were specially directed to the point, a slight prolongation of the cannon-sound might well escape observation; and it would be all the more likely to do so if the echoes were so loud and prompt as to form apparently part and parcel of the direct sound.
I should be very loath to transgress here the limits of fair criticism, or to throw doubt, without good reason, on the recorded observations of an eminent man; still, taking into account what has just been stated, and remembering that the minds of Arago and his colleagues were occupied by a totally different problem (that the echoes were an incident rather than an object of observation), I think we may justly consider the sound which he called "instantaneous" as one whose aërial echoes did not differentiate themselves from the direct sound by any noticeable fall of intensity, and which rapidly died into silence.
Turning now to the observations at Montlhéry, we are struck by the extraordinary duration of the echoes heard at that station. At the South Foreland the charge habitually fired was equal to the largest of those employed by the French philosophers; but on no occasion did the gun-sounds produce echoes approaching to twenty or twenty-five seconds duration. It rarely reached half this amount. Even the siren-echoes, which were far more remarkable, more long-continued than those of the guns, never reached the duration of the Montlhéry echoes. The nearest approach to it was on the 17th of October, 1873, when the siren-echoes required fifteen seconds to subside into silence.
On this same day, moreover (and this is a point of marked significance), the transmitted sound reached its maximum range, the gun-sounds being heard at the Quenocs buoy, which is 1612 nautical miles from the South Foreland. I have already stated that the duration of the air-echoes indicates "the atmospheric depths" from which they come.[1] An optical analogy may help us here. Let light-fall upon chalk, the light is wholly scattered by the superficial particles; let the chalk be powdered and mixed with water, light reaches the observer from a far greater depth of the turbid liquid. The chalk typifies the action of exceedingly dense acoustic clouds; the chalk and water that of clouds of moderate density. In the one case we have echoes of short, in the other, echoes of long duration. These considerations prepare us for the inference that Montlhéry, on the occasion referred to, must. have been surrounded by a highly-diacoustic atmosphere; while the shortness of the echoes at Villejuif shows the atmosphere surrounding that station to have been acoustically opaque.
Have we any clew to the cause of the opacity? I think we have. Villejuif is close to Paris, and over it, with the observed light wind, was slowly wafted the air from the city. Thousands of chimneys to windward of Villejuif were discharging their heated currents, so that an atmosphere non-homogeneous in a high degree must have surrounded that station. At no great height in the atmosphere the equi-
- ↑ "Philosophical Transactions," 1874, Part I., p. 202.
