50 



SCIENCE. 



[N. S. Vol. XXIII. No. 576. 



maticlie intorno a due nuove seienze at- 

 tenenti alia mecanica et i movimenti 

 locali' (1638).' He composed it while con- 

 fined to a house at Arcetri, near Florence, 

 under the close watch of the Inquisition, 

 strictly forbidden to publish anything and 

 struggling with ill-health and the infirmities 

 of old age which were soon to deprive him 

 completely of his eyesight. Considering 

 these circumstances of its composition, the 

 marvelous freshness and wealth of ideas of 

 this work, which makes Galileo the first 

 mathematical physicist, would be incompre- 

 hensible if we did not know from his corre- 

 spondence that the materials for it had 

 largely been in his mind ever since his 

 early youth. If this be taken into account, 

 the beginnings of both mechanics (apart 

 from statics) and mathematical physics 

 may be dated back to about the year 1600. 

 One of the two new sciences originated 

 by Galileo in the 'Discorsi' is mechanics as 

 the science of motion, especially in its appli- 

 cation to falling bodies and projectiles. 

 The genius of Newton, of Huygens, of 

 Leibniz, was soon to prove the correctness 

 of Galileo's prophetic insight in claiming 

 for his speculations on motion the name of 

 a new science. What Newton and his fol- 

 lowers in the eighteenth century did for 

 mechanics is too well known to be here re- 

 hearsed. By his careful formtdation of 

 the fundamental postulates and definitions 

 and by his bold assumption of the law of 

 universal gravitation, Newton laid the 

 lasting fotindations for astronomical me- 

 chanics; and his fluxional calculus opened 



= It is to be regretted that there exists no good 

 modern translation of this classical work. The 

 German translation published in Ostivald's 

 Klassiker der exakten Wissenschaften (Nos. 11, 

 24, 25), while it contains some helpful notes, is 

 not always exact and trustworthy. The original 

 has recently been edited with great care by A. 

 Favaro in Vol. VIII. (1898) of the 'national edi- 

 tion ' of Galileo's Works. 



up for this science a wide range of develop- 

 ment. 



The other of Galileo's two new sciences 

 deals with the internal structure of matter 

 and the so-called resistance of materials; 

 it is the germ of the mechanics of deform- 

 able hodies. Progress along this line 

 proved a far more difficult task. The 

 seventeenth and eighteenth centuries con- 

 tributed but little to the theory of elas- 

 ticity. Indeed, a new mathematical tool, 

 the theory of partial diiferential equations, 

 had to be invented, and a physical phe- 

 nomenon hitherto neglected, vibratory and 

 wave motions, had to attract the attention 

 of mathematicians, before the mechanics 

 of deformable bodies could become a true 

 science. Besides, the conception of me- 

 chanics itself had to be broadened; and 

 this was accomplished by Lagrange in his 

 'Mecanique analytique' (first edition 1788, 

 second edition 1811-15). 



In view of the use made in the course of 

 the nineteenth century of Lagi-ange's gen- 

 eralizations (it may suffice to mention the 

 theory of the potential, the Lagrangian 

 equations of motion with their generalized 

 idea of force, the general 'principles' such 

 as the principle of least action) it is, I be- 

 lieve, not too much to say that Lagrange's 

 work is as great an advance on Newton's 

 as Newton's was on that of Galileo. 



By the contemporaries of Lagrange this 

 advance was perhaps not fully appreciated. 

 We find the physicists of the beginning of 

 the nineteenth century still very strongly 

 attached to. the idea that all natural phe- 

 nomena not only may, but must, be ex- 

 plained on the basis of NcAvton's laws^ by 

 central forces acting instantaneously at a 

 distance. Newton's mechanics had done 

 such admirable service in astronomy that 



^ See, however, Laplace, ' Mfieanique Celeste,' 

 livre I., Chap. VI. ('Oeuvres,' Vol. I., 1878, pp. 

 74-79 ) , a passage to which E. and F. Cosserat have 

 recently called attention. 



