28 



NA TURE 



\Nov. II, 1875 



volumes, the first of which is to appear in the present 

 month, the second in the spring, and the third during the 

 summer of 1876, and will be arranged under the following 

 divisions : — (i) Motions of the Bodies of the Solar 

 System ; (2) Spherical Astronomy ; (3) Theory of Instru- 

 ments ; (4) Stellar Astronomy ; (5) Mathematics ; (6) 

 Geodesy ; (7) Physics, and (8) Various. A portrait and 

 short life of Bessel is to be attached to the first volume. 

 Dr. Busch's complete list of Bessel's works, inclusive of 

 astronomical notes in various scientific periodicals, as the 

 Moiiatliche Correspondoiz of Zach, the Berliner Jahr- 

 buch, &c., which is appended to vol. xxiv. of the Konigs- 

 berg Observations, contains 385 titles ; but many of the 

 shorter contributions being of minor or ephemeral inte- 

 rest, it is probable that the selection proposed will include 

 all the writings of the illustrious astronomer which can 

 now possess value. 



AMONG THE CYCLOMETERS AND SOME 



OTHER PARADOXERS* 



II. 



MR. H. H ARBORD, who hails from Hull, has put forth 

 three letters, with which we have been favoured. 

 " The Circle Squared" (in November 1867) has, we guess, 

 been noticed by Prof. De Morgan. There is a nicely drawn 

 diagram, two concentric circles, two squares, said to be 

 their respective equivalents, all in black ; an equilateral 

 triangle and its circumscribing circle in red ink ; the 

 former is described on a side of the smaller square, and 

 the red circle passes through the extremities of the same 

 side. A statement is made, which appears to be a state- 

 ment and nothing more, for it proves nothing. From 

 "Squaring the Circle" (April 15, 1S74) we learn that the 

 writer has leisure {fans ct origo vialil), and so has ven- 

 tured to amuse himself by considering the relation of the 

 equilateral triangle, the square, and the circle. He 

 obtains the positive altitude of an equilateral triangle on 

 a side of the square to be 775448559771 1 125, and requires 

 the exact side of the square and the proportion of the 

 triangle to the square and the equivalent circle. He 

 winds up, like many of his race, with the following reflec- 

 tions : — " I think if the learned in geometry, mathematics, 

 and trigonometry, abandoned approximating theories, and 

 would take the trouble to elucidate the above- stated pro- 

 positions, they would undoubtedly be able to subvert all 

 anomalous and vague theorems, free the study of geo- 

 metry, &c., from ambiguity, enable tutors to explain 

 correctly, remove burthens imposed on the mind of the 

 pupil, and establish a system of teaching which shall be 

 correct and intelligible, for it is evident the result of 

 minute calculations proves there is no mystery in geo- 

 metry, mathematics, or trigonometry ; they are uniform, 

 and may be more easily taught and comprehended with 

 perfect truthfulness without approximation." To prevent 

 trouble, this man of leisure appends the rule ; it is : Add 

 one-seventh to the altitude, and we get the base ; and so 

 on. Not satisfied with the above remarks, we have a note 

 to the " learned " (see above) ; and it is the following 

 curious sentence : — " It is worthy of remark, and more 

 especially to those who are interested in the forthcoming 

 * Transit of Venus,' when the true distance of the earth 

 from the sun is to be determined, and a difference of 

 about three millions of miles accounted for, to be in a 

 position to prove the fact. Now all this can be accom- 

 plished by anxious, minute observation and correct calcu- 

 lation ! " He then appends (we don't see the connection) : 

 " Length of an arc of one degree, "017 ... to twenty-seven 

 places final." We got the last communication a few days 

 ago ; it is, "Construction of the Perfect Ellipse" (Dec. 22, 

 1874). This is a fine large figure on a sheet of paper 

 some eighteen inches by fourteen. He finds that the true 



* Concluded from vol. xii, p. 560. 



ellipse is only to be described on the perpendicular of the 

 equilateral triangle. Mr. Harbord has evidently an idea, 

 and that is, that the equilateral triangle is the key t< 

 unlock many geometrical mysteries. 



