TRAINS OF REASONING. 239 



ference was, that a certain government was not likely to be 

 overthrown ; this inference was drawn according to a formula 

 in which desire of the public good was set down as a mark of 

 not being likely to be overthrown ; a mark of this mark was, 

 acting in a particular manner ; and a mark of acting in that 

 manner was, being asserted to do so by intelligent and dis- 

 interested witnesses : this mark, the government under discus- 

 sion was recognised by the senses as possessing. Hence that 

 government fell within the last induction, and by it was brought 

 within all the others. The perceived resemblance of the case 

 to one set of observed particular cases, brought it into known 

 resemblance with another set, and that with a third. 



In the more complex branches of knowledge, the deduc- 

 tions seldom consist, as in the examples hitherto exhibited, of 

 a single chain, a a mark of 6, b of c, c of d, therefore a a mark 

 of d. They consist (to carry on the same metaphor) of several 

 chains united at the extremity, as thus : a a mark of d, b of e, 

 c of/, d ef of n, therefore a b c a mark of n. Suppose, for 

 example, the following combination of circumstances ; 1 st, 

 rays of light impinging on a reflecting surface ; 2nd, that sur- 

 face parabolic; 3rd, those rays parallel to each other and to the 

 axis of the surface. It is to be proved that the concourse of 

 these three circumstances is a mark that the reflected rays 

 will pass through the focus of the parabolic surface. Now, 

 each of the three circumstances is singly a mark of something 

 material to the case. Bays of light impinging on a reflecting 

 surface, are a mark that those rays will be reflected at an 

 angle equal to the angle of incidence. The parabolic form of 

 the surface is a mark that, from any point of it, a line drawn 

 to the focus and a line parallel to the axis will make equal 

 angles with the surface. And finally, the parallelism of the 

 rays to the axis is a mark that their angle of incidence coin- 

 cides with one of these equal angles. The three marks taken 

 together are therefore a mark of all these three things united. 

 But the three united are evidently a mark that the angle of 

 reflection must coincide with the other of the two equal angles, 

 that formed by a line drawn to the focus ; and this again, by 



