MATHEMATICAL SCIENCES-SEVENTEENTH CENT. 161 



this can be altered without changing the colours, and the rays which 

 go towards F may even be bent more than those which are here going 

 towards H, but still they exhibit red colour, while those towards H show 

 blue ; nor is reflection necessary, for here there is none ; nor a number 

 of refractions, for here there is but one. But I judged that at least one 

 was necessary, and one the effect of which must not be destroyed by 

 a contrary refraction ; for experience shows that if the surfaces M N 

 and N P were parallel, the rays, being as much made straight by one as 

 they are bent aside by the other, would produce no colours. I did not 

 doubt that light also was necessary, for without that nothing is seen j; 

 and, besides that, I observed that there must be shade or limitation of 

 that light ; for, if the opaque body on N P be removed, the colour no 

 longer appears ; if the opening be made wider, the colours are not 

 extended, but the middle space on the screen becomes white." Des- 

 cartes almost seems to be here approaching to Newton's discovery 

 of the composite nature of white light ; but he leaves the path of ex- 

 periment and induction to explain deductively the production of the 

 colours by his theory of light, which he regards as the movement of a 

 very subtile matter, the parts of which must be imagined as little balls 

 rolling into the pores of terrestrial bodies. Rotations, various in direc- 

 tion and velocity, are impressed on these balls, and the greater or less 

 velocity of their rotations affects the eye as different colours. 



In a short tract on Mechanics, published in 1668, Descartes states 

 in the clearest terms the true general principle of the so-called me- 

 chanical powers and of other machines. He says that all the engines 

 and machines, by help of which a heavy load can be moved by the 

 application of a small power, are founded on one single principle. 

 " The same force which is able to raise a weight, for example, of one 

 hundred pounds, to the height of two feet, can also raise a weight of 

 two hundred pounds to the height of one foot, or one of four hundred 

 pounds the height of half a foot, and so on." The proof of this which 

 he advances is based on the assumed principle that " the effect must 

 always be proportional to the cause ;" so that, if it is necessary to em- 

 ploy the action which raises one hundred pounds two feet high to the 

 raising only one foot high of some other weight, that weight must weigh 

 two hundred pounds ; for it is the same to raise two hundred pounds 

 one foot as to raise one hundred pounds first one foot, and then one 

 hundred pounds again one foot. Descartes illustrates the general prin- 

 ciple by considering the cases of the pulley, the inclined plane, the 

 wedge, the wheel and axle, the screw, and the lever. 



In the chapter devoted to Galileo we refrained from giving an ac- 

 count of certain discoveries in mechanical science for which the great 

 Florentine is justly celebrated. This was done with a view of here 

 presenting a more connected account of the rise of modern physical 

 science, with which the names of Galileo and his disciples must be 

 associated. While Galileo was still a young man studying at the 



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