INTRODUCTION. 47 



doubtfully discerned. And again, when this step has been made by 

 the principal discoverers, there may generally be observed another 

 period, which we may call the Sequel of the Epoch, during which the 

 discovery has acquired a more perfect certainty and a more complete 

 development among the leaders of the advance ; has been diffused to 

 the wider throng of the secondary cultivators of such knowledge, and 

 traced into its distant consequences. This is a work, always of time 

 and labor, often of difficulty and conflict. To distribute the History 

 of science into such Epochs, with their Preludes and Sequels, if suc- 

 cessfully attempted, must needs make the series and connections of its 

 occurrences more distinct and intelligible. Such periods form resting- 

 places, where we pause till the dust of the confused march is laid, and 

 the prospect of the path is clear. 



Inductive Charts} — Since the advance of science consists in collect- 

 ing by induction true general laws from particular facts, and in com- 

 bining several such laws into one higher generalization, in which they 

 still retain their truth ; we might form a Chart, or Table, of the prog- 

 ress of each science, by setting down the particular facts which have 

 thus been combined, so as to form general truths, and by marking the 

 further union of these general truths into others more comprehensive. 

 The Table of the progress of any science would thus resemble the Map 

 of a River, in which the waters from separate sources unite and make 

 rivulets, which again meet with rivulets from other fountains, and thus 

 go on forming by their junction trunks of a higher and higher order. 

 The representation of the state of a science in this form, would neces- 

 sarily exhibit all the principal doctrines of the science ; for each general 

 truth contains the particular truths from which it was derived, and 

 may be followed backwards till we have these before us in their sepa- 

 rate state. And the last and most advanced generalization would 

 have, in such a scheme, its proper place and the evidence of its valid- 

 ity. Hence such an Inductive Table of each science would afford a 

 criterion of the correctness of our distribution of the inductive Epochs, 

 by its coincidence with the views of the best judges, as to the substan- 

 tial contents of the science in question. By forming, therefore, such 

 Inductive Tables of the principal sciences of which I have here to 

 speak, and by regulating by these tables, my views of the history of 

 the sciences, I conceive that I have secured the distribution of my his- 



» Inductive charts of the History of Astronomy and of Optics, such as are here 

 referred to, are given in the Philosophy, hook xi. ch. 6. 



