56o 



iSTATURE 



\Oct. 28, 1875 



have before us five slips. The first addressed " To the 

 Scientific of University College, London, 1871. The 

 Curve a Progressing Wheel Curve. A wheel four feet dia- 

 meter with a nail in its rim : when traversing fo^-ward, 

 the nail will form a curve, and much longer than the 

 circumference 0/ the wheel. Query : How much longer? 

 and what must be the diameter of a circle-^^r a part 

 of the said circle to SHOW THE SAID CURVE 1 " And then 

 there follow two other geometrical questions, the one to 

 divide a trapezium into two equal 

 parts. On the back is pasted (all 

 in writing) : '" A Problem within a 

 Problem. History record {sic) Py- 

 thagoras discovered the demon- 

 stration of the three squares to sur- 

 round a Right Angle Triangle ; 

 the Two smallest when added to- 

 gether to equal the largest of twenty- 

 five square Feet. I ask to find 

 the Dimentions to demonstrate the 

 Three Triangles dotted out into proportionally ««equal 

 parts, that when added to each square they produce the 

 same result ; viz. Two to equal the largest Figure. 

 " N.B. — From the Figures 3, 4, and 5, 

 They can be wrought perfective." 

 Dated Oct. 2, 1871. 



So far there is not much harm in J. D. H. 

 Another slip addressed, in ink, " To University College, 

 London," is a bit of Hailesian Astronomy, and is, " Astro- 

 nomy is Paradoxical." The N.B. is of interest in the 

 light of the recent Transit Expeditions. " Those Transit 

 of Venus measurers that try for the distance of the sun by 

 Paradox, are in error. Let them try to find the distan ce 

 by demonstration. I say it can be done." The back of 

 this page is devoted to " Astronomy and Longitude," and 

 opens with the following doggrel : — 



Science the Lock of Bible Truth, all the Works Divine, 

 Magnetic Key, unlock the Truth, and give true Mean Time. 

 In the Time of Joshua the Sun stood over Gibeon, the Moon 



over Azalon ; 

 It was at the Summer Solstice, 2548 frofu Adam, DISPROVE WHO 



CAN? 

 The Sun began to go back on the Dial of Ahaz at 40/ past Noon. 



This last line is in ink. We have then a rule to find 

 tiue longitude at sea by time, sun, and moon. The 

 speUing is a caution, and the calculation a fitting com- 

 panion. This is dated Oct. i6th, 1870 ; the former page 

 Oct. 6th, 1871. Our last document from Mr. Hailes was 

 sent to the British Association, 1868, and is entitled " My 

 Calculated Time of Christ's Crucifixion, A.D. 30," with a 

 number of dates : " And now I challenge all the astro- 

 nomers in the world justly to dispute my above-given 

 times for the above-given events." Verily, Mr. J. D. H. 

 believes wisdom will die with him. Stand down ! you 

 will not do much harm, Mr. Hailes. 



Mr. W. Upton, B.A. (B. of P., pp. 256-258) brought out 

 in 1872 (E. and F. Spon), "The Circle Squared : Three 

 famous Problems of Antiquity geometrically solved — i. 

