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This, together with the fundamental importance of the work must be our excuse for its repetition. It may be mentioned that we have tried to obtain formulated objections to these experiments but without success. The following are the only points which have occurred to us as being susceptible of improvement.

1st. The elimination of accidental displacement of the fringes by deformation of the glass ends of the tubes, or unsymmetrical variations of density of the liquid, etc., depends on the assumption that the two pencils have traveled over identical (not merely equivalent) paths. That this is not the case was proven by experiment; for when a piece of plate glass was placed in front of one of the pencils and slightly inclined, the fringes were displaced.

2d. The arrangement for producing the motion of the medium necessitated very rapid observation — for the maximum velocity lasted but an instant.

3d. The tubes being of necessity of small diameter and only their central portion being available (since the velocity diminishes rapidly toward the walls) involved considerable loss of light — which, having to pass through a slit was already faint.

4th. The maximum velocity (in the center of the tube) should be found in terms of the mean velocity. (Fizeau confessedly but guesses at this ratio.)

These are the suggestions which determined the form of apparatus adopted, a description of which follows:

The Refractometer. — After a number of trials, the following form was devised and proved very satisfactory. Light from a source at a (fig. 5) falls on a half silvered surface b, where it divides; one part following the path b c d e f b g and the other the path b f e d c b g. This arrangement has the following advantages: 1st, it permits the use of an extended source, of light, as a gas flame; 2d, it allows any distance between the tubes which may be desired; 3d, it was tried by a preliminary experiment, by placing an inclined plate of glass at h. The only effect was either to alter the width of the fringes, or to alter their inclination; but in no case was the center of the central white fringe affected. Even holding a lighted match in the path had no effect on this point.

The tubes containing the fluid were of brass, 28^{mm} internal diameter; and, in the first series of experiments, a little over 3 meters in length, and in the second series, a little more than 6 meters. The ends of these tubes were closed with plane parallel plates of glass which were not exactly at right angles but slightly inclined so as to reflect the light below the telescope, which would otherwise be superposed on that which passed through the tubes. The tubes were mounted on a