" On finding the Longitude ly Lunar Ohservations." 345 



selves masters of the whole mystery, so that by and by there would 

 be no use in going to school, and neglect to attend school ? 



Dr. Hooke's quadrant with one reflector was quite correct in 

 theory, and had precisely the same property of halving the angle. 

 Indeed we would not necessarily in rlieory alter that property, by 

 increasing the number of fixed reflectors; for this very good rea- 

 son, that it has no dependence upon them at all. 



Mr. R. afterwards accuses me of ignorance of the true defini- 

 tion of parallax, and out of his great goodness and compassion 

 informs me what it is. But in order to show which of us has the 

 most correct idea of it, I beg leave to adduce Professor Playfair's 

 definition, as certainly of higher authority than any pedantic de- 

 finition invented for a particnlar purpose. It is as follows: *' The 

 parallax of any object in the heavens is the difference of its an- 

 gular position as it would be seen from the centre of the earth, 

 and as it is seen from a point on the surface." (Nat. Philosophy, 

 vol. ii. art. 74.) We are therefore at liberty to take any point of 

 a heavenly body for our object of observation j as for instance, 

 a point in the boundary of the lunar disk, as I have done. Your 

 readers will readily see that Professor PI ayfair understood parallax 

 precisely in the same "unusual sense" as I do; since he makes 

 no mention of the centre of a heavenly body having more to do 

 with parallax than any other point. Indeed the very circumstance 

 of the impracticability of applying an instrument to the centre, 

 puts tliat out of the question ; and besides, our most eminent 

 practical astronomers always apply the correction for parallax to 

 the limb, and not the centre. Of this I certainly stand fully as 

 much in the way of being correctly informed as Mr. Riddle can; 

 had he thought of that in time, he certainly would never have 

 coined his counterfeit definition, the currency of which cannot go 

 beyond the walls of his own school. 



I formerly stated that the difference of the parallaxes for any 

 two diametrically opposite limbs constitutes the augmentation of 

 the diameter; and by any ^ifo such limbs or extremities of a 

 diameter, I am still disposed to abide*. In order to refute that 

 statement, Mr. R. with great ingenuity has done for me what I 

 could not; he has invented the learned absurdity of a case with 

 four limbs D, E, F and G (page 248); and then shows his very 

 superior skill in refuting his own favourite delusion. Does he 

 suppose I shall remain silent whilst he would father his own 



• In order to show the truth of tills, it is only necessary to consider, that 

 by applying the correction for parallax to each extremity of the diameter, wo 

 brinir that diameter into its proper place, and of course reduce it to its pro- 

 j)cr length. But since the change of lengtli is manifestly the diUcrence of 

 the parallaxes reckoned in the direction of that diameter, it follows neces- 

 sarily that the difference of the parallaxes is the augmentation of their dia- 

 meter, four- 



