to four different charges ; 
we can calculate then, for each of these observations, the value of the propor- 
tion 
The following table contains these numbers, with the charges to which they 
refer. The latter are expressed in centimetres: 
Diameter of the orifice, 3 millimetres. 
Charges. Number of vibrations. 
Stee nS Lele a olalais-a aaa rie Subecyareuato amie tehoyl & GAStite Senta sapere entre 600 
WR erstet. Me tiotele sitar eee nel ton Ae Ly sieroreje. areta eisietia 853 
Mp mrs seit eis ae stt Hef S oa ois GS Ge Mensa (ee SARL Lie Se aldne Seles 1,024 
Ee OCTET Pa Srey Pie 2 EU ENS peer eepyen Beek 1,843 
We may conclude, from the results detailed in the note to § 74, that when 
the diameter of the orifice amounts to 3 millimetres, that of the contracted 
section is almost exactly eight-tenths of this quantity; consequently, if we re- 
tain the centimetre as the unit of length, which gives 0.3 for the value of the 
diameter of the orifice in question, we shall have 
E05 «0:0 0.24, 
Lastly, the numbers of vibrations, and therefore the values of n, supposing 
the second taken as the Unit of time, and the values of 2 and & being reduced 
to the centimetre as the unit of length, we must make g—980.9. 
Substituting in the formula (a) these values of & and g, as also those of h 
taken from the above table, and those of ” obtained by taking the respective 
halves of the numbers of vibrations contained in the same table, we shall find, 
Aine : 
for the proportion 7 the four following numbers: 
4.39 
4.37 
4.46 
4.29 
and we see that, in fact, these numbers closely approximate to each other, and 
very nearly amount to 4. The mean of these numbers, 7. e., 4.38, gives us 
then, very nearly, the constant value which, commencing with a suitable charge, 
the proportion of the length of the nascent divisions of a vein of water to the 
diameter of the contracted section of this vein assumes. 
This is also evidently the value of the proportion of the length of all the 
divisions of the continuous portion of a vein of water to the diameter of the 
contracted section, when the charges are sufficiently considerable for the move- 
ment of transference of the liquid to be perfectly uniform throughout the 
whole extent of this contiauous portion. In experimentally determining, in 
20 8 
