«ct. in] DISSERTATION SECOND. 107 



ration. Here, however, Galileo was under a mistake, as 

 the motions in the chord and in the arch are very dissimi- 

 lar. The accelerating force in the chord remains the same 

 from the beginning to the end, but, in the arch, it varies 

 continually, and becomes, at the lowest point, equal to no- 

 thing. The times in the chords, and in the arches, are 

 therefore different, so that here we have a point marking 

 the greatest distance in this quarter, to which the me- 

 chanical discoveries of Galileo extended. The first per- 

 son who investigated the exact time of a vibration in an 

 arch of a circle was Huygens, a very profound mathema- 

 tician. 



To this list of mechanical discoveries, already so im- 

 portant and extensive, we must add, that Galileo was the 

 first who maintained the existence of the law of continuity, 

 and who made use of it as a principle in his reasonings on 

 the phenomena of motion. * 



The vibrations of the pendulum having suggested to 

 Galileo the means of measuring time accurately, it ap- 

 pears certain that the idea of applying it to the clock had 

 also occurred to him, and of using the chronometer so 

 formed for finding the longitude, by means of observations 

 made on the eclipses of the satellites of Jupiter. How 

 far he had actually proceeded in an invention which re- 

 quired great practical knowledge, and which afterwards 

 did so much credit to Huygens, appears to be uncertain, 

 and not now easy to be ascertained. But that the project 

 had occurred to him, and that he had taken some steps to- 

 wards realizing it, is sufficiently established. 



One forms, however, a very imperfect idea of this phi- 

 losopher, from considering the discoveries and inventions, 

 numerous and splendid as they are, of which he was the 



1 Opere de Galileo, Tom. IV. Dial. L p. 32, Florence edi- 

 tion, and in many other part=. 



