536 KOVtTM OROANUM. [bOOX tL 



the flower^ and then tlie more eartliy part, which disturbs the 

 perfume ; so that if the violets be steeped a whole day, a much 

 fainter perfume is extracted than if they were steeped for a 

 quarter of an hour only, and then taken out ; and since the 

 odoriferous spirit in the violet is not abundant, let other and 

 fresh violets be steeped in the vinegar every quarter of an hour, 

 as many as six times, when the infusion becomes so strengthened, 

 that although the violets have not altogether remained there for 

 more than one hour and a half, there remains a most pleasing per- 

 fume, not inferior to the flower itself, for a whole year. It must 

 be observed, however, that the perfume does not acquire its full 

 strength, till about a month after the infusion. In the distil- 

 lation of aromatic plants macerated in spirits of wine, it is Avell 

 known that an aqueous and useless phlegm rises first, then water 

 containing more of the spirit, and lastly, water containing more 

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

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

 suffice as examples.' 



* The experiments of the two last 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 ot the 

 earth, the velocity of falling bodies at its surface, the distance of tlie 

 moon, and the speed with which she describes her orbit, before the rela- 

 tion 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 collec- 

 tive 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 inci- 

 dence makes with the superficies which bounds the two media deter- 

 mines that which the refracted ray makes with the same superficies. 

 Now, all experiment can do for us in this 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 possible case deduces 

 one of these a'?gles 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 constant though unknown relation subsists between two angles, 

 or two variable qualities of any kind, and when an indefinite number of 

 values of those quantities are assigned, furnishes infallible means of dis- 

 covering that unknown relation 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 ot pheno- 



