91 DISSERTATION SECOND. [part i. 



Hence, the route which leads to many of the richest and 

 most fertile fields of science, is not precisely that which 

 Bacon pointed out ; it is safer and easier, so that the voyager 

 finds he can trust to his chart and compass alone, with- 

 out constantly looking out, or having the sounding-line per- 

 petually in his hand. 



Another remark I must make on Bacon's method is, that 

 it does not give sufficient importance to the instantiae radii, 

 or those which furnish us with accurate measures of physi- 

 cal quantities. The experiments of this class are introduced 

 as only subservient to practice ; they are, however, of in- 

 finite value in the theoretical part of induction, or for ascer- 

 taining the causes and essences of the things inquired into. 

 We have an instance of this in the discovery of that important 

 truth in physical astronomy, that the moon is retained in 

 her orbit by the force of gravity, or the same which, at the 

 earth's surface, makes a stone fall to the ground. This 

 proposition, however it might have been suspected to be 

 true, could never have been demonstrated but by such ob- 

 servations and experiments as assigned accurate geometri- 

 cal measures to the quantities compared. The semidiame- 

 ter of the earth ; the velocity of falling bodies at the earth's 

 surface ; the distance of the moon, and her velocity in her 

 orbit ; — all these four elements must be determined with 

 great precision, and afterwards compared together by cer- 

 tain theorems deduced from the laws of motion, before the 

 relation between the force which retains the moon in her or- 

 bit, and that which draws a stone to the ground, could pos- 

 sibly be discovered. The discovery also, when made, car- 

 ried with it the evidence of demonstration, so that here, as 

 in many other cases, the instantiae radii are of the utmost 

 importance in the theoretical part of physicks. 



Another thing to be observed is, that, in many cases, the 

 result of a number of particular facts, or the collective in- 



