(b) This same method permits one to control or rectify periodically the measurement of the altitude. Thus, suppose the observer A operating as has just been said; the signal of observer B announcing the passage of the machine in the next azimuth will be heard: either at the same time as the lower end of the rule crosses the said azimuth drawn on the plotting-board, in which case the altitude has not changed; or before the reaching by the lower end of the rule of the azimuth, in which case the machine has gone higher; or after the passage of the lower end of the rule on the azimuth, in which case the machine has come down.

In the last two cases the observer A, as soon as he hears the signal, will recall or send back his rule along the sighting plane so as to replace it on the azimuth announced; from this will result the rectification of the reading of the altitude and also the rectification of the horizontal projection of the flying machine. (2) The linear velocity may be measured in the following way (fig. 7):

A given length of a horizontal wire, for instance, 1 cm. representing 100 meters and thus corresponding to a scale of 1/10,000, is stretched across a vertical aperture at such a height above the plane of the board as to represent the altitude of the flying machine (for example, 20 cm. representing 2 kilometers).

The observer A, after having trained the aperture in such a way that the machine aimed at appears as if following the wire, registers the time taken by the machine to cross the aperture from one side to another.

This time gives the measure of the horizontal linear velocity and the bearing of the plane of the aperture indicates the actual direction of the flying machine.

(3) The extrapolation or prediction results from the knowledge both of this actual direction and of the linear velocity.

As has already been said, this extrapolation gives the azimuth of the point to be aimed at; and, in this azimuth, the angle of sight (fig. 8).

The altitude of the point to be aimed at in the extrapolated azimuth is supposed to be equal to the last altitude that has been measured. The angle of sight results from the knowledge of the altitude and of the abscissa; the latter is given by the intersection of the azimuth with the extrapolated horizontal direction.

(4) The ballistic coordinates (angle of departure, fuse-setting) are read on the diagram of the trajectorial and isopyrical curves; a diagram on which the point to be aimed at has just been fixed by the knowledge of its angle of sight and of its altitude (or merely of its abscissa and ordinate).

(5). If one proceeds by measurement of angular velocities instead of by measurements of linear velocities the instruments used are the continuous electric cinemometers already mentioned above, and then the extrapolation is determined as follows:

(a) Azimuth. The extrapolated azimuth is obtained by the extrapolation of the horizontal angular velocity and this in starting from the last azimuth in which the flying machine has been observed prior to the firing of the shot.

(b) Angle of Sight. In the same way, the extrapolated angle of sight is obtained by the extrapolation of the angular velocity in the plane of sight where the flying machine has been observed prior to the firing of the shot.

CONCLUSIONS

In ending this comment, which inevitably is of a very general character, it seems necessary to insist upon the great importance that should be attached to the fact that, as far as possible, the nature of the firing conditions should be such as not to disturb the continuity of the flight of the flying machine between the moment at which the measurements that determine the firing data have been taken and the moment at which the shot reaches its destination.

As has been said, a flying machine may cover about 700 meters during the flight of the projectile. During this period the race is most unequal.

On one hand, the projectile, just carrying away the measurements and the intentions of the battery commander, is merely an inert instrument of a previous will. It clings helplessly to its trajectory and will inevitably burst once the combustion of its fuse has come to an end. On the other hand, the aerial ship has maintained the full power of her free will, her trajectory is

not compulsory and may be altered in accordance with her own desires.

Therefore, if she becomes conscious that a projectile intended for her is on the way, she is in a position to baffle all the calculations of which this projectile is the unconscious carrier.

What, then, is any observation worth, even though it be minutely exact, that the gunner can figure out in regard to the deviations between his points of burst and the objective? To what extent do these deviations indicate an error of firing which is subject to rectification? To what extent are they the effect of a modification in the continuity of the flight of the objective, voluntarily brought about by the pilot during the course of the projectile?

The first burst that will take place and which the pilot will see will give him the alarm and from this moment on, what craftiness, what feat of strength in case of need, will he not make use of in order to avoid falling into the net of subsequent trajectories?

Are not these points of interrogation sufficient to make it clearly understood that the systems of anti-aircraft firing based solely on ranging must be condemned as being ineffective and excessively expensive?

Are they not sufficient to show that so long as there shall not have been found a gun of a fantastic muzzle velocity, capable of pouring into space projectiles of a speed infinitely superior to that of the flying machine, the gunner must concentrate all his attention and all his ingenuity in operating sudden and dense barrages on points of extrapolation silently determined by measurements as accurate as possible?

CRYSTALLOGRAPHY.-The assignment of crystals to symmetry classes. EDGAR T. WHERRY, Bureau of Chemistry. The thirty-two classes of crystals are founded on so firm a basis that it has become customary to regard the assignment of a crystallized substance to one or the other of them as one of the fundamental aims of crystallography. Evidence has been accumulating for some time, however, that certain substances are in a sense intermediate between classes, possessing simultaneously