April 4, 1901] 



NATURE 



539 



loud or at all comparable with such as are heard there (and felt 

 too) when gunnery practice with big guns is going on near 

 Portsmouth. This is what might have been expected, since the 

 nearest distance from the firing line was 9^ miles from a point 

 close to the west end of the double line of ships, and the distance 

 from its extremities about \o\ miles. Hence the sound im- 

 pulses from the whole line arrived within the interval required 

 by sound to travel f of a mile, or about 3J seconds, and thus 

 concentrated were audible, although a line of downs 400 to 500 

 feet high intervened at a distance from Shanklin of about 4 

 miles. 



At Yarmouth a gentleman, who went on to the pier specially 

 to listen, heard " not a single gun." This is explained by the 

 fact that he was so near the prolongation of the firing line west- 

 ward that, though only \o\ miles from the western end, he was 

 18 miles from the eastern extremity, and so the sound impulses, 

 spread over an interval corresponding to ']\ miles, or about 36 

 seconds, must have arrived at intervals of a little more than a 

 second as separate sounds from the successive ships, each by 

 itself too feeble to be audible. 



The same explanation holds for Bournemouth west and a 

 little south of the prolongation, and for Chichester east and a 

 little north of the same, where the sounds were not heard, the 

 impulses being spread over an interval of about 33^ seconds. 



Winchester is 20 miles nearly due north from the western end 

 of the firing line, and its distance from the eastern end is about 

 21 A miles. The difference of i^ miles corresponding to about 

 7 seconds might perhaps have been expected to have produced 

 sufficient concentration to make the reports audible, but th^y 

 were not heard, and probably this is partly due to the interven- 

 tion of the downs at the foot of which Winchester lies. 



As to Southampton I have no information, but as it corre- 

 sponds in position to the N. of the line almost exactly to Yar- 

 mouth on the S., there can belittle doubt but that there too the 

 firing was inaudible. 



Thus far an explanation founded on the supposition of a still 

 atmosphere of uniform temperature appears to be sufficient. 

 But we have good evidence of the reports having been dis- 

 tinctly heard at distances of sixty, seventy, and even to seventy- 

 five miles from Portsmouth in directions varying, from the 

 eastern prolongation of the firing line, northwards through 

 north-east to due north ; but, so far as I know, not west of the 

 north line. For these, at any rate for stations not far from the 

 prolongation of the firing line, some totally different explana- 

 tion must be found, and the first step must be to consider the 

 effect of the wind. 



Prof. Sir G. Stokes first pointed out in 1857 that, if the 

 speed of the wind increases with the height above the earth's 

 surface, the path of a sound ray cannot be straight, but must be 

 curved and bent downwards towards the surface for rays in 

 the direction of the wind, but upwards against the wind. 



Now on February i there was a steady gentle wind, esti- 

 mated at somewhere about five miles an hour, from the west 

 with a cloudless sky, and no visible irregularities of cloud or 

 fog to interfere with the normal propagation of sound. Hence 

 for places west of the firing line the sound rays, on Stokes's 

 principle, were diverted upwards into the upper atmosphere, 

 and so passed over the heads of places at even moderate dis- 

 tances, so that no sound reached them. For places east of 

 the same the contrary effect was produced, and closer examina- 

 tion is necessary to trace the consequences. 



Proceeding Irom Stokes's principle, it is shown in Lord 

 Rayleigh's "Treatise on Sound," ch. xiv., that on the hypo- 

 thesis of the speed of the wind increasing upwards from the 

 surface in direct proportion to the height, the path of a ray of 

 sound advancing with the wind would be a catenary whose 

 axis is vertical and directed downwards from its vertex, so that 

 the ray, after ascending in its curved path to the vertex, would 

 descend in a similar path again to the horizontal line through 

 the point whence it started. Thus a ray starting from A (Fig. 2) 

