The integrator, another and still more ingenious instrument, by M. J. Amsler-Laffon, was invented theoretically shortly after the planimeter just described (in the year 1855), but was first constructed for practical use in the year 1867, the first instrument made being exhibited in the Paris International Exhibition in the year named. It was not introduced into England till the year 1878, and although adapted for other uses than those involved in scientific calculations connected with shipbuilding it was in this connection that attention was first seriously directed towards it. In 1880 the late Mr C. W. Merrifield described the instrument, and traced the mathematical principles upon which it is based, before the Institution of Naval Architects, and in 1882, before the same body, Mr J. H. Biles, naval architect for the firm of Messrs J. & G. Thomson, called attention to the usefulness of the instrument in stability investigations, showing by specimen calculations and other particulars its great adaptability to this class of work, even in the hands of youthful and untrained operators. A still more recent and exhaustive paper devoted to the claims of the integrator upon naval architects was read before the same Institution by Dr A. Amsler, the son of the inventor, at its last meeting. This paper was chiefly concerned with demonstrating the advantages of the integrator in respect of time saved, as well as in respect of its great accuracy. [Illustration: FIG. 27. AMSLER’S MECHANICAL INTEGRATOR.] The object of the integrator is to find at one operation the area, the statical moment, and the moment of inertia of any closed curve or figure by simply tracing out the curve with a pointer, the results being read off directly from the instrument, as in the case of the planimeter, and with a correspondingly small amount of after calculation. As shown by Fig. 25, the essential parts of the integrator are a rail =L=, having groove with which to guide the wheels _p_ and _q_ of a carriage provided with rollers =D_{1}= =D_{2}= =D_{3}= moving on the surface of the drawing. The contour of the figure to be dealt with is traced—in the direction of the movement of the hands of a watch—by the pointer =F=, this pointer being attached to an arm moving on the vertical centre of the instrument while the whole mechanism runs to and fro on the rail =L=. Under these conditions the rollers =D_{1}= =D_{2}= =D_{3}= execute movements partly rolling, partly sliding, and by readings taken from the divisions engraved upon their circumferences at the beginning and the end of the whole movement, together with simple arithmetical processes, the nature of which may be inferred from the explanations given of the planimeter readings, the three quantities sought are arrived at.