|377 378 379 380 381 382 383 384 385 386|
The curve constructed with, these numbers coincides almost perfectly with the curve
V = (l—X7)
r* 1 .165 ft
The total flow is therefore 2tu (l—a;3) xdx = . The area
of the tube being jt, the mean velocity = °? ^e mum; or the maximum velocity is 1*165 times the mean. This, then, is the number by which the velocity, found by timing the flow, must be multiplied to give the actual velocity in the axis of the tube.
Let I be the length of the part of the liquid column which is in motion.
u = velocity of light in the stationary liquid. v = velocity of light in vacuo.
6 = velocity of the liquid in the axis of tube.
Ox = acceleration of the light.
The difference in the time required for the two pencils of
I 1/ 216x
light to pass through the liquid will be-tt;---t*-= —*~
U~~OX U “p 0%, u
very nearly. If A is the double distance traveled in this time in air, in terms of A, the wave-length, then
MOtfx . Xv .
whence x = ■A
Xv 4 ln*d
X was taken as *00057 cm. v = 30000000000 cm.
n2 = 1*78.
The length I was obtained as follows: The stream entered each tube by two tubes a, b (figs. 1, 2) and left by two similar ones e£, c. The beginning of the column was taken as the intersection, o, of the axes of a and 5, and the end, as the intersection, o', of the axes of d and c. Thus l=oo'. A is found by observing the displacement of the fringes; since a displacement of one whole fringe corresponds to a difference of path of one whole wave-length.
Observations of the doable displacement A.
1st Series. 1= 3*022 meters.
0 = 8*72 meters per second.
A = double displacement; w = weight of observation.
If these results be reduced to what they would be if the tube were 10m long and the velocity lm per second, they would be as follows:
The final weighted value of A for all observations is 4= *1840. From this, by substitution in the formula, we get
x = *434 with a possible error of ±*02.
The experiment was also tried with air moving with * a velocity of 25 meters per second. The displacement was about of a fringe; a quantity smaller than the probable error of
observation. The value calculated from —— would be *0036.
It is apparent that these results are the same for a long or short tube, or for great or moderate velocities. The result was also found to be unaffected by changing the azimuth of the fringes to 90°, 180° or 270°. It seems extremely improbable that this could be the case if there were any serious constant error due to distortions, etc.
Am. Jour. Sci.—Third Series, Vol. XXXI, No. 185.—May, 1886.