2»'» S. N" GC, April 4. '57.] 



NOTES AND QUEKIES. 



275 



wanting only pains and patience to carry tlie ap- 

 proximation to any desired extent. The problem 

 of the perpetual motion is a physical absurdity. 

 The arithmetical quadrature of the circle has 

 been proved impossible in finite terms, but 607 

 decimal places of the interminable series have 

 been found, and 441 of them verified. Of the 

 geometrical quadrature an asserted proof of im- 

 possibility exists, which no one who has read it 

 ventures to gainsay, but in favour of which no 

 one speaks very positively. The trisection of the 

 angle has no alleged proof of its impossibility. 

 But were this the proper place, an account might 

 be given of those considerations which lead all 

 who have thought much on the subject to feel 

 sure that the difficulty arises from the restrictions 

 placed upon the means of solution amounting to 

 a little too much dictation to the nature of things. 

 For it must be remembered that the problem is 

 not to square the circle, nor to trisect the angle, 

 but to square the circle or trisect the angle with- 

 out recourse to any means except those afforded 

 by Euclid's first three postulates. This limita- 

 tion is frequently omitted ; and persons are led to 

 conclude that mathematicians have never shown 

 how to square a circle, or to trisect an angle, than 

 which nothing can be more untrue. I may take 

 occasion to raise a Query in some future commu- 

 nication, whether these difficulties would ever 

 have existed if Euclid's ideas of solid geometry 

 had been as well arranged as his ideas of plane 

 geometry. 



The reader may find details on this subject in 

 the articles Quadrature and Trisection in the 

 Penny CyclopoEdia. But fuller information will 

 be found in Montucla's Histoire des Recherches 

 sur la Quadrature du Ccrcle, Paris, 1831, 8vo. 

 (second edition). This work contains, besides the 

 vagaries of the insufficiently informed, an account 

 of the attempts of older days, which ended in use- 

 ful discovery. In later times, the whole subject 

 has lapsed into burlesque ; the i^vr who have 

 made rational attempts being lost in the crowd 

 who have made absurd misconceptions of the pro- 

 blem. To square the circle lias become a byword, 

 though many would not know the problem under 

 a change of terms, say the rectification of the cir- 

 cumference. For example, when Mr. Goulburn 

 was a candidate for the University of Cambridge 

 in 1831, some wags of the opposite faction sent 

 the following to a morning paper, which actually 

 inserted it (May '4) in triumphant answer to the 

 objection against their candidate's want of Cam- 

 bridge knowledge : — 



" We understand that although, owing to circum- 

 stances with which the public are not concerned, Mr. 

 Goulburn declined becoming a candidate for University 

 honours, his scientitic attainments are far from incon- 

 siderable. He is well known to be the author of an 

 Essay in the Philosophical Transactions on the accurate 

 rectiiication of a circular arc, and of an investigation of 



the equation to the Lunar Caustic — a problem likely to 

 become of great use in nautical astronomy." 



I need hardly say that mathematicians know no 

 lunar caustic, except what the chemists call ni- 

 trate of silver. And so much for the impossible 

 problems, which have caught so many ingenious 

 minds, and almost always held them tight. For 

 this reason, I should advise any one not to try 

 them ; 



" . . . . Video quod vestigia 

 Intrantium multa, at nulla exeuntium." 



A. De Morgan. 



MUSICAL bachelors AND MUSICAL DOCTOES. 



(2"^S. iii. 48. 73. 115.) 



When people do wrong, they are certain to get 

 into a mess, and oftentimes to get innocent par- 

 ties into a mess also. The account given by M.A. 

 of Coll., Oxon., of the condition of the Musi- 

 cal Doctors in that University is shocking. He 

 describes that as " most vague and unsatisfactory," 

 which all who read this work must think very 

 deplorable and much to be pitied. It was a most 

 ungracious proceeding on the part of the Heb- 

 domadal Board, to banish the Oxford Musical 

 Doctors from the semicircle — to eject these viri 

 perpoliti — to translate these apprime docti pro- 

 fessors to the organ gallery, and there lay them 

 in ambush behind portraits of deceased celebrities. 

 Just think now of men arrayed like so many 

 virgin-brides, in robes of rich white damask silk, 

 appropriately turned up with satin — all rose and 

 blush-colour — invidiously "consigned to the up- 

 per gallery on the south :" "that is to say, in the 

 organ gallery, a far worse position than that oc- 

 cupied by undergraduates." Think of rose, and 

 satin, and velvet, and gold, driven to a spot 

 "where they could neither see nor be seen ;" and 

 where the occupants of all this magnificence are 

 "virtually excluded from every participation in 

 the proceedings." Sitting, too, behind a dead 

 emperor ! Surely a live doctor is better than a 

 dead king ! And ought he not to be asked rather 

 to sit for his portrait, than to sit behind one ? 

 This transportation into the upper regions of the 

 Oxford theatre was a novel illustration of the 

 oft-quoted line — 



" Small by degrees, and beautifully less." 

 Nor was this all : a further indignity awaited these 



unfortunate doctors, and which M.A. of Coll., 



Oxon. touches in most artistic and delicate manner. 

 After alluding to misplacings, displacings, consign- 

 ments, assignments, ejectments, and mistakes — 

 invidious and illiberal — he writes, that the musi- 

 cal doctors were deprived of their title, and re- 

 christened " Inceptores in arte Alusicd." Like the 

 great Grecian painter, he draws a veil over the 



