ON  THE  MOTION  OF  PENDULUMS.
75
The work of this pressure during the time dt corresponding to the element of surface dx dz, is equal to
Hence the work exerted over a given portion of the surface is equal to
2fj,m^sc*dt ffda dz.
In the absence of pressures AP_2, AT_3 at the surface, this work must be supplied at the expense of ms viva. Hence 4/j,m^8c*dt ffda dz is the vis viva lost by friction, which agrees with the expression obtained in Art. 51, as will be seen on performing in the latter the integration with respect to y, the limits being y = 0 to y = oo .