Page:MichelsonMorley1886.djvu/7

Width of fringe	48.8		60.5
Mean width		54.6 + (3.0=index error)
Displacement	57.7		46.0
Mean displacement		51.8

$\Delta ={\frac {51.8}{57.6}}=.899$

(Long tube, vertical fringes, full current.)

Velocity of water. — The velocity of the water in the tubes was found by noting the time required to fill a measured volume in the tank, and multiplying by the ratio of areas of tank and tube. This gave the mean velocity. In order to find from this the maximum velocity in the axis of the tube the curve of velocities for different radii had to be determined. This was done as follows: a tight fitting piston ab (fig. 4) containing two small tubes $tt,\ t_{\prime },\ t_{\mathit {\prime }}$, was introduced into the tube containing the water. The ends of the tubes were bent at right angles in opposite ways, so that when the water was in motion the pressure would be greater in one than in the other. The other ends of the small tubes were connected to a U tube containing mercury, the difference in level of which measured the pressure. The pressures were transformed into velocities by measuring the velocity corresponding to a number of pressures. Following is the table of results: —

Pressures.	Velocities.	${\frac {v}{\sqrt {p}}}$
26 108 190 240	393 804 1060 1190	77.1 77.1 76.9 76.8

It is seen from the approximate constancy of the last column that within limits of error of reading, the square roots of the readings of the pressure gauge are proportional to the velocities.

To find the curve of velocities along a diameter of the tube, the piston was moved through measured distances, and the corresponding pressures noted. The diameter of the tube was about $28^{mm}$, while that of the small tubes of the gauge was but $2^{mm}$, so that the disturbance of the velocity by these latter was small except very close to the walls of the tube. The portion of the piston which projected into the tube was made as thin as possible, but its effect was quite noticeable in altering the symmetry of the curve.

In all, five sets of observations were taken, each with a different current. These being reduced to a common velocity all gave very concordant results, the mean being as follows: x=distance from the axis in terms of radius; v=corresponding velocity in terms of the maximum.