so ROYAL SOCIETY OF CANADA 



ations in the method of adiiiittini;- water, and the measurement of the 

 oritices by means of the comparator, instead of assuming that they had 

 been cut by the die exactly to the size intended. These elaborations are 

 described elsewhere in this paper. 



Throughout the experiments every care was taken to ensure as far 

 as possible that normal conditions prevailed • and the attempt was con- 

 stantly made to reduce as far as possible any error due to personal bias 

 in observation. 



The coefficient of discharg-e is the ratio of the actual discharge per 

 unit time to the quantity which would be discharged in the same time in 

 a stream of the same sectional area as the orifice and travelling with the 

 theoretical velocity \/'2gh due to the head //. 



The actual discharge per unit time is got by measuring the amount Q 



which flows in a time t. 



Q 

 Thus actual discharge per unit time = . • 



The theoretical discharge is obtained by multiplying the volume in 

 a unit length of a stream of sectional area equal to the orifice, by the 

 theoretical velocity- with which the stream is moving. 



Thus theoretical discharge = AV = A ^2gJi. 



, , actual discharge Q/t Q 



.-. Coetncient of discharge = n r- — nr- — i = — "' — =:=• 



•^ theoretical discharge ^4 ^2(jh At^2r/h 



It is necessary to determine the values for ditîercMit cases of all the 

 différent factors in this expression. 



The methods of determination of A the area of the orifice, and //. the 

 head of water, have been indicated under the general description of the 

 tank and its appurtenances. 



The value for g used tln-f)iighout is that obtained for Montreal in 

 1893 by Commandant Detlbrges, in the course of a series of observations 

 for different centres in the Xorth American continent. 



The values of Q and t have to 1)0 supplied in the formula. 



The quantity of water was found by running the water into a cop- 

 IK'r measure of 100 gallons capacity. This measure was carefully cali- 

 brated at a standard temperature before commencing the series of experi- 

 ments. The quantity of water used in an experiment was between 96 

 and 100 gallons. The excess over 9(i gallons was taken by measuring the 

 height of the water level al)0ve the 96 gallon mark. The error due to 

 difference of temperature was very small, and was neglected. 



The lime of the experiment was taken l)y means of an automatic 

 chronograph, which i-ecoided the start and finish of an exi)eriment ; two 

 shoots were arranged on a ])ivoted stand in front of the orifice, so that 

 one or other of them caught the water issuing from the orifice. Before 

 the start of an ex])erimentthe water was allowed to run to waste through 



