On an Integrating Machine having a New Kinematic Principle. (James Thomson). (+) On an Instrument for calculating (.), the Integral of the Product of two given Functions. (+) Mechanical Integration of the Linear Differential Equations of the S. - [THE "HARMONIC ANALYZER", THE FIRST AUTOMATIC ANALOG COMPUTING MACHINE.]

London, Taylor and Francis, 1876-79. Witout wrappers as three issues from "Proceedings of the Royal Society of London", Vol. 24, No. 167+ Vol. 27, No.187+ Vol. 28, No. 191. Pp. 250-344, pp. 284-408 a. pp. 103-232. Papers: In No. 167:pp. 262-265 (James Thomson), pp. 266-68, pp. 269-271, pp. 271-275. In No. 187: pp. 371-373. In No. 191: pp. 111-113 (W. Thomson). Titlepages to vols. 24, 27 a. 28 present. 2 papers with textillustrations. First appearance of all the 6 founding papers around the invention of the "Harmonic Analyzer" and with the mathematical theory for the differential analyzor, containing both the mathematical theories and the practical descriptions of the analyzer and further also having the paper by Lord Kelvin's brother (the first paper offered) in which the machinery is shown for the first time."A ball and disk integrator was the vital invention needed to build the FIRST AUTOMATIC ANALOG COMPUTING MACHINES. Lord kelvin used this integrator -devised for a planimeter in the 1860s by his brother, James Thomson - on two new kinds of analog computers: a harmonic analyzer and a tide predictor. he later specified a more general machine - a differential analyzer."(Eames in "A Computer Perspective")."The harmonic analyzer was used in conjunction with Thomson's tide predictor.The present paper ("Harmonic Analyzer") contains the first full description of the harmoniz analyzer, which was "designed rudimentally" (p. 371) in Thomson's "On an integrating machine having a new kinematic principle"(also offered here),James Thomson's integrator - "one of the first really workable integrating devices" (Williams 1985, 207) - served as the basis for other analog machines designed by William Thomson for solving simultaneous linear equations and integrating differential equations. Thomson first described such a machine, composed of several Thomson integrators connedted together, in his paper on "Mechanical integration of the linear differentialequations of the decond order." (also offred here)" however the "idea could then hardly be carried out, forone reason because an integrator, which is simply a variable- speed drive, could not then be buitl both accurate and capable of carrying sufficient load to move numerous mechanical parts" (Bush 193, 450). The full realization of Thomson's idea did not come until fifty years later, when Vannevar Bush invented the torque amplifier for use in his differential analyzer."(Hook and Norman).…