Intelligence and Miscellaneous Articles. 399 



known angles ; but the objective, instead of being fixed, is mounted 

 upon one of the brancbes of a diapason animated, during the ex- 

 periment, with a known vibratory movement. In this second tele- 

 scope the eyepiece is replaced by a plane mirror inclined 45° to its 

 optic axis, and reflecting the luminous rays to a parallel mirror 

 situated in the first telescope. This second mirror is transparent, 

 so that it transmits the rays coming from the fixed objective. The 

 observer, then, perceives simultaneously two luminous images of 

 the trajectory. That given by the fixed telescope will appear 

 under the form of a rectilinear stroke of fire ; the other, trans- 

 mitted by the vibrating objective, will have the form of a sinusoid, 

 of which the rectilinear stroke will be the axis. If the number of 

 vibrations of the diapason in the unit of time be chosen so that the 

 number of branches of the sinusoid comprised between two parallel 

 wires of the reticule does not exceed five or six, the observer will 

 be able to count them instantaneously, and also to remember which 

 wires pass through the intersection of the sinusoid with its central 

 line. These two elements will give immediately the angular velo- 

 city of the projectile ; and on multiplying it by the distance from 

 the observer to the projectile (given by the operation previously 

 described), we shall have the linear velocity sought. 



The following is a second process, based on the same principle. 

 Its realization will, it is true, be more complicated ; but it will 

 have the double advantage of offering several means of controlling 

 the results obtained and of occasioning less fatigue to the observer. 

 Let the vibrating lens be replaced by a wheel carrying, say, 5 lenses 

 at its periphery, and making 20 turns in a second. At the instant 

 of the passage of the projectile the observer will see parallel 

 rectilinear strokes of fire, the number of which will be proportional 

 to the time employed by the projectile in traversing the field of the 

 telescope. It will then be sufficient for him, as before, to re- 

 member the number of strokes comprised between two wires, in 

 order thence to infer the velocity sought. In fact, each of the 

 bright strokes sent by the moving lenses represents in direction 

 the resultant of a parallelogram, the sides of which are propor- 

 tional to the angular velocities of the projectile and of the lenses 

 (round the observer as a centre). Now the magnitude and direc- 

 tion of the velocity of the lenses are known ; and, knowing the 

 directions of the resultant velocity and of the velocity of the pro- 

 jectile, we shall be able to find the amount of the latter. To deter- 

 mine with precision the directions of these two velocities, it will 

 only be requisite to put one of two special wires of the reticule 

 parallel to each of them ; and this operation (provided the succes- 

 sive discharges of the gun be identical) will be susceptible of greater 

 precision than that described in the first process. 



These means are evidently applicable to all bodies in motion ; 

 and it is precisely by making use of them to measure velocities 

 known beforehand that we shall be able to judge of the degree of 

 precision to be attained by them. Not being in favourable circum- 

 stances for carrying out experiments of this kind, I should be 



