Jan. 24, 1878] 



NATURE 



243 



of succets. After many experiments with rockers of different sizes 

 and angles, Mr. Spice obtained a formula by which a perfectly 

 satisfactory rocker can be constructed, as several trials since 

 then, both in America and Europe, have convinced me. Be- 



lieving that there are many other professors who feel interested 

 in this matter I communicate to the readers of Nature, at Mr. 

 Spice's request, his analysis of the rocker. 



Let A B c D be the principal section of the rocker. Draw an 

 indefinite base-line through the points c and D. From the point 



B let fall the perpendicular be, and from F the perpendicular 



FD. 



When the lead support raises (by expansion) the point D 

 the point C becomes the fulcram, and the line D E represents the 

 complimentary arm of an imaginary lever c D E of the third 

 order. In proportion as the distance c D is very small in com- 

 parison with the distance D e, in a like proportion will greater 

 force be required to raise the rocker, and vice versa. 



By experiment on a right-angled prismatic rocker {i.e. if the 

 lines AC and bd be produced the angle at their intersection 

 would be a right-angle) it was found that the most certain and 

 pleasing effect was obtained when the distance c D was to the 

 distance D e as 2 : 5. 



In the case of a right-angled, rocker as above, of course the 

 dis^tance d E = the distance D F. 



By making the rocker-angle less than a right-angle, the 

 distance D F would exceed the distance D E. This, it is believed, 

 would be an advantage, as the leverage would remain constant 

 and the additional weight would have the effect of raising 

 the note. 



The length of the rockerj should be equal to twice A B. The 



length of the handle should be four times A B. Finally, in prac- 

 tice, the angles c and d are slightly flattened, by filing, to 

 prevent adhesion to the lead by siakage, also to gain a larger 

 heating surface. 



The lead should have the forni shown in the section below, 

 and should weigh from three to four pounds. 



Samuel H. Frisbee 

 I r, rue des Recollets, Louvain 



No Butterflies in Iceland 



A FEW months ago. at a meeting of the Linnean Society, Mr. 

 McLachlan, when speaking of the various species of butterflies 

 brought to England from the far north by the last English Arctic 

 expedition, mentioned incidentally that^there were no butterflies 

 in Iceland. 



On looking up some old books on the subject, in which I had 

 the most able assistance of Mr. Erickr Magnussen, of Cam- 

 bridge, we found at folio 602 of a book entitled, Olaffson 

 (Eggert) Reise giennem, Island. Soro, 1772. 



Lepidoptera. 

 Z. phalcBuce. 



,, maxima. 



,, fluctuata. 



,, geometra. 



,, tota aurea. 



Again, in a work by R. Mohr, 1786, folios 90-9 1, under the 

 head "Lepidoptera," we have — 



Z. phalancc. 



,, graminis. 

 ' ,, betularia. 



,, ohvacea. 



,, lucerina. 



,, vaccina. 



,, fluctuata. 



,, pratella, &c., &c., 



all of which are named as butterflies of Iceland. 



Mr. McLachlan is a very high authority, and not at all likely 

 to assert as a fact that there are now "no butterflies in Iceland," 

 unless it were true. 



The only possible way in which these perfectly opposite autho- 

 rities can be reconciled (unless we throw aside those of a hundred 

 years ago as worthless), is to suppose that in the interval the 

 butterflies and their larvae have been destroyed — not an impos- 

 sible circumstance in Iceland, which has been almost, if not 



wholly, covered with"poisonous volcanic ashes from time to 

 time. John Rae 



Kensington, January 18 



The Great Pyramid 



I have been reading in Mr. Piazzi Smyth's book on this 

 subject ("Our Inheritance," &c.). From the meaiurementa 

 made or cited by the author it appears tolerably clear that if the 

 vertical height of the pyramid, as originally built, be taken as I ", 

 the total length of the four base lines will be twice 3'I4I59, &c., 

 the number which expresses the circumference of a circle whose 

 diameter is i. At first sight this statement seems starthng, but 

 I think it may readily be acceded to, and that neither Mr. P. 

 Smyth nor anyone need believe that by inspiration or otherwise, 

 the architect knew the above relation of diameter to circumfer- 

 ence, or was a circle-squarer in any special sense. I conceive 

 the architect to have done something like the following : — 

 Deciding first upon the vertical height of his intended pyramid, 

 he took a cord, equal in length to that vertical height, and with 

 it as a radius described a circle on level ground. Along the 

 circumference of this circle he laid 'another cord, the ends ot 

 which met and were fastened together. The circle being thus 

 formed, he drove four pegs, at equal distances inside the cord, 

 so as to stretch it out into a square. The square thus formed 

 gave the lines for the base of the pyramid ; and it is obvious 

 that thus the ratio of diameter to circumference would necessarily 

 be built into the pyramid, however ignorant the architect might 

 be. Working drawings (actual size) of surfaces, angles, cham- 

 bers, passages, and other things would easily be laid out on tht 

 ground. The dimensions of the so-called King's chamber, and 

 of a coffer or stone chest therein, which appear to involve the 

 above ratio of i to 3'I4I59, &c. , were, I think, arrived at by a 

 somewhat similar process of construction. 



Now as to the religious aspect of the case and an easy bit of 

 "development." A cone is a well-known ancient religious 

 symbol (of the kind denounced by Mr. P. Smyth as unclean), 



