38 REPORT—1848, 
opportunities have existed of observing any phenomena in which the velocity of the 
observer has been sufficient to affect the character of sounds. The author having 
had occasion to make observations on railway trains moving at high velocities, has 
been led to notice some very curious effects in sounds heard at 50 and 60 miles an 
hour. These effects are not heard by an observer who is stationary. He found 
that the sound of the whistle of an engine stationary on the line was heard by a 
passenger in a rapid train to sound a different note—in a different key from that in 
which it was heard by the person standing beside it. The same was true of all 
sounds. The passenger in rapid motion heard them in a different key, which might 
be either louder or lower in pitch than the true or stationary sound. The explana- 
tion of this was given as follows. The pitch of a musical sound is determined by 
the number of vibrations which reach the ear in a second of time—32 vibrations per 
second of an organ-pipe give the note C, and a greater or less number give a more 
acute sound or one more grave. These vibrations move with a velocity of 1024 feet 
per second nearly. If an observer in a railway train move at the rate of 56 miles 
an hour towards a sounding body, he will meet a greater number of undulations in 
a second of time than if at rest, in the proportion which his movement bears to the 
velocity of sound; but if he move away from the sounding body he will meet a 
smaller number in that proportion. In the former case he will hear the sound a 
semitone higher, and in the second a semitone lower than the obseryer at rest. In 
the case of two trains meeting at this velocity, the one containing the sounding body 
and the other the observer, the effect is doubled in amount. Before the trains meet 
the sound is heard two semitones too high, and after they pass two semitones too 
low—being a difference of a major third. There were next explained the various 
effects which the noises of a train produced on the ears of passengers at high velo- 
cities. The reflected sounds of a train, from surfaces like those of bridges across 
the line, were at ordinary velocities sent back to the ear changed by less than a 
tone, so as to cause a harsh discord, which was an element of the unpleasant 
effect on the ear, of passing a bridge. In a tunnel also the sounds reflected from 
any irregularities in the front of the train or behind it were discords to the sounds 
of the train heard directly. He showed however that at speeds of 112 miles an 
hour these sounds might be those of a harmony with each other and become agree- 
able, for the sounds reflected in opposite directions would have the interval of a 
major third. 
On the Lengths and Velocities of Waves. By Capt. Stantey, RN. 
* (Extract from a Letter to the Rev. Dr. Whewell.) 
The method I adopted for the determination of the length and speed of the sea, 
was to veer a spar astern by the marked lead-line, when the ship was going dead 
before the wind and sea, until the spar was on the crest of one wave while the ship’s 
stern was on the crest of the preceding one. After a few trials, I found that when 
the sea was at all regular I could obtain this distance within two or three fathoms 
when the length of wave was fifty. 
In order to ascertain the speed of the sea, the time was noted when the crest of 
the advancing wave passed the spar astern, and also the time when it reached the 
ship ; and by taking a number of observations, I have every reason to believe we have 
obtained a result not very far from the truth. The officer noting the time in all 
these observations having only to register the indications of the watch when the 
observer called stop, had no bias to induce him to make the differences more regular. 
For measuring the height of the waves, I adopted a plan recommended to me by 
Mrs. Somerville, which I have tried for ten years with great success. When the 
ship is in the trough of the sea, the person observing ascends the rigging until he 
can just see the crest of the coming wave on with the horizon, and the height of his 
eye above the ship’s water-line will give a very fair measure of the difference of level 
between the crest and hollow of a sea. Of course in all these observations the mean 
of a great many have been taken, for even when the sea is most regular apparently 
there is a change in the height of the individual waves. 
I regret that we have had so few opportunities of making these observations, but 
it is only under very favourable circumstances, when the ship is going directly 
before both wind and sea, that they can be made with any chance of success; but 
