82 Lord Rayleigh on [^ a 7 15, 



In applying this formula it must be remembered that A is the area 

 of the section of the jet. and not the area of the aperture. 

 We might indeed deduce the value of A from the area of the 

 aperture by introduction of a coefficient of contraction (about *62) ; 

 but the area of the aperture itself is not very easily measured. 

 It is much better to calculate A from an observation of the 

 quantity of fluid (V). discharged under a measured head (h'). com- 

 parable in magnitude with that prevailing when \ is measured. Thus 

 A = V (2gli')~ t . In the following calculations the C.Gr.S. system of 

 units is employed. 



In the case of the elliptical aperture of Table II. the value of A 

 was found in this way to be '0695. Hence at a head of 10*7 the wave- 

 length should be 



s^xio-;) x (•■•■■•:■■• 



3-38* 6 



the value of g being taken at 981. The corresponding observed value 

 of X is 2-55. 



Again, in the case of the experiments recorded in Table IV. it was 

 found that A= , 0660. Hence for 7z = 29"0 the value of the wave- 

 length should be given by 



. (2q x 29-0) x 00660)* „ _ 5 

 3 33x y6 



The corresponding observed value is 3*95. 



VTe will next take the triangular orifice of Table V. The value of 

 A was found to be '154. Hence for a head of 9"2 the value of X, 

 calculated a priori, is 



,_ ,^x9'2)xr-15^ _ 1 , 00 

 3-3Sx ; 24 ^ 3 



as compared with 2*3 found by direct observation. 



For the square orifice of Table VIL we have A— T53. Hence, if 

 1=16-7, 



, /(2axl6-7)x f-153)* ! 



A = ' n c ■ -=l , ' , -' 



as compared with T?5 by observation. 



It will be remarked that in every case the observed value of \ 

 somewhat exceeds the calculated value. The discrepancies are to be 

 attributed, not so much. I imagine, to errors of observation as to 

 excessive amplitude of vibration, involving a departure from the 

 frequency proper to infinitely small amplitudes. The closest agree- 

 ment is in the case of Table IV. where the amplitude of vibration was 

 smallest. It is also possible that the capillary tension actually 



