Editorial note — Recent Scientific Discoveries.

[Footnote 198: Suppose the sum of the velocities of the trains to be one-ninth of that of sound, and that the whistle is, at a given moment, 1140 feet (which is about the distance travelled by sound in a second) from our ear. The vibrations emitted at this instant will reach us in one second; and all those emitted in the nine seconds required for the train to arrive will be condensed into the remaining eight. Their frequency will then be nine-eighths of what it would be without the motion. It will be diminished in nearly the same ratio after the passage; since the vibration emitted nine seconds afterward will require an additional second to reach us; thus, the frequency will now be nine-tenths of what it would be without the motion, or four-fifths of what it was before meeting; corresponding to a flattening of two whole musical tones. This would require a relative velocity of 127 feet a second, or 87 miles an hour; which gives the rule, that, for every half-tone of flattening, the sum of the velocities, or the velocity of the moving train, if we are at rest, is 22 miles an hour.]