i 9 2 PROGRESS OF SCIENCE. 



or other peculiarity of the curve, indicates some peculiarity 

 in the equation. It is impossible to describe in an adequate 

 manner the importance of this discovery : the advantage was 

 twofold algebra aided geometry, and geometry gave reci- 

 procal aid to algebra. Curves such as the well-known sections 

 of the cone were found to correspond to quadratic equations. 

 The way was thus opened for the algebraic treatment of 

 motions and forces, without which Newton's Principia could 

 never have been worked out. He showed the mechanical 

 fact that every curvilinear deflection is due to a controlling 

 force." He understood and explained the RISE OF WATER 

 in an exhausted space : ft The weight of water," says he, 

 " counterbalances that of the air." As a physicist, he 

 invented a new barometer, made of mercury and a liquid 

 to magnify the effect of the mercurial barometer. He 

 enunciated the UNDULATORY THEORY OF LIGHT (see 

 Fresnel and Young), and formulated the two LAWS OF 

 REFRACTION (confirming Snell's results) after experiments 

 by means of A PRISM, which exhibited the exact colours of 

 the rainbow. It was reserved to Newton to explain the 

 cause of the phenomenon which Descartes pointed out, as 

 it was reserved to Fresnel and Young to elucidate and prove 

 the undulatory theory. (See Appendix VI.) 



1616 1703. Wallis gave an additional impulse to 

 ANALYTICAL GEOMETRY by his Arithmetica Infinitorum, and 

 his improvement of Cavalieri's method of application. 



!6 2 3 62. Pascal invented a CALCULATING APPARATUS, 

 much improved by Leibnitz, Babbage, Scheutz, Thomas, 

 Sir W. Thomson, and Tait, which would have reconciled 

 Francis Bacon to the science he despised, for it made "all 

 men equal in arithmetic." Pascal invented also the humble 

 WHEEL-BARROW an application of the law of the lever; he 

 established the doctrine of THE WEIGHT AND PRESSURE OF 

 AIR, confirming Torricelli's theory, after the barometric ex- 

 periment carried out under his direction by his friend Perrier 

 on the summit of the Puy de Dome ; he also established the 

 law of equality of pressure in liquids, called PASCAL'S LAW : 

 *' Pressure exerted anywhere upon a mass of liquid is trans- 

 mitted undiminished in all directions, and acts with the same 



