402 Continuation of the Reply to Mr. Riddle's Remarks 



and within what limits it may be used with safety. It is un- 

 doubtedly owing to some such causes as the above, that one na- 

 vigator finds water where another placed the land ; or that 

 islands have been known to dive and swim alternately at plea- 

 sure. 



It must, no doubt, be acknowledged that another person will 

 often discover what the author of a paper did not himself ob- 

 serve ; and in this respect Mr. R. has shown much acuteness, 

 since most of the things he has discovered do not exist in my 

 paper at all. In order to set me in as odious a light as possible, 

 he says, " It would indeed appear that I am not aware that the 

 central distance of the objects is what is required." But it is 

 past his power to produce the " appearance " of any such thing ; 

 and after all the contempt he affects to throw on the " excen- 

 tric point," he is not able to show that it will ever produce any 

 *^ error" whatever. The rule however which 1 gave on page 37, 

 is plainly meant as approximate, and not as strictly correct in 

 low altitudes. 



In perusing my paper in your last Number, which was written 

 in too great haste, I am really sorry to find that I have expressed 

 myself very incorrectly about the augmentation of the moon's 

 diameter. I was led into that mistake by adhering too closely to 

 Mackay's remark, which Mr. Riddle says is " theoretically truej" 

 whereas it is no such thing, as he may soon find at his leisure. 

 What I have said about the augmentation being greatest in a 

 vertical direction is entirely a mistake ; but as the error, and in- 

 deed the whole dispute, is merely about a small fraction of a se- 

 cond, it is useless to say any thing further about a quantity that 

 can do neither good nor ill. 



With regard to what I formerly advanced respecting the prin- 

 ciples of the quadrant, and on which Mr. R. animadverted with 

 so much groundless severity, I would beg to observe, that in ex- 

 plaining the principles of any instrument, it is certainly of the 

 last importance to assign to each particular part its proper use or 

 effect; otherwise, it does not deserve the name of an explana- 

 tion at all ; and can at best convey vague or erroneous ideas of 

 the nature of the instrument. Had Mr. Riddle himself been the 

 iirst to discover the popular mistake in (|uestion, that vvould have 

 altered the case. But it vvould indeed have been too mucii for 

 any other person but himself to have had the merit of discovering 

 *' that a mistaken idea was generally entertained respecting the 

 theory of an instrument of such importance." 



I shall now proceed to demonstrate that the.halving of the ob- 

 served angle is completely effected by the first, the single reflec- 

 tion ; and in so doing, I hope I shall not be taxed with produ- 

 cing a demonstration of the principles of the instrument which is 



to 



