302 A SHORT HISTORY OF SCIENCE 



Leibnitz' sense of mathematical form was also well exemplified 

 by his important algebraic invention of determinants. In regard 

 to numbers he says : 



The imaginary numbers are a fine and wonderful refuge over 

 the divine spirit, almost an amphibium between being and not being. 



Leibnitz's discoveries lay in the direction in which all modern pro- 

 gress in science lies, in establishing order, symmetry, and harmony, 

 i.e. comprehensiveness and perspicuity, rather than in dealing 

 with single problems, in the solution of which followers soon at- 

 tained greater dexterity than himself. Merz. 



Leibnitz believed he saw the image of creation in his binary arith- 

 metic, in which he employed only two characters, unity and zero. 

 Since God may be represented by unity, and nothing by zero, he 

 imagined that the Supreme Being might have drawn all things from 

 nothing, just as in the binary arithmetic all numbers are expressed 

 by unity with zero. This idea was so pleasing to Leibnitz, that he 

 communicated it to the Jesuit Grimaldi, President of the Mathematical 

 Board of China, with the hope that this emblem of the creation might 

 convert to Christianity the reigning emperor who was particularly 

 attached to the sciences. Laplace. 



HALLEY : PREDICTION OF COMETS. In applying Newton's 

 theories to known comets his friend and disciple Halley made the 

 astonishing discovery that some of them instead of visiting the 

 solar system once for all, actually described elliptical orbits of 

 vast extent and great eccentricity about the sun. Among these 

 he found one which having appeared in 1531, 1607, and 1682, 

 should, if his identifications were correct, return in 1759. This 

 bold prediction was fulfilled, and Halley's comet has not only 

 reappeared in 1835 and 1910, but has even been traced back almost 

 to the beginning of our era. A second similar prediction of Halley 

 awaits verification in the year 2255. 



In physics, Halley enunciated for spherical lenses and mirrors 



the correct formula - = -f and that for the barometric 

 / i 2 



determination of altitudes. His mathematical work included 

 graphical discussion of the cubic and biquadratic equations, a 



