Septembers?, 1895.] 



SCLENGE. 



415 



dency, but it Avill be done, if at all, only after 

 an unduly prolonged, wasteful adherence to the 

 parallelogram. 



In treating of the development of dynamics, 

 attention is confined principally to the achieve- 

 ments of Galileo, Huygens and Newton. The 

 exposition of the work of Galileo is excellent, 

 marking out in clearest lines his superiority as 

 a truly scientific investigator over all his prede- 

 cessors and most of his successors. His greatest 

 work, of course, was his determination of the 

 laws of falling bodies, and consequently of uni- 

 formly accelerated motion. In everything con- 

 cerning the relation of motion to the circum- 

 stances that affect it, Galileo had to make his 

 way as a pioneer. After first examining whether 

 the velocity of a falling body varied directly as 

 the distance, and abandoning this for the as- 

 sumption that it varied as the time, he was led 

 to a correct idea of acceleration, and also to 

 that of force as measured by the product of 

 mass and acceleration. Owing to the phys- 

 ical limitations under which he was obliged 

 to perform his experiments, it was necessary for 

 him to make various assumptions, whose valid- 

 ity always had to be proven. For instance, he 

 retarded the motion of falling bodies by caus- 

 ing them to descend inclined planes, and then 

 examined the peculiarities of their motion upon 

 the assumption that ' ' a body which falls 

 through the height of an inclined plane attains 

 the same final velocity as a body .which falls 

 through its length." 



The reasoning by which he felt w'arranted in 

 in making this assumption brought him to the 

 conclusion that if a body, in falling down the 

 length of an inclined plane, acquired a velocity 

 different from that gained by falling through 

 its height, " a heavy body could, by an ap- 

 propriate arrangement of inclined planes, be 

 forced continually upwards solely by its own 

 weight." But besides justifying the assump- 

 tion logically he verified it experimentally. 

 Both his reasoning and his experimentation 

 were confined to the action of single bodies. 

 Later, when Huygens solved the problem of 

 the centre of oscillation of a compound pendu- 

 lum he made use of a principle which, in its 

 ultimate nature, was like that employed by 

 Galileo, as follows : " In whatsoever manner the 



material particles of a pendulum may by mutual 

 interaction modify each other's motions, in every 

 case the velocities acquired in the descent of the 

 pendulum can be such only that by virtue of 

 them the centre of gravity of the particles, 

 whether still in connection or with their con- 

 nections dissolved, is able to rise just as high as 

 the point from which it fell. Huygens found 

 himself compelled, by the doubts of his contem- 

 poraries as to the correctness of this principle, 

 to remark that the only assumption implied in 

 the principle is that heavy bodies of themselves 

 do not move upwards ;" (p. 174), and this prin- 

 ciple, as Professor Mach points out, is a gener- 

 alization of one of Galileo's ideas. 



The author regards Huygens as in every re- 

 spect the peer of Galileo, a rank which perhaps 

 few would deny him. The above principle 

 which he introduced makes what we now call 

 the loork done on a body by gravity, the condi- 

 tion determinative of the velocity it acquires, 

 and this, more than anything else, marks the 

 difference between Huygens' point of departure 

 and that of Galileo and of Newton. All three 

 recognized the fact of accelerations which they 

 ascribed to force as a cause whose nature was 

 unknown. Says the author : "That which in 

 the mechanics of the present day is called force 

 is not a something that lies latent in the natural 

 processes, but a measurable, actual circumstance 

 of motion, the product of the mass into the ac- 

 celeration." (p. 246.) But this product is only 

 one way of measuring the mutual actions in- 

 volved, for not only do bodies influence one 

 another as to velocities, but also as to displace- 

 ments, and either of these may be made the 

 basis of measuring the force. ' ' We may, there- 

 fore, as it suits us, regard the time of descent or 

 the distance of descent as the factor determina- 

 tive of velocity. If we fix our attention on 

 the first circumstance, the concept of force ap- 

 pears as the original notion, the concept of work 

 as the derived one. If we investigate the in- 

 fluence of the second fact first, the concept of 

 work is the original notion. * * * In this 

 case we know force only as the limiting value 

 of the ratio which increment of work bears to 

 increment of distance. 



Galileo cultivated by preference' the first of 

 these two methods. Newton likewise preferred 



