2»<»s. NO 86., Aw. 22, '67.] NOTES AND QUERIE& 



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sale " — is, that the publisher thought fit to spread 

 out what might, and should, have been one very 

 moderate volume into two. I forget what the 

 price was ; but as the two volumes of about 400 

 pages each were handsomely printed in large type, 

 on good paper, with ample margin, and engraved 

 portraits of Cowper and Mrs. Unwin, I have no 

 doubt that it was considerable. I scarcely recol- 

 lect having seen a more barefaced and shameless 

 specimen of book-making. It now lies before me ; 

 and as far as I can judge from very slight calcu- 

 lation, the Note of IIahvardiensis (occupying 

 rather more than one page and a half of " N. & 

 Q.") would, if printed in one of these volumes, 

 have occupied rather more than eight pages. 

 Since I wrote the foregoing sentence it has oc- 

 curred to me that some excuse of making the 

 work like Hayley's Life of Coivper may have been 

 pleaded ; but it is not surprising that, when pre- 

 sented to them in such a form, men turned in dis- 

 gust from volumes which, if they had read them, 

 they might have found to be, on more than one 

 ground, as it regards both style and sentiment, 

 worthy of their serious study, and entitled to a 

 place in the first and highest class of English lite- 

 rature. It was a just retribution that left " a 

 thousand copies remaining in the publisher's 

 warehouse." Surely, however the volumes may 

 have been picked over, and made use of, in more 

 recent publications, there must be many persons 

 who would gladly give more for them than the 

 price of " waste paper." This, however, is not my 

 business ; but perhaps I may be allowed to ex- 

 press my satisfaction in finding that Cowper and 

 his works are more highly appreciated in America 

 than they seem to be in his own country. It is, 

 • indeed, lamentable that the work of biography and 

 editing should have been undertaken or meddled 

 with hy men like Hayley and Southey — book- 

 makers who, whatever pretensions they might 

 have to criticise the poet, were so void of sym- 

 pathy with the man, that they could not be ex- 

 pected to form a true opinion, or deliver a just 

 view, of his thoughts, language, and circum- 

 stances. To be told by such men that they have 

 picked out all that is worth having, and pieced it, 

 or kneaded it, into their own work, is a trial of 

 one's temper. Perhaps others besides myself 

 would be glad to see in " N. & Q." a brief notice 

 (if only a mere list) of American editions of Cow- 

 per, and works relating to him, if Harvardiensis 

 can furnish such a thing. S. R. Maituand. 



Gloucester. 



QUADRATURE OP THE CIRCIiE. 



(2"'i S. iv. 57.) 



When I say- that by consent of geometers, the 

 word geometrical is restricted to that which uses 



Euclid's allowance of means, of course I deny that 

 the circle can be squared geometrically " by other 

 means : " for other means constitute that which by 

 definition is ungeometrical. But I apprehend that 

 when the question asks whether the thing can be 

 done geometrically by other means, the adverb 

 signifies constructively, without recourse to calcu- 

 lation. It may be used in two senses : either as 

 implying perfect accuracy of result, if perfect ac» 

 curacy of additional means be postulated ; or as 

 implying graphical correctness, that is, practical 

 drawing on paper, with as much accuracy as tbo 

 best draughtsman requires. 



As to the first meaning, it is well known that if 

 the reasoner be allowed an additional curve, be- 

 sides the circle, of which, by postulate, he ia 

 granted the perfectly accurate construction, ho 

 can square a cii'cle as accurately as Euclid squares 

 a triangle ; the same kind of perfection existing in 

 both cases. Give him the spiral of Archimedes, 

 or the involute of the circle, or the cycloid, &c., 

 &c., and the thing is done. But in each of these 

 cases, the new assumption is at least of as difficult 

 a character as the difficulty which it is to solve. 

 This, hov/ever, is to be said, that there are many 

 curves, any one of which, being admitted, will 

 conquer, not merely the quadrature of the circle, 

 but the rectification of any arc, and the division 

 of the angle into any number of equal parts. Of 

 all these curves the cycloid is perhaps the most 

 simple. 



Many attempts have been made, and some very 

 close ones, to give a sufficiently good graphical 

 construction of the circumference of a circle, from 

 which the square equal to the circle is readily 

 found. Several of these are given in the twelfth 

 edition of Hutton's Course, and in the Mechanics^ 

 Magazine for January, 1846. But the old sur- 

 veyor's rule for finding an arc approximately 

 would do very well. From three times the chord 

 of half the arc, take away the third part of the 

 sum of the chord of the arc and the chord of half 

 the arc : the remainder is the length of the arc, 

 very nearly. The smaller the arc chosen, the 

 nearer to the truth is this rule. Apply it to an 

 arc whose chord is the radius, and we have the 

 sixth part of the circumference, not wrong by one 

 part in seven thousand. A. De Morgan. 



BICHAHD III. AT LEICESTER. 



(2"<i S. iv. 102.) 



In your publication of the 8th of August ap>. 

 pears an extract from a work by Sir Roger Twys- 

 den, made by one of your correspondents, relating 

 to the bedstead on which Richard III. slept while 

 a guest at the Blue Boar Inn, Leicester, on the 

 few nights immediately preceding the battle of 

 Bosworth Field. 



