[2] Wellenlehre, 1852.
[3] Mémoires de Physique Mécanique. Paris, 1848.
If the pipe were a mere line, the time of a vibration would be the time in which a vibration travels from one end of the pipe to the other; and thus the note for a given length (which is determined by the time of vibration), is connected with the velocity of vibration. He thus found that the velocity of a vibration along the pipe in sea-water is 1157 mètres per second.
But M. Wertheim conceived that he had previously shown, by general mathematical reasoning, that the velocity with which sound travels in an unlimited expanse of any substance, is to the velocity with which it travels along a pipe or linear strip of the same substance as the square root of 3 to the square root of 2. Hence the velocity of sound in sea-water would be 1454 mètres a second. The velocity of sound in air is 332 mètres.
M. Wertheim also employed the vibrations of rods of steel and other metals in order to determine their modulus of elasticity—that is, the quantity which determines for each substance, the extent to which, in virtue of its elasticity, it is compressed and expanded by given pressures or tensions. For this purpose he caused the rod to vibrate near to a tuning-fork of given pitch, so that both the rod and the tuning-fork by their vibrations traced undulating curves on a revolving disk. The curves traced by the two could be compared so as to give their relative rate, and thus to determine the elasticity of the substance.
BOOK IX.
PHYSICAL OPTICS.