## The science of mechanics: a critical and historical account of its development, by Ernst Mach: supplement to the 3rd English ed. containing the author's additions to the 7th German ed |

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absolute space Adolf Mayer ancient Archimedes Aristotle Benedetti body calculus of variations Cardano CEuvres Chicago and London conception of mass Conservation of Energy convenient German Daniel Bernoulli Descartes Dictionnaire Philosophique Discorsi discovery Duhem Dynamics Encykl equations equilibrium Euler experience fifth corollary fixed stars Galileo Gauss German translation gravity historical Huygens inclined plane investigations Jellett Jordanus Joseph Bertrand Lagrange Lagrange's Lange last line law of inertia Least Action Leipsic Leonardo lever line 13 line 9 Mach's Mechanics math Maupertuis Maupertuis's Mechanik memoir Micanique Monist for April Monist for July motion of falling motu Newton Newtonian notes Oettingen Ostwald's Klassiker PAcad paper Paris Petzoldt Philip E. B. Jourdain Principia principle of least principle of virtual recognised remarks Roberval rotation seqq seventh German edition Stevinus supposition system of co-ordinates system of reference theorems theory tion Vailati velocity virtual displacements Voss weight Wiss Wohlwill xxii

### Popular passages

Page 53 - Die Leitgedanken meiner naturwissenschaftlichen Erkenntnislehre und ihre Aufnahme durch die Zeitgenossen " (Scientia: Rivista di Scienza, vol. vii, 1910, No. 14, 2 ; or Physikalische Zeitschrift, 1910, pp. 599-606).

Page 34 - V The motions of bodies included in a given space are the same among themselves, whether that space is at rest or moves uniformly forwards in a right line without any circular motion.

Page 80 - ... radius — but now they were mathematically true, excepting only for the slight deviation from a perfectly spherical form of the sun, earth and planets. We can imagine the effect of this sudden transition from approximation to exactitude in stimulating Newton's mind to still greater efforts. It was now in his power to apply mathematical analysis with absolute precision to the actual problems of astronomy.

Page 34 - But how we are to collect," says Newton in the Scholium at the end of the Definitions, "the true motions from their causes, effects, and apparent differences, and vice versa ; how from the motions, either true or apparent, we may come to the knowledge of their causes and effects, shall be explained more at large in the following Tract.

Page 35 - Galileo's happy discovery could only hold approximately for small times and spaces, during which the rotation did not come into question. Instead of that, Newton's conclusions about planetary motion, referred as they were to the fixed stars, appeared to conform to the law of inertia. Now, in order to have a generally valid system of reference, Newton ventured the fifth corollary of the Principia (p. 19 of the first edition). He imagined a momentary terrestrial system of co-ordinates, for which the...

Page 43 - ... knowledge of the immediate connections, say, of the masses of the universe. There will hover before him as an ideal an insight into the principles of the whole matter, from which accelerated and inertial motions result in the same way. The progress from Kepler's discovery to Newton's...

Page 33 - This appeared to him to cause the difficulty of distinguishing between true (absolute) and apparent (relative) motion. By this he was also impelled to set up the conception of absolute space. By further investigations in this direction — the discussion of the experiment of the rotating spheres which are connected together by a cord and that of the rotating water-bucket (pp.

Page 79 - Newton's eyes when he realised that these results, which he had believed to be only approximately true when applied to the solar system, were really exact ! Hitherto they had been true only in so far as he could regard the sun as a point compared to the distance of the planets, or the earth as a point compared to the distance of the moon, — a distance amounting to only about sixty times the earth's radius — but now they were mathematically true, excepting only for the slight deviation from a...

Page 33 - Try to fix Newton's bucket and rotate the heaven of fixed stars and then prove the absence of centrifugal forces. 4. It is scarcely necessary to remark that in the reflections here presented Newton has again acted contrary to his expressed intention only to investigate actual facts. No one is competent to predicate things about absolute space and absolute motion; they are pure things of thought, pure mental constructs...

Page 36 - ... interfering with its usability, impart to this system any initial position and any uniform translation relatively to the above momentary terrestrial system. The Newtonian laws of force are not altered thereby; only the initial positions and initial velocities - the constants of integration - may alter. By this view Newton gave the exact meaning of his hypothetical extension of Galileo's law of inertia. We see that the reduction to absolute space was by no means necessary, for the system of reference...