[ 241 ] 



XLI. Remarks on Mr. Meikle's Paper on finding the Longi- 

 tude by Lunar Observations. Bxj Mr. Edward Riddle. 



To Mr. Tilloch. 



■y^j Trinity-House School, Newcastle-on-Tyne, Sept. 25, 1819. 

 Sir, — W H£N a person who undertakes to animadvert upon 

 the views of others, executes his purpose with moderation and 

 candour, all that the public is concerned in knowing is, whether 

 his objections are vvell founded. But when, in the plenitude of: 

 self-satisfaction, such a person in every paragraph of his inqurry- 

 aflFects to hold in derision the talents of all who have previously 

 considered the subject; it is necessary not only that the justness 

 of his particular objections should be quite indisputable, but that 

 the correctness of his belief in the superiority of his own ac- 

 quirements should either be apparent, or admit of being easily 

 proved. 



The immediate cause of these remarks is a miscellaneous let- 

 ter on the subject of lunars, &c., by Mr. H. Meikle, printed in 

 your Magazine for July. A perusal of that letter will show even 

 those who may be unacquainted with the subject of it, the spirit 

 in which it is written. 



What confidence may be put in the author's assertions, what 

 weight attached to his judgement, or what regard ought to be 

 paid to his censures, I purpose at present to inquire. 



He censures in severe terms the deduction which, in low alti- 

 tudes, is sometimes made from the semidiameters of the sun and 

 moon, before they are applied to the observed distance. He says, 

 " we shall afterwards see that this is an elaborate way of creat- 

 ing new errors." As I do not afterwards see, in Mr. M.'s letter, 

 a satisfactory reason to believe any such thing, I shall show, be- 

 fore I proceed further, that in the principle of the correction no 

 error exists. 



Conceive A B D to represent the upper 

 half of the moon's disk, and let us suppose 

 that it is an ellipse whose horizontal and ver- 

 tical semidiameters are A C and B C. Sup- 

 pose also that F is a star, and FE its mea- 

 sured distance from the nearest point E of 



the moon's disk. Even when — has the 



AC 



least value which, in the practice of lunars, it can ever acquire 

 from the effect of refraction ; and when, from the position of F, 

 the angle F E C is also a minimum ; and further, when F E is 

 the least distance that is used in the solution of the problem ; — 

 Vol. r>4. No. 258. Oct. 1819. Q FE 



