120 Hydraulic Investigations, 



,5 1 6, c :=> '0001063, e^= td : rf =. '22, and v = ^ (M + e 1 ) 

 — c =3 1 18-46, which agrees with the experiment within -^ 

 of the whole. I had at iirst employed for a the formula 



430 5Jf l 



; , , ,. — , -f r -f ,. ,,» but I found that the value, thus 

 1 -f- i 2 : d a orid r { 



determined, became to lien d was about 20, and too 



small in some other eaSes. Coulomb's experiments on the 

 friction of fluids, made by means of the torsion of wires, 

 give about *00014 for the value of c, which agrees as nearly 

 with this table, as any constant number could be expected 

 to do. I have however reason to think, from some experi- 

 ments communicated to me by Mr. Robertson Buchanan, 

 that the value of a, for pipes about half an inch in diameter, 

 is somewhat too small ; my mode of calculation, as well as 

 Dubuat's, giving too great a velocity in such cases. 



If any person should be desirous of making use of Du- 

 buafs formula, it would still be a great convenience to be- 

 gin by determining v according to this method; then, tak- 

 ing b = , ^_ - a m ? or rather, as Langsdorf makes it, l — 



. ' . jfr/lftj fr to proceed in calculating v by the formula v 



I \ T?| • ( V l - H.L. S { b + V6 ) ~ • 00 ')' 

 this determination of b will, in general, be far more 



accurate than the simple expression b = -, , and the 



continued repetition of the calculation, with approximate 

 values of v, may thus be avoided. Sometimes, indeed, the 

 values of v found by this repetition will constitute a diverg- 

 ing! instead of a converging series, and in such cases we 

 cm only employ a conjectural value of v, intermediate be- 

 tween the two preceding ones. 



Wiving' sufficiently examined the accuracy of my for- 

 mula, I shall now reduce it into English inches, and shall 

 add a second table of the. coefficients, for assisting the cal- 

 culation. In this case, a becomes '0000001 (413 + ~r .— 



1410 180 \ / gOOdd 1 

 — - ), c — '0000001 ( -~ ^ 4- — r 



4 x. 12 S d + -J55/ 5 \dd + 113(5^ ^ d 



(1085 



