For accurate measurement of the displacements of lines of stellar spectra which are produced by the relative motion of star and observer in the line of sight, a very beautiful instrument has been devised by Dr J.
By means of vibrations or shocks transmitted through the - Sub water, or by displacements in the balance or position of the animal, the otoliths are caused to impinge against the bristles of the sensory cells, now on one side, now on the other, causing shocks or stimuli which are transmitted by the basal nerve-fibre to the central nervous system.
Let x, y, z be the co-ordinates of any particle of the medium in its natural state, and, 7 7, the displacements of the same particle at the end of time t, measured in the directions of the three axes respectively.
" Let E = o,7 7 = o, =f (bt - x) be the displacements corresponding to the incident light; let O l be any point in the plane P (of the wave-front), dS an element of that plane adjacent to 01; and consider the disturbance due to that portion only of the incident disturbance which passes continually across dS.
If do is the angular displacement of the roller corresponding to displacements, dO of the disk, and ds of the point of application of P, a, and C constants, then d4) = x _ ¢Pds = C.Pds, and therefore 4) = C f 82 Pds; that is, the angular displacement of the roller measures the work done during the displacement from s 1 to s 2 .