March 21, 1895J 



NATURE 



501 



disc, but an idle wheel is introduced which rolls on the outside 

 of both the discs. Slip is avoided by placing steel bands be- 

 tween the idle wheel and the discs, one end of each of Ihc- two 

 bands being fixed to Ihe circumference of the idle wheel, while 

 the other ends are fixed, one to the circumference of each of 

 the discs. Back-lash is prevented by means of a spiral spring 

 attached to a point on the smaller disc ; this point being so 

 chosen that it moves nearly perpendicular to the direction in 

 which the spring acts. Hence the spring is always stretched 

 to nearly the same amount, and no extra strain is brought to 

 bear on the driving-clock in different positions of the instru- 

 ment. Prof. S. P. Thompson considered that the best method 

 to employ when using sunlight was to incline the telescope, 

 &c., parallel to ihe polar axis, under which circumstance the 

 mirror of the heliostat need only rotate about a vertical axis. — 

 A paper, on a simple form of harmonic analyser, was read by 

 Mr. G. U. Yule. At a former meeting of the Society, Prof. 

 Henrici showed a form of analyser in which the paper on 

 which the curve is traced was given a to-and-fro movement, a 

 planimeter being used as an integrator. The author being 

 struck with the advantages of the use of a planimeter, both as 

 regards cheapness and simflicity, has devised another form of 

 analyser in which a planimeter is used. The principle on which 

 this instrument works is as follows : — Suppose we have a straight 

 line (X X) which can move parallel to the base line of the given 

 curve, so (hat every point in this line describes a perpendicular 

 to the base ; further, suppose that a disc, the circumference of 

 which is some aliquot part of the base of the curve, say 2ijn 

 where 2 /is the base length, is capable of rolling on the line 

 (X X) without slip. If the centre of the disc is brought over the 

 initial point of the curve, and any point (D) at a distance r from 

 the centre on a horizontal diameter is marked, then if the 

 centre of the disc is made to describe the curve which is to be 

 analysed, the area of the curve described by the point D is 

 given by the equation 



R, = a + cos«7r — '^ / ys\ati9dx, 

 I \ - I 



where o is the area of the curve to be analysed. Similarly, if 

 the point D is taken originally on a vertical diameter, the 

 area of the curve traced out is 



R., = a + cos tm ^^ / y cos ni dx. 

 I J -I 

 In any practical case it is convenient to take >" some multiple of 

 l/ir units of length, sayao, then the above equations become 



Rj = o + cos « Tt. 10 ». B„ 

 and 



R^. = a + cos « v. ion. A„ 



where B„ and A„ are the coefficients of sin «9 and cos k9 in 

 the Fourier series expressing the equation to the curve. The 

 areas of the curves traced out by the point D (R, and Ro) are 

 obtained by allowing the tracing-point on an Amsler planimeter 

 to rest in a small conical hole at D. The line X X is the edge 

 of a rolling parallel ruler which has a rack cut along it. A 

 series of toothed wheels give the coefficients of the different 

 terms in the series. In the instrument exhibited there were 

 wheels to give the first four terms, but the author said it was 

 possible to work with wheels which gave the sixth term. The 

 above analyser was the outcome of a simple step-by-step in- 

 tegrator which the author had devised. In this case the base 

 line of the curve having been divided into a number of equal 

 parts, then, by means of a scale of sines attached to the instru- 

 ment, the tracing-point of a planimeter is set at a point whose 

 abscissa is sin «9, while it is moved parallel to the axis of y 

 through a distance hy corresponding to one of the elements 

 into which the base was divided. Prof. Henrici said he had at 

 one time considered the question of constructing an analyser 

 which should employ a planimeter as the integrator, and he was 

 particularly pleased with the instruments exhibited. Since the 

 area required was the difference between the areaof the original 

 curve, which is traced out by the centre of the disc (K), and the 

 curve traced out by the point D, and since this area is really the 

 area swept out by the straight line K D, if we attach an in- 

 tegr.ating wheel to the disc, with its axle parallel to K D, Ihe 

 icquired area can be directly obtained from the reading on this 

 wheel. In addition, if a second integratingwheel were fixed to 

 the disc, with its axle perpendicular to K D, the coefficients of 

 cos «fl and sin nO could both be obtained by going round the 

 curve once. The instrument devised by Mr. Yule was practically 



NO. 



«325, VOL. 51] 



the inverse of one :he [(Prof. Henrici) had invented. Dr. 

 Burton pointed out some incorrect signs in the proof givea ; 

 these, however, do not affect the final expressions obtained. 

