330 G. H. KNIBBS. 
Now as previously pointed out, when shewing that Reynolds 
was in error in stating that he was the first to recognise the law 
U* x I, it has long been known that for pipes n is, at least generally, 
less than 2; if it differ sensibly from that number there appears 
to be no cogent reason for adopting it. 
10. Experimental proof of St. Venant’s law, viz., that U®x I for 
pipes.—We are here concerned only with the proof that this law 
holds for the second or turbulent régime, that it holds for rectilinear 
flow is beyond question, n being in that case unity. Reynolds 
has given the following values for the index, as the result of his 
investigation of his own and Darcy’s experiments, viz.— 
1:723 Perfectly jointless glass tube. 
1-746 Lead and bituminous pipes. 
1:79 Glass and lead pipes. 
1°82 Varnished lead, new cast iron and glass pipes. 
1-91 Cleaned iron pipes. 
1:92 Cast iron pipes. 
2-00 Incrusted iron pipes. 
See however the values deduced later on, herein. 
The best available material for the discussion of the question is 
Darcy’s, because his experimental work was carefully conducted— 
it is incomparably more accurate than the general run of hydraulic 
experiments—and in a great many instances he gives temperatures: 
Reverting to St. Venant’s and Hagen’s equation, it may, for 
provided the temperature of the water, be kept constant. Hence 
taking the logarithm of both sides, and dividing by n 
gk 1 
log U = son WS OB Tes oases (20) 
the equation of a straight line, determined by plotting the values 
1 It is greatly to be regretted that he failed to do this always: at the 
time it was thought unessential. A very little relative increase of the 
nse these experiments might have been made to furnish all the 
requisite material for a thorough examination of the whole question. 
