VIII NOTES BY THE EDITOR 



follow, and in various kinds in point of difficulty, and thus adapted to 

 the progress they may have made, from Mr. Marcet's plain and 

 elementary explanations, up to the treatises of learned professors like 

 those of the Astronomer Royal, Sir D. Brewster, and Professor de 

 Morgan. So great and varied are the helps afforded to students in 

 humble life that it has been said that there can be no such thing 

 now as a self-taught person. Let us only reflect how mighty would 

 have been the comfort to such students in former times could they 

 have enjoyed such facilities. What would Franklin have given 

 for them, who, living on a vegetable diet on purpose to save a few 

 pence from his day's wages for the purchase of books, was fain to 

 learn a little geometry from a treatise on navigation he had been 

 happy enough to pick up at a bookstall, something of arithmetic by 

 having fallen upon a copy of Cocker, and from an odd volume of 

 the Spectator gained a notion of the style he afterwards so powerfully 

 used? What would Simpson have given for access to books, who 

 could only get, from the accident of a peddler passing the place where 

 he was kept by his father working at his trade of a weaver, the copy 

 of Cocker containing a little Algebra, and even when grown up could 

 only, by borrowing Stone's translation of L' Hopital from a friend, ob- 

 tain an insight into the science of infinitesimals, on which two years 

 after, he published an admirable work, while continuing to divide his 

 time between his toil as a weaver and as a teacher ? Brindley, the 

 great engineer, was through life an uneducated man ; Rannequin is 

 said never to have learnt the alphabet ; and both executed great works, 

 but with difficulties and delays which reading would have spared them. 

 Harrison, too, though he had received an ordinary education, yet only 

 while working in his trade of a carpenter, became acquainted with 

 science by some manuscript lectures of Sanderson falling in his way ; 

 and so hard did he find it to obtain adequate knowledge on the subjects 

 connected with his mechanical pursuits, that forty years were spent in 

 perfecting his admirable improvements on the construction of time- 

 keepers, and bringing them into use. It would be going too far to hold 

 that Franklin's genius, both in physical and political science, could have 

 done greater things had his original difficulties in self-education been 

 removed ; but we may safely affirm that both Brindley, Rannequin, 

 and Harrison, would have effected far more with the helps which their 

 successors have had ; and of Simpson no doubt can be entertained that, 

 even amid the distractions of his trade, his short life would have been 

 illustrated by far greater steps in mathematical science. For it is an 

 entire mistake to suppose, with some of his biographers, that his 

 genius was not original, and fitted to make great advances in his 

 favorite study. The late proceedings respecting Sir Isaac Newton's 

 monument, have led to ascertaining that Simpson had made the same 

 approaches towards the modern improvement of the calculus which its 

 illustrious inventor himself had done, but kept concealed ; and no 