 Mr. Inwards .suggested that errors due to back-lash might be 

 avoided by using either a double wheel or a double rack, so 

 that by means of a spring each side of the teeth which were 

 engaged might be in contact at the same time. — Prof. Minchin 

 gave a short account of a paper by Mr. H. N. Allen, entitled 

 "The Energy Movements in the Sledium Separating Electri- 

 fied or Gravitating Particles. " The object of the paper is to trace 

 out the equipotential surfaces and lines of flow for two electrified 

 points or gravitating Iparticles, and then to consider the paths 

 along which the " energy cells " move when the charged points 

 or gravitating particles either move towards or away from one 

 another. By energy cell the author understands the small 

 volume of the dielectric bounded by the walls of a tube of 

 force, and by two neighbouring equipotential surfaces, which 

 can be looked upon as containing a certain definite amount of 

 energy. The author gives two figures showing the paths of the 

 energy cells : (i) when the charged particles come together and 

 meet ; (2) when they separate and move off to infinity in 

 opposite directions. Using Maxwell's expression for the pres- 

 sure along the lines of force, and the equal tension at right 

 angles required by his theory to account for the attraction 

 exerted by the sun on the earth, the author has calculated the 

 energy density in the medium at the surface of the sun. The 

 value obtained is l6-horse power-hours per c.c. Hence he 

 concludes that, at a distance from all gravitating bodies, a c.c. 

 of ether contains at least this amount of energy. Prof. 

 Minchin showed how, by the use of polar coordinates the ex- 

 pressions given by the author could be simplified. He also 

 gave a graphical method of obtaining the equipotential sur- 

 faces for any configuration having given those for any other 

 configuration. He pointed out that by a similar line of reason- 

 ing to that used by the author, the energy per c.c of the 

 maJium at the surface of Arcturus must be 8100 times as great 

 as at the surface of the sun, so that the minor limit given 

 above by the author must be multiplied by 8100 at least. 



Entomological Society, March 6. — Prof. Raphael 

 Meldola, F.R.S , President, in the chair — Mr. B. G. Nevin- 

 son exhibited a long series of Heliothis pcUigera. He stated 

 that the specimens were bred from larvae found on the Dorset- 

 shire coast during July 1894, feeding on the flowers of Ononis 

 arvtnsis, which were extremely luxuriant. A few also were 

 taken on Hyoscyamus iiiger. He added, that all the larva: went 

 down by the end of July. The first emergence took place on 

 August 20, and they continued coming out at the rate of about 

 five a day, through the rest of that month and September; only 

 five emerged in October, and the last one appeared on Novem- 

 ber It. Mr. G. T. Bethune- Baker, Mr. Eustace Bankes, 

 Mr. B. A. Bower, the Rev. Seymour St. John, and Mr. 

 H. Goss made remarks on the habits and distribution of 

 the species in England. — Mr. Bower exhibited a variable series 

 of Seofaria basislrigalis, Knaggs, showing light, intermediate 

 and dark forms, taken at Bexley, Kent, from June 12 to July 

 7, 1891-94. He said the species appeared to be poorly repre- 

 sented in collections, and when present was almost invariably 

 misnamed. Mr. Bankes commented on the rarity of the species, 

 and said the specimens exhibited formed the most interesting 

 collection of it and its varieties which he had ever seen. — Lord 

 Walsingham, F. R.S. , exhibited larva; of Promtba ynccasella^ 

 which he received more than four years ago from Colorado, and 

 which were still living. One specimen of the moth had 

 emerged two years ago. — Mr. Goss exhibited, for Mr. G. C. 

 Bignell, a pupa of a Tortrix, with the larval legs, and also a 

 specimen of a Sawfly, Emphyliis cinctus, L., with eight legs. 

 Mr. G. H. Verrall and Mr. McLachlan made some remarks on 

 the latter species, and a? to the insertion of the fourth pair of 

 legs. — Prof. Meldolaexhibileda wooden bowl from West Africa, 

 from which, after arrival in this country, a number of beetles 

 (Dcrmestes vulpinus) bad emerged. Specimens of the latter 

 were also exhibited. It was not clear to the exhibitor whether 

 the larvK had fed upon the wood, or had simply excavated the 

 cavities which were apparent in the interior of the bowl for the 

 purpose of pupating. Mr. McLachlan, Mr. J. J. Walker, Herr 

 Jacoby, and Lord Walsingham made some remarks on the 

 habits of Dermestes. — Mr. Champion read a paper entitled 

 "On the Heteromerous Coleoplera collected in .\ustralia and 

 Tasmania by Mr. J. J. Walker, R. N., during the voyage of 

 H.M.S. Penguin, with descriptions of new genera and species. 



