708 PLATEAU ON THE PHiENOMENA OF A FREE LIQUID MASS 



tions per second corresponding to this charge and this orifice ; 

 for then the value of /* will be given, that of k may be deduced 

 from the diameter of the orifice employed, we shall find that of 

 n by taking (see preceding section) half the number of vibrations 

 found, and lastly, that of ^ is known. It is unnecessary to re- 

 mark, that the values of /*, k, and ^r must be reduced to the same 

 unit of length. ' Now Savart's observations relative to the first 

 law, give us, for an orifice of 3 millims., the number of vibrations 

 per second corresponding respectively to four dilFerent charges ; 

 we can calculate then, for each of these observations, the value 



of the proportion t-- 



The following table contains these numbers, with the charges 

 to which they refer. The latter are expressed in centimetres : — 



We may conclude, from the results detailed in the note to 

 § 74, that when the diameter of the orifice amounts to 3 millims., 

 that of the contracted section is almost exactly eight-tenths of 

 this quantity ; consequently, if we retain 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 



A: = 0-3x 0-8 = 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 h and k being reduced to the centimetre as the unit of length, 

 we must make ^ = 980*9. 



Substituting in the formula [a] these values of k and g, as 

 also those of h taken from the above table, and those of n ob- 

 tained by taking the respective halves of the numbers of vibra- 

 tions contained in the same table, we shall find, for the propor- 

 tion 7^, the four following numbers : — 



4-39 

 4-37 

 4-46 

 4-29 