Mr. Michael Callanan, of Cork (September 1874), '"ij 

 in a position to demonstrate before any appointed numbei 

 of scientific gentlemen, the perfect quadrature of the! 

 circle, rendering it as clear as the most simple, plain {sid) 

 rectilineal figure. The Circle, that colossal mystery, to 

 prove the area of which has been looked upon as the 

 climax of geometrical science ; and, although the object of J 

 search by the mathematicians of all nations, their greatest 

 efforts have failed ; every attempt, as yet, to square the 

 circle being undemonstrable, and offering no reward to 

 the anxious investigator beyond mechanical or approxi- 

 mate measurement — a manipulation of the great problem. 

 My solution will be found original and thoroughly demon- 

 strative in all its details, without having anything what- 

 ever to do with the given or polygonal rules for approxi- 

 mation. Entirely new ground is opened up in the path of 

 science which I have chosen, guided only by positive 

 mathematical laws, combined in the most strict logical 

 arrangement, and thus proved to demonstration. I now 

 proclaim the absolute fact of being able to set aside for 

 ever any further doubt as to the complete quadrature of 

 the circle, and thereby confound those scientific prophets 

 who pronounced it an impossibility." Local circum- 

 stances offer many impediments in bringing the matter 

 before the scientific world, and " being a geometrical 

 secret, the law of Patent cannot be applied." He then 

 puts himself in the same position with other inventors and 

 discoverers, but he asks for an accredited tribunal " from 

 which I would ask an impartial hearing, so as to verify 

 these statements, and also to be identified and protected 

 as the discoverer." For this end he is willing to attend 

 at any selected place in England, Ireland, or Scotland. 

 He then glances at some of the immediate results in the 

 realisation of this problem. " At the proper time will be 

 published a comprehensive work, including all the new 

 diagrams necessary to carry out and complete the demon- 

 stration." And this is all we know of Mr. Callanan's 

 " Secret of 'the Circle' solved." 



Our next claimant for notice is not a Circle- squarer, 

 but he would certainly have got a warm corner in the 

 " Budget." Middleton's " new process of measuring the 

 height of the sun," an observation for latitude demon- 

 strated by geometry, proving the sun's height less than 

 the latitude of observer. On this leaflet our paradoxer 

 says, " the sun's height is under 3,000 miles." The prin- 

 ciples of this discovery are published in the West Lon- 

 doner. Mr. Empson E. Middleton, Poet (Naval and Mili- 

 tary Club), sends us a further document (May 5th, 

 1873) : ";^ioo Reward to the first, who disproves the 

 following Diagram — Middleton's Geometrical Proof that 

 the Earth is Flat." Proof is said to turn upon the SPHINX 

 SOLUTION, — " a globe demands six cardinal points." 

 Having disposed of this point to his satisfaction, he 

 " challenges all the mathematicians to support their state- 

 ment that a perpendicular line and a line at right angles 

 are the same ; one is JIat, the other up}'ioht. \ under- 

 take to prove that the perpendicular line is 7iot the same 

 as a line at right angles, though the two are utterly con- 

 fused in every school-book of the day. I undertake to 

 meet in public and to confute any of our mathematical 

 professors who may have the manliness to come forward 

 and discuss this question of the perpendicular, a question 

 which forms the fundamental basis of the whole science of 

 geometry, and is of the very first importance. I remain 

 faithfully, to the Majesty of Truth." Mr. Middleton has 

 published a translation of " the first two books of the 

 ^neid of Virgil" to supersede Mr. Connington's {sic) : 

 he has a work " On Space " unpublished, and one " On 

 Man" awaiting demand. 



Naturally, after this we should turn to Parallax, or to 



