REVIEWS 341 



Galileo himself and to whom he refers as " our Academician " (p. 6), Sagredo, and 

 Simplicio, who represents the opinions of Aristotle. It is generally, and with 

 justice, supposed that Galileo's work shows a decisive breaking away from the 

 physics of Aristotle and antiquity in general, but we must not lose sight of the fact, 

 that is shown in the historical work of Wohlwill, Duhem, and others, that the 

 breaking away only came about gradually ; and it would have been very welcome 

 if the translators had given an introduction about how the great gap between the 

 ancient and the Galilean mechanics, as described in this maturest work of Galileo, 

 is to be filled up. This work is, as Galileo himself said, " superior to everything 

 else of mine hitherto published " ; but it is very important, both for the historian 

 and the intelligent student, that good translations of all Galileo's early work which 

 is scientifically relevant should be published. In particular, the reviewer has 

 heard that there are some important manuscripts of Galileo in the library of Eton 

 College, and it is well known that Galileo's Delia scienza meccanica contains an 

 approximate statement of Newton's important third law of motion. It is especially 

 important to us Britons that a detailed study should be made of Galileo's work 

 both in mathematics and in dynamics ; besides the more obvious effect of Galilean 

 ideas on Newtonian mechanics, it is extremely probable that Galileo's frequent use 

 of infinitesimal ideas and fluxional ways of considering these ideas influenced 

 Newton through Barrow and possibly others. 



The first day of these dialogues begins on the subject of the resistance offered 

 by solid bodies to fracture, and continues with a large number of interesting 

 digressions. Of these digressions the most important are the considerations on 

 the subject of geometrical continuity (pp. 27 ff.), on infinity and indivisibility 

 (pp. 30 ff.), the suggestion for the determination of the velocity of light (pp. 42 ff.), 

 the refutation of Aristotle's opinion that heavier bodies fall more quickly than 

 lighter ones (pp. 62 ff.), and the investigation of the vibrations of the pendulum 

 (pp. 94 ff.). We must remember that such digressions were not formerly con- 

 sidered out of place in a treatise on physics : we need only remember Aristotle's 

 own Physics, which is principally a discussion of infinity and continuity. Galileo's 

 speculations on infinity are very remarkable ; he observed that square numbers 

 appear to be as numerous as whole numbers, because there is a one-one corre- 

 spondence between the two infinite classes, though the former is a part of the 

 latter, and concluded that the paradox is solved by denying that the attributes 

 "equal," "greater," and "less" are applicable to infinite quantities. The 

 dialogues on the other days do not contain any digressions. That on the 

 second day is shorter and contains many theorems on the resistance of bodies 

 to breaking or bending. That on the third day is on " local motion," or the 

 motion of naturally falling bodies. After various propositions on uniform 

 motion, we have a section on uniformly accelerated motion, and the subject is 

 treated very much in Euclidean manner, interspersed with the ingenious experi- 

 ments with which Mach's Mechanics has made us familiar and which form a 

 splendid foundation for elementary instruction. The first mention of the problem 

 of the Brachistochrone is interesting (p. 230). The dialogue on the fourth day 

 consists of (i) researches on the paths of projectiles, and (ii) the beginning of a 

 discussion on percussion, which has been praised by Mach as showing heights of 

 Galileo's genius which have often been inaccessible to meaner mortals. Galileo 

 contemplated a dialogue for a fifth day, which was to have treated " of the force 

 of percussion and the use of the catenary," because in 1638 he had plunged more 

 deeply than ever " into the profound question of percussion " and " had almost 

 reached a complete solution " (p. xiii). Following the example of the national 



