196 PROGRESS OF SCIENCE. 



ijj* 1855. Gauss, one of the masterly mathematicians 

 of the XlXth century, established the theory of the 

 DIVISION OF THE CIRCLE ; discovered the LAW OF 

 ERRORS ; was a great master in Transcendental Arithmetic ; 

 found new methods of calculating planets' orbits, explained 

 in his THEORIA MOTUS ; improved geodesy ; invented the 

 MAGNETOMETER for determining the angles which the plane 

 of magnetic meridian makes with the plane of the astro- 

 nomical meridian ; calculated that the total magnetic action 

 of the earth is the same as that which would be exerted if in 

 each cubic yard there were eight bar-magnets each weighing 

 one pound. From data collected by Piazzi, he calculated the 

 whereabouts of Ceres so accurately, that directing his telescope 

 to the probable point he rediscovered this asteroid, which 

 had been lost sight of for months (1801). 



1789 1857. Cauchy discovered the method for finding 

 d priori the number of roots; simplified the THEORY OF 

 ASYMPTOTES. 



17931880. Chasles introduced the adoption of SIGNS 

 IN PURE GEOMETRY, thereby creating uniformity of method ; 

 found the theory of the surfaces of the second degree the 

 starting point of fine discoveries. 



!8o5 1865. Hamilton (Sir W. Rowan) brought into 

 existence the system of QUATERNIONS, an extensive method 

 of mathematical reasoning comparable to the invention of 

 logarithms for power, but of infinitely more value in higher 

 mathematics, for " whatever problem involves the threefold 

 dimensions of space, is treated by a symbolic method of the 

 most comprehensive simplicity" (Jevons). 



1806 1871. De Morgan endeavoured to effect the 



UNION OF LOGIC AND MATHEMATICS " one of the most 

 important steps in the history of science " a connection 

 brought about by Boole. De Morgan effected a great 

 generalisation, for his double algebra is true not only of 

 space relations, but of forces, so that the triangle of forces 

 is reduced to a case of pure geometrical addition ; and more, 

 the triangle of lines, the triangle of velocities, the triangle of 

 forces, the triangle of couples, are reduced by analogy to one 

 simple theorem which amounts to this, " that there are two- 



