1904.] The Flow of Water through Pipes. 353 



Table II. Reynolds' Observations on Pipes 2 and 3 reduced to a 

 Pipe 1-05 cm. in diameter. 

 V c in metres y c in me tres 



Temperature. per sec. Temperature. per sec 



22 1-086 6 1-849 



1-478 6 1-869 



1-489 6 1-838 



1-505 6 1-957 



11 1-528 6 1-978 



11 1-556 4 1-981 



4 1-891 



4 2-027 



In the next table we give a summary of the observations which we 

 obtain for our larger brass pipe at various temperatures. 



Table III. 



Temperature. V in feet, per sec. V in metres per sec. 



21'3 3-458 1-054 



34-5 2-059 0-628 



40-0 1-791 0-546 



51-0 1-362 0-415 



55-0 1-115 0-340 



70-8 0-631 0-192 



73-6 0-777 0-237 



These results are plotted in Fig. 2 and represented by circled 

 dots. The general slope of the two curves is the same and, although 

 the agreement between the different determinations is not perfect, it is 

 sufficient to show that the upper limit falls off more rapidly than the 

 theoretical law. 



The temperature variation of the upper limit may, from these 

 observations, be represented by the formula 



P = (1 + 0-0300 T + 0-000704 T 2 ). 



We do not think that the divergence indicates a temperature 

 variation for the critical velocity different to the theoretical, but 

 rather that it shows, as we have pointed out in a previous part of this 

 paper, that the true critical velocity is at the lower limit. The inverse 

 diameter law does not hold for our larger pipe, as will be seen by 

 reference to the plot, and we have shown that it does not hold for the 

 upper limit in the case of our other large pipes. 



Temperature Variation of the Lower Limit.* 



In a note by one of the authors (H. T. B.), read before the Belfast 

 meeting of the British Association, it was announced that the thermal 

 * Compare also E. Q. Coker and S. B. Clement, loc. cit. 



