VELOCITY OF WHITE AND OF COLOURED LIGHT. 
233 
the other one B, The light reflected from A is eclipsed with a slower revolution of 
the toothed wheel than that from B ; because the number of revolutions required is 
N, and we have 
N=— 
4 mD 
But D a (the distance to A) is greater than D B (the distance to B); hence N A (the 
speed of revolution producing the first eclipse with A) is less than N B (the speed of 
revolution producing the first eclipse of B). 
After the light from A has been eclipsed it begins to increase in brightness, while 
that from B is still diminishing. In the method of the present research we determine 
the speed of revolution when the two lights appear to be of equal brightness. 
When we proceed to the second, third, &c., eclipses the difference in speed required 
to produce an eclipse in A and in B increases, and it may happen that at a certain 
speed the light from A reaches a maximum at the time when that from B is at a 
minimum, or vice versa. 
The superiority of this method over that of M. Fizeau seemed to be that instead 
of having to determine the instant at which a light disappears we have only to 
determine the instant at which two lights seem to be of equal brightness. Every one 
who has been engaged in photometry is aware that the former is an operation of 
great difficulty and doubt, whereas the latter is one of very great delicacy. 
The particular way in which we deduce the velocity of light from an observation 
of the equality of these two lights will now be explained. It must be especially 
noticed that we never have occasion to use the lights when near an eclipse, at which 
time, as Cornu has shown, irregularities are introduced into the formula). 
We found that a great simplification was introduced in the formulse by observing 
the 12th and 13th equalities (the ratio D B to D A being that of 12 to 13); so that 
two observations, one at each of these equalities, sufficed to give us a value of the 
velocity of light. We were also able to utilise some pairs of observations at the 13th 
and 14th equalities. 
This method enabled us to use the electric light, which was in many ways the most 
convenient to us ; for we are not dependent upon the absolute brightness of the light 
(which of course is liable to variations) but only on the proportionate brightness of 
the two reflected stars; and to prevent any error arising from any variation in this 
proportion (owing to fog, &c.), we never used a pair of observations which were 
separated in time by more than a few minutes. 
Mathematical theory of our method. 
If ^ b e tl ie width of a tooth, and 1 —h be the width of the space between two teeth, 
and if E be the brightness of the star of light seen by reflection from the distant colli¬ 
mator when the toothed wheel is not in position, then the brightness of that star 
MDCCCLXXXII. 2 H 
