Defence of English Periodical Mathematical Works. 367 



sented to have by some witnesses. It is therefore hkely that 

 the two characters of " streaks of a Hghter hue on the body, and 

 three vellow collars on the neck," may be added to its descrip- 

 tion. ' The collars are described as about two inches broad, and 

 one foot apart. 



8. Dr. Mitchill informs me that General Hawkins has written 

 a memoir on the Sea Serpents of Massachusetts, which he has 

 sent, with a drawing, to Sir Joseph Banks ; it is a paper of some 

 length, and much interest, as it relates facts, and all the circum- 

 stances attending the appearance and natural history of those 

 huge animals, taken upon oaths of eye witnesses. He attempts 

 to prove, with much probability, that several individuals have 

 been seen, and two at least, if not three species ; one with three 

 collars, another without any, and a smaller one. 



LXH. Defence of English 'Periodical Mathematical IVorks, in 

 Reply to Mr. Meikle. By A Correspondent. 



To Mr. Tilloch. 



Sir, — It has been said that the great Newton owed every thing 

 to the native force of his genius, and scarcely any thing to his 

 reading; and it would seem as though this were the case with 

 your learned correspondent, Mr. Meikle. In your last Number 

 he advances, with an air of novelty, three distinct properties of 

 the ellipse, one of which has been long known, while the other 

 two are the simplest possible deductions from equally well-known 

 propositions; welt-known, I mean, to a plain man like myself, 

 who dare never venture upon announcing a proposition as new, 

 until I have pretty carefully examined a few of the best treatises 

 on the subject to which my supposed novelties belong. 



Mr. Meikle first demonstrates that H G is less than C D. (I 

 refer to the diagram at p. 291 of your last Number.) But this is 

 an immediate deduction from a well-known property. ^ Let CX 

 be drawn, a semidiameter parallel to the tangent P K ; then it 

 has been shown (see Robertson's Conic Sections, book ii. props. 

 19, 21) that HG:CX::CD:CB. But C X, the consequent 

 of the first ratio, is always less tiian C B, the consequent of the 

 second : therefore H G, the antecedent of the first ratio, is less 

 than C D, the antecedent of tlie second. 



Mr. Mciklc's second proposition, namely, that M H is greater 

 than C B, is a simple deduction of the same kind ; as he may find 

 at his leisure. 



With regard to the third jjropcrty announced by Mr. M. viz. 

 that G H : H M : : D E^ : A BS it is certainly " very elegant ;" 



but 



