The equation of motion of a mechanical seismograph is −ẍ=ÿ+2kẏ+p2y where x is the ground displacement and y the seismograph deflection. This equation may be solved for y when x is supposed known or for x when y has been observed as a function of the time. In this paper both of these ways of solving the equation are considered. The motion of the seismograph due to a train of waves starting at t=0 is considered and also the motion due to the arrival of a single wave. In each case seismographs with several periodic times and either undamped or critically damped are considered. Curves are given showing the motion of the ground and the calculated motion of the seismograph. The motion of the ground corresponding to several simple assumed seismograms is also worked out and shown by means of curves. The motion corresponding to a given seismogram depends greatly on the periodic time and damping of the seismograph. Finally the ground motion is deduced from two actual seismograms due to dynamite explosions. An integraph is described which enables the calculations to be done more quickly.