22 



NA TURE 



[May 2, 1878 



as an established institution. The gathering at Cockermouth on 

 Monday and Tuesday last week was large and successftil. The 

 event of the meeting was no doubt Sir George Airy's Address, 

 which we hope to give next week, but there were other addresses 

 and papers read which would do credit to more pretentious 

 associations. The president, Mr, Isaac Fletcher, M. P., F,R.S,, 

 in his address, gave an interesting sketch of George Graham, the 

 eminent horologist of the eighteenth century, who was a Cumber- 

 land man, Mr. Clifton Ward, to whom the success of this 

 Association is largely due, read a valuable paper on Quartz in 

 the Lake District, The telephone of course was exhibited, 

 and several interesting excursions made ; and last, not least, the 

 Report tells us that the Association and its affiliated Societies 

 are prosperous. Why should not each county or group of 

 comities, have a similar association ? The Midland Union of 

 Natural History Societies, numbering over 2,000 members, are 

 to have their meeting at Birmingham on May 27 and 28 ; and 

 judging from the brief programme it promises to be an interesting 

 one. With independent sources of many-sided and vigorous 

 activity in the country like Birmingham, there is no danger of 

 over-centralisation. 



An alarmuig paragraph recently appeared in the Swiss corre- 

 spondence of a German paper, which, affecting as it' does the 

 existence of the St, Gothard tumiel, we are sxirprised that it has 

 not been even referred to in English journals. The paragraph 

 stated that the great engineering undertaking of • boring through 

 the St, Gothard was threatened by the possibility of a severe 

 check in a direction hitherto unexpected. "The geologists 

 engaged in the work," it was stated, "have lately noticed a 

 peculiar depression of the strata through which the tunnel is 

 jDrogressing, leading to the suspicion that a subterranean sea 

 occupies the interior of the mountain chain at this point. The 

 last report laid before the Swiss Federal Council, states that 

 these indications are becoming more and more decided, and it 

 is expected that the next 700 feet of boring will yield decisive 

 proofs for or against this theory. If the fears prove true, the 

 whole of the work on this magnificent undertaking, will come 

 to an abrupt and unfortunate conclusion." These sentences par- 

 take of the usual character of what may be called "newspaper 

 science." They contain just enough of scientific phraseology to 

 impress the ordinary reading public with the importance of their 

 announcement ; while at the same time their statements are so 

 vague as to afford the reader \Aho knows something of the subject 

 no means of deciding whether the thing is a hoax or may have 

 some kind of foundation in fact. Happily the apparently insu- 

 perable difficulty has been boldly faced with the usual results. 

 A recent report of the inspector of the tunnel states that the 

 irregular : character of [the formations pierced by the timnel, 

 which led to the above fears, has entirely ceased, and that the 

 M'ork is now progressing through uniform regular strata. On 

 the south side the boring progresses at the rate of ten feet daily 

 through gneiss. The rate is somewhat less on the north side, 

 where the tunnel is not yet out of the serpentine. The thickness 

 of this stratum of serpentine now being pierced is already the 

 double of that estimated by geologists from the surface indica- 

 tions. 



The forty-ninth anniversaiy meeting of the Zoological Society 

 was held on Monday, The report of the Council stated that 

 the number of fellows, fellows-elect, and annual subscribers, 

 at the close of the year 1877 had amounted to 3,358, showing 

 a net addition to the list of 47 members during the year 1877. 

 The income of the Society in 1877 ^^^ amounted to 30,988/., 

 being, Mith the exception of 1876, a larger total than the re- 

 ceipts of any previous year since the foundation of the Society. 

 The total ordinary expenditure of the Society in 1877 had been 

 27,290/., the remaining sum of 1,711/. having been devoted to 



certain special objects, such as new buildings. The Society has 

 purchased the freehold of the present house (11, Hanover 

 Square), and of the house immediately adjoining it at the back 

 (314^, Oxford Street). The total assets of the Society on 

 December 31, 1877, had been calculated to be 17,989/., while 

 the liabilities were reckoned at 4,019/. The total number of 

 visitors to the Society's gardens during the year 1877 had been, 

 according to the report, 781,377, a number gi-eater than had 

 been recorded in any previous year except in 1876. With re- 

 gard to the state of the menagerie, it was stated that the total 

 number of animals belonging to the first three classes of verte- 

 brates living in the Society's menagerie at the close of 1877 had 

 been 2,200. The total number of i-egistered additions to the 

 menagerie in 1877 had been 1,260. The Marquis of Tweeddale, 

 F.R.S., was re-elected president; Mr, Robert Drummond, trea- 

 surer ; and Mr, Philip L, Sclater, Ph,D,, F,R.S., secretary to the 

 Society for the ensuing year. The new members of the Coun- 

 cil elected were — Sir Joseph Fayrer, K.C.S.I., F.R.S., Lieut.- 

 Col. Godwin-Austen, Dr. Giinther, F.R.S., Dr. Edward 

 Hamilton, and Prof. Huxley, F.R.S. 



Dr. F. V. Hayden sends us a first proof of a plate to 

 appear in one of the volumes of the Bulletin of the U.S. 

 Geological Sursey, in which is represented the greater part of 

 a fossil skeleton of a very remarkable new bird about to be 

 described by Mr. Allen under the name Palaospiza lella. 



Though we have not heard of or from Mr. Benson for some 

 time, he has not been idle. Two papers by him are now before 

 us. In one of these ("Facts and Figures for Mathematicians ; 

 or, the Geometrical Problems which Benson's Geometry Alone 

 can Solve ") the problem is, " given the area of a circle, say of 

 one acre, to find that of another circle, which being described 

 from a point as centre, on the circumference of the given circle, 

 shall have that portion of its area outside the given circle equal 

 to the area of the given circle." A similar problem to this 

 vexed us in our undergraduate days. We were required to find 

 by purely geometrical means (if possible) the length of a chain 

 which, fastened to a stake in the boundary of a circular field, 

 would aflow an ass to graze over just half the field. Mr. Benson 

 says the solution depends upon the actual, not the supposititious 

 properties of the circle, and therefore the result as given in the 

 Scientific American (where the ratio of i to i •158728 is stated to 

 be the one required) " which is based upon the false supposition 

 that the circle has similar properties to those of the polygon " 

 is erroneous. It may be remembered that Mr. Benson will have 

 it that the value 3*1415926 X R^ for the area of a circle is 

 wrong. As we stated in our notice of the " Geometry," oiu: 

 author maintains that the reasoning mathematicians employ to 

 get this result is fallacious, and in his opinion he makes this 

 easily evident. He still holds that 3R^ is the area. 



" A man convinced against his will 

 Is of the same opinion still." 



Mr, Benson argues more suo in the twenty-two pages which 

 he devotes to the problem. The second publication (" New 

 Mathematical Discoveries ") is a four-page one, and is 

 concerned with the discovery of Archimedes that the pro- 

 portion between the parabola: and the rectangle on abscissa 

 and ordinate is in the proportion of 2:3, From the 

 proof employed to show this, he comes round to the circle 

 again, and gets area = 3R^, To judge by the printed letters, 

 Mr. Bensoii has adherents to his views; among them one a 

 graduate of the Polytechnic School in Paris, writes that "they 

 (these discoveries) will revolutionise the mathematical world," 

 and he is translating them for publication in France, Mr, Ben- 

 son (whose motto should be " indefessus agendo ") is engaged 

 upon "Philosophic Thoughts in all Ages" and "Geometer's 

 Manual," containing history of geometry and correspondence 



