Page:Lowell Hydraulic Experiments, 4th edition.djvu/80

removed, consequently the passive resistance arising from the friction of the step, was much greater than in the other experiments.

108. Fig. 6, plate VII., is a diagram representing the experiments; the abscissas represent the ratios of the velocities of the exterior circumference of the wheel, to the velocities due to the falls acting upon the wheel, as given in column 14, of table V.; the ordinates represent the ratios of the useful effects to the powers expended, as given in column 11; the points, representing experiments 12 and 13, are connected by a broken line, because the latter experiment is not strictly comparable with the others, in consequence of the removal of the counterbalance.

109. The following table contains the successive steps of the calculation for the ordinates of the path of the water in experiment 3, represented at figure 4, plate VII; the operations are all similar to those explained in articles 83 and 119. The ordinates in column 10 are obtained by the formula

$$O={{R'\omega AH} \over {Q''}}$$

in which

${\textstyle O}$	is the ordinate,
${\textstyle R'}$	the corresponding value of the radius in column 1,
${\textstyle \omega ,}$	the angular velocity ${\textstyle ={{850\times 2\pi } \over {551.5}}=9.684}$,
${\textstyle AH,}$	the corresponding volume in column 9,
${\textstyle Q'',}$	the mean quantity discharged by each aperture in the wheel ${\textstyle ={2.1681 \over 36}=0.06022}$.

1 Value of R and successive values of $R'$, in inches.	2 Areas in square inches, of circles of the radii in column 1.	3 Ares in square inches, of the complete rings.	4 1/36 of the areas of the rings in column 3, in square feet.	5 Correction for the thickness of the bucket, in square feet.	6 True areas of the partial rings, in square feet.	7 Height of the partial rings, in feet.	8 Volumes of the partial rings, in cubic feet.	9 Volumes between $R$ and the successive values of $R'$, in cubic feet.	10 Ordinates in feet, measured on arcs of the radii in column 1.
11.487	410.9386
11.000	380.133	30.803	0.005942	0.000262	0.005680	0.23844	0.001331	0.001331	0.1962
10.500	346.361	33.772	0.006515	0.000350	0.006165	{{{1}}}„	0.001445	0.002776	0.3906
10.250	330.064	16.297	0.003144	0.000198	0.002946	{{{1}}}„	0.000691	0.003467	0.4762
10.000	314.159	15.905	0.003068	0.000228	0.002840	{{{1}}}„	0.000666	0.004133	0.5538
9.875	806.354	7.805	0.001506	0.000156	0.001350	{{{1}}}„	0.000316	0.004449	0.5887
9.750	298.648	7.706	0.001486	0.000175	0.001311	{{{1}}}„	0.000307	0.004756	0.6214