 The Quadrature or Circle Squared. 2. Diameter defi- 

 nitely expressed in terms of the circumference. 3. The 

 circumference equalised by a right line. The whole ren- 

 dered intelligible for arithmeticians as well as for geo- 

 meters, and ndapted for the higher classes in schools of 

 both sexes, \\ v ate students, collegians, &c." We think 

 the day is not very near at hand when this subject 

 will occupy the minds of schoolboys j the present genera- 

 tion have enough to do to secure time for the study of 

 the elements in the " Conflict of Studies " which is being 

 now waged. Mr. Upton, if now living, must be in his 

 83rd year, and can hardly be expected to write much 

 more on this subject. In his preface he acknowledges to 

 previous failure with respect to the trisection, " but has it 

 now complete." (De Morgan demolished his former 

 essays ; one we have seen appears to depend upon a 



construction familiar to practical geometers. The neatest 

 of practical methods we believe to be that hit upon by 

 J. J. Sylvester, F.R.S., recently referred to in the columns 

 of Nature.) His aim (in the quadrature) has been at 

 practical utility, not rigidly subject to all the extreme 

 niceties of mathematical strictness. The more general 

 treatment he has not gone into on account of the expense 

 (he has not apparently the purse of a James Smith or a 

 "Kuklos") He pledges himself to the satisfactory fulfil- 

 ment of all that the following advertisement sets forth : — 

 " I. The full development of the Quadrature, analytically 

 and s) nthetically, in its threefold aspect — arithmetical, 

 geometrical, and trigonometrical ; containing— 2. The so 

 greatly coveted and despaired of desideratum of equalis- 

 ing a circular segment by a rectihneal figure, which deter- 

 mines at once the complete solution of the Quadrature. 

 3. An appendix, with diagrams, &c." All this to be pub- 

 hshed on or before Jan. i, 1873, or much sooner if a 

 sufficiency of early subscription warrants it. This work 

 we have not seen ; we infer, then, that there were not 

 found eighty subscribers of sufficient faith in Mr. Upton's 

 word and sufficiently interested in the question to come 

 down with the requisite 3^. 6d. each. What an oppor- 

 tunity for a liberal-minded man ! A trifle of 14/. in the 

 one scale, and in the other a vexed question set at rest. 

 Nor is this all ; he could, too, satisfactorily account for 

 the real origin and inspired nature of mythology, but for 

 the present he confines himself to the more immediate 

 subject. " Certain Hebrew letters and Greek mythology, 

 nay, even Scripture itself, seem to bear distinct allusions to 

 matters touching upon the origin of the square and circle." 

 He winds up with a singular excursus upon the Hebrew 7 

 " distinctly representing the square and circle ; the level 

 line answering for base of the one and diameter of the 

 other ; the perpendicular for the adjoining side of the 

 square ; and the curve for a quadrant of the circle : each 

 with an appearance of string at the extremity to intimate 

 its being carried on to completion^' There is a " Supple- 

 ment " (diagram and five pages, free of charge), from 

 which an estimate of the value of the work may be got 

 on the author's own showing : " The precise difference is 

 therefore not equivalent to the impression of a pin's 

 point ; so that the author considers himself fully justified 

 in looking upon the two areas as arithmetically equal. 

 Moreover, in a geometrical solution, which is the real 

 object of the problem, it is evident that so invisible a 

 difference can have no possible effect." 



Again, if he should be enabled to publish his proposed 

 treatise, he can " show by three or four distinct but con- 

 current proofs that the circle itself not only admits of, 

 but — more surprising still — actually suggests the forma- 

 tion of a right-lined figure equal in area to the circular 

 segment belonging to each quadrant ! This is what may 

 indeed be esteemed as the true secret, the virtual key of 

 the Quadrature ; which the author will give to his readers 

 and apply for them in the annexed diagram. He would 

 have reserved the fact till he could have given it with the 

 several proofs complete. But, as the fact itself, and its 

 application to the diagram, ought to prove sufficient to 

 produce conviction as to the truth of his assertion, he will 

 proceed to apply it without further preface." We gather 

 from his remarks that they turn upon the lengthening of 

 a line by a point from a pencil which can make no per- 

 ceptible difference in the geometrical construction. It 

 seems only necessary to make this statement, and leave 

 our mathematical readers to draw their own conclusions 

 therefrom. {To be continued.) 



INTERNATIONAL METEOROLOGY* 

 T T may be truly said that all the large questions which 

 ■*■ fall within the province of meteorology can only be 

 adequately discussed by data collected in accordance 



* Report of the Permanent Committee of the First International Congress 

 at Vienna, for the year 1874. Printed by authority of the Meteorological 

 Committee. (London : Stanford, 1875.) 



