194 Canon Moseley on the steady Flow of a Liquid. 



the expedients he adopted, the water was made to arrive at the 

 third pressure-gauge with its velocity already acquired, which 

 velocity was maintained in it against the resistance of the hori- 

 zontal pipe up to the first gauge by a pressure which is repre- 

 sented by the difference h of the heights of the water in the 

 third and first gauges. The additional head of water which 

 communicated to it this velocity before it reached the third gauge 

 was represented by the difference between the heights of water 

 in that gauge and in the fifth gauge. 



Since ( — ) was approximately independent of the kinds and di- 

 mensions of the pipes used in M. Darcy' s experiments and of 

 the heads of water, and dependent only on the value of r, 



wi 

 it follows that in those experiments — was constant. Tf this be 



the case, then determining its value as given by any experiment 

 and representing it by 7*, the relation of the velocity v of any 

 film whose radius is r to that v of the central filament will be 

 represented in all the experiments approximately by the equation 



v-v Q e~v r (13) 



This supposes the values of v and v to have been determined 

 in that experiment with perfect accuracy. That cannot, how- 

 ever, have been the case in any experiment. Admirable as are 

 the experiments of M. Darcy, and far surpassing any others in 

 accuracy that have ever been attempted, the means used (the 

 only ones perhaps possible) are in their nature defective. He 

 has applied corrections to his results ; but the authority of these 

 is perhaps sometimes doubtful, and it is rather the general 

 laws observable in the experiments than the precise results on 

 which reliance is to be placed. On this point I will quote his 

 own words : — " Les quelques differences qui existent ne peuvent 

 etre attributes qu'a la difficulte d'obtenir plus de precision dans 

 les experiences. La moindre erreur, en effet, dans Vindication des 

 instruments qui donnent les vitesses entieres doit infiuer d'une 

 maniere tres-sensible sur les differences des vitesses si Perreur 

 ne porte pas a la fois sur les deux vitesses." (P. 152.) 



In the experiments of M. Darcy the lengths of the pipes 

 between the first and third gauges were 100 metres. It is only 

 to this portion of each pipe that the velocities recorded in 

 Table I. refer. 



* wi wh wv 2 ( ,. . 



7 ~7 ^ = 2^ (equatlon8) ' 



_wi _wh _ wv 2 



y yl tyyi' 



