178 THIRD REPORT 1833. 



-' The conclusions to be derived from these Tables are, 



1st, That for complete orifices of twenty centimetres square 

 and high charges, the coefficient is 0*000 ; with the charge 

 equal to four or five times the opening of the orifice, the co- 

 efficient augments to 0"605 ; but beyond that charge the co- 

 efficient diminishes to 0"593. 



2ndly, That the same law maintains for orifices of ten and 

 five centimetres in height, the coefficients being for ten centi- 

 metres 0'61], 0-618, 0"611 respectively, and for five centi- 

 metres in height 0-618, 0-631, 0-623. 



Lastly, That with orifices of three, two and one centimetres 

 in height, the law changes very rapidly, and the coefficients 

 increase as the opening of the orifice becomes less, being for 

 one centimetre 0-698, the smallest height of the orifice, to 0-640 

 for three centimetres. 



These remarkable discrepancies from the results of Bidone 

 and others are attributed by MM. Lesbroa and Poncelet to 

 diflferences in the construction of the apparatus or in the mode 

 of measurement adopted by the latter gentlemen ; but in gene- 

 ral the coincidences are sufficiently satisfactory, and they are 

 the more accurately confirmed by the subsequent investigations 

 of MM. D'Aubuisson and Castel at Toulouse *. As respects 

 water issuing from the openings or notches made in the sides 

 of dams, or what we should term incomplete orifices, it appears 

 that the coefficient obtained by the ordinary formula of Dubuat, 

 or I h V 2gh, augments from the total charge of twenty-two cen- 

 timetres when it is from 0-389 to two centimetres when it be- 

 comes 0-415 ; hence we may safely adopt M. Bidone's coefficient 

 of 0-405, or, according to MM. Poncelet and Lesbros' theory 

 0-400, for calculating expenditures through notches in dams. 

 From these and other experiments the authors are led to con- 

 clude, that the law of continuity maintains for indefinite heights 

 both with complete and incomplete orifices, and that the same 

 coefficient can be obtained by adopting in both cases the same 

 formula. The avithors observe that the area of the section of 

 the greatest contraction of the vein, considered as a true 

 square, is exactly two thirds of the area of the orifice ; a fact 

 which goes to prove that there is no certain comparison be- 

 tween the mean theoretical or calculated velocities, by means 

 of the formula now used, and the mean effective velocities de- 

 rived from the expenditure. 



The authors conclude their memoir by recommending their 

 experiments for adoption in all cases of plate orifices situated 



* 4nnales de Chimie et de Physique for 1830, torn. xliv. p. 225. 