 in the direction AT would reach B in the horizontal line through 

 A by the path acb of the catenary, whose vertex is c, midway 

 between a and b ; and hence all the sound energy, which in 

 air with no differential motion of its strata would have been 

 spread over the circular sector tab, must be concentrated be- 

 tween the curve acb and the horizontal base ab. Now the 

 angle tab, when not large, is very nearly proportional to the 

 distance ab, and hence in a vertical plane the concentration of 

 the energy is proportional to the distance ab. On the other 

 hand, in the horizontal plane the energy is spread out in azimuth 



proportionally to the distance ab, and thus the concentration 

 in the vertical plane is balanced by the spread in the horizontal 

 plane, so that the sound energy reaching two observers at 

 different distances from a in the horizontal line ab would be 

 about the same in amount. 



There is, however, this difference, that, as the distance ab is 

 greater, the difference in length between the curved path acb 

 and the direct line AB is greater, and this produces a greater 

 retardation in time between the extreme curved ray and the 

 horizontal ray, so that, the same energy being received in a 

 longer time, the impression on the ear at a distant station 

 would be enfeebled as compared with a nearer one. 



Assuming this general reasoning to be correct, I have en- 

 deavoured to apply it quantitatively to the case of Eastbourne, 

 or rather Beachy Head, for which we have the valuable obser- 

 vations of your correspondent, " H. D. G." 



The firing line extended eastward passes directly to Beachy 

 Head over a sea surface, with the exception of about two miles 

 across the low peninsula of Selsea Bill. I have assumed the 

 direction of the wind to coincide with this line, as it approxi- 

 mately did, and, farther, in the absence of definite data as to 

 the rate at which the wind speed increased upwards, I have 

 assumed it to amount to five miles per second for each mile of 

 vertical height. I find then that at the distance of sixty miles 

 from any firing point, which is about the distance of Beachy 

 Head from Spithead, all sound rays starting at a less elevation 

 above the horizon than about 11° 23' would be bent round to 

 the horizon between these two points, the extreme ray having 

 reached an elevation of just over three miles ; and the length 

 of its path exceeding the direct horizontal distance by about 

 four-tenths of a mile, it follows, from the known speed of sound, 

 that the sound energy from a single gun would be at Beachy 

 Head spread over an interval of very nearly two seconds. I 

 conclude, therefore, that no single gun or pair of guns could have 



Fig. 2. 



been heard there. But since the interval along the line between 

 successive ships or pairs of ships corresponds only to a sound 

 interval of just over one second, the sound impulses from suc- 

 cessive ships would overlap (as they would not do at smaller 

 distances, such as Chichester), and might so reinforce one another 

 as to become audible. Doubtless the reflections of rays from 

 the smooth sea surface would also contribute to this result. 



Of course, the assumed data are too hypothetical for any 

 dependence to be paid to these figures as exact results, but I 

 think they suffice to show that the observations of '* H. D. G." 

 may thus be fairly accounted for. 



His description of the sound heard as " er-er-pup-pup " would 

 correspond with the general roll and the explosion from a pair of 

 guns in the double line not fired exactly simultaneously, while 

 the duration which he notes of about eleven seconds for the 

 whole sound would correspond fairly well with the interval, 

 some eighteen seconds, by which the sound from the last ships 

 of the double line would be behind that from the first, and would 

 seem to prove that the sounds from the single line farther west- 

 ward were inaudible. 



It is well known that the speed of sound in air does not de- 

 pend directly on the density, but is affected by temperature, so 

 that in an atmosphere of varying temperature the course of a ray 

 must be curved. In the normal condition it is stated that the 

 fall of temperature is about 1° C. in 330 feet of vertical height, 

 and the consequence is that every ray of sound must be deflected 

 upwards, and so at a little distance from the source would pass to 

 the upper regions of the atmosphere over the heads of observers 

 on the same horizontal line. This effect is probably small com- 

 pared with that due to the wind. It would add to the upward 

 bending effect for rays proceeding against the wind (in our case 



NO. 1640, VOL. 63] 



