404 Continuation of ills Reply to Mr. Riddle's Remarks 



fleeted from a revolving mirror, the .mngle described by the reflected 

 ray will be double of that described by the mirror," — a statement 

 meaning neither more nor less than that the halving of the ob- 

 served angle is completed by the single reflexion of that one re- 

 volving mirror. And yet in a little after he would like to prove 

 the contrary ; but on account of the impossibility of the task, he 

 contents himself with trying to palm the popular error in ques- 

 tion, on the demonstration he had copied from some elementary 

 work ; and, strange to relate, he at length brings out the extra- 

 ordinary conclusion, that there is nothing " vague or insignifi- 

 cant" in ascribing the above effect to the " double reflexion!" 



Mr. R. lastly admits, though reluctantly, that I had correctly 

 stated the error of certain tables *, but that I had " disingenu- 

 ously converted that into an argument against putting confidence 

 in any tables of the kind." Now this accusation is totally un- 

 founded ; since it is to his own candour and moderation that I 

 owe its extension to " any tables of the kind." My own words 

 are : — " It is not difficult to perceive what confidence ought to 

 be put in such tables j" — obviously meaning the tables only which 

 contained the gross error, and by no means any tables of the 

 kind. It is then Mr. R. himself who " has betrayed the aberra- 

 tion from rectitude of intention," by disingenuously laying so 

 many erroneous things to my charge, which he might have been 

 content to have attributed to his own misconstruction. 

 I am, sir, 



\ our most obedient servant, 

 Berners street, Dec. 3, 1819. HenRY MeikLE. 



p.S. — In your last Number, Mathematicus, among other 

 things, accuses me of advancing three distinct properties of the 

 ellipsis " with an air of novelty." Now that this accusation, so 

 far as " novelty" is concerned, must be very incorrect, is obvious 

 to any one who merely looks at the uncertain mode in which I 

 have announced that proposition. 



With regard to my other crin)e of not reading, I would beg to 

 inform him, that I had turned over several very complete trea- 

 tises on Conic Sections, some of those he mentions not excepted; 

 but then I was only in quest of the other two properties, without 

 concerning myself at all about the third " long known " one, 

 until writing out the demonstration, I merely marked it down as 

 an obvious consequence of the other two ; and I had scarcely sent 

 away that paper, when on turning over the second volume of Pro- 



• This error is of no trifling nature, since by it a ship may appear to 

 change her latitude sixteen miles at the end of twelve hours, althotigh she 

 do not stir out of the spot, and that too in any part of the globe. 



fessor 



