242 NOW Id ORGANUM 



aroma; and many observations of the like kind, well worthy 

 of notice, are to be made in distillations. But let these 

 suffice as examples. 80 



The experiments of the last two classes of instances are considered only 

 in relation to practice, and Bacon does not so much as mention their infinitely 

 greater importance in the theoretical part of induction. The important law of 

 gravitation in physical astronomy could never have been demonstrated but by 

 such observations and experiments as assigned accurate geometrical measures 

 to the quantities compared. It was necessary to determine with precision the 

 demi-diameter of the earth, the velocity of falling bodies at its surface, the dis 

 tance of the moon, and the speed with which she describes her orbit, before 

 the relation could be discovered between the force which draws a stone to the 

 ground and that which retains the moon in her sphere. 



In many cases the result of a number of particular facts, or the collective 

 instances rising out of them, can only be discovered by geometry, which so far 

 becomes necessary to complete the work of induction. For instance, in the 

 case of optics, when light passes from one transparent medium to another, it 

 is refracted, and the angle which the ray of incidence makes .with the super 

 ficies which bounds the two media determines that which the refracted ray 

 makes with the same superficies. Xow, all experiment can do for us in thia 

 case is, to determine for any particular angle of incidence the corresponding 

 angle of refraction. But with respect to the general rule which in every pos 

 sible case deduces one of these angles from the other, or expresses the constant 

 and invariable relation which subsists between them, experiment gives no direct 

 information. Geometry must, consequently, be called in, which, when a con 

 stant though unknown relation subsists between two angles, or two variable 

 qualities of any kind, and when an indefinite number of values of those quanti 

 ties are assigned, furnishes infallible means of discovering that unknown rela 

 tion either accurately or by approximation. In this way it has been found, 

 when the two media remain the same, the cosines of the above-mentioned 

 angles have a constant ratio to each other. Hence, when the relations of the 

 simple elements of phenomena are discovered to afford a general rule which 

 will apply to any concrete case, the deductive method must be applied, and the 

 elementary principles made through its agency to account for the laws of their 

 more complex combinations. The reflection and refraction of light by the rain 

 falling from a cloud opposite to the sun was thought, even before Newton s 

 day, to contain the form of the rainbow. This philosopher transformed a prob 

 able conjecture into a certain fact when he deduced from the known laws of 

 reflection and refraction the breadth of the colored arch, the diameter of the 

 circle of which it is a part, and the relation of the latter to the place of the 

 spectator and the sun. Doubt was at once silenced when there came out of 

 his calculus a combination of the same laws of the simple elements of optics 

 answering to the phenomena in nature. Ed. 



