March 22, 1894] 



NA TURE 



499 



formed by bending down the nib of an unfinished and un- 

 hardened barrel pen, so as to rest against the under-side of the 

 nib of an ordinary fine grey steel pen, the space between the 

 two nibs holding sufficient ink to draw the finest and most 

 elaborate patterns without the ink running in'o blots. The most 

 beautiful curves are those obtained by compounding two circular 

 motions whose periods are nearly but not quite in the propor- 

 tion of, say, two to one. To do this, however, a certain amount 

 of skill is requisite in starting the machine. — On the buckling 

 and wrinkling of plating supported on a framework under the 

 influence of oblique stresses, by Mr. G. H. Bryan. The 

 present investigation is chiefly interesting as forming an addition 

 to the small class of soluble problems in which the question of 

 stability arises in connection with the theory of elasticity. In 

 a previous communication the author discussed the kind of 

 buckling which arises when a rectangular plate has to support 

 thrusts in its own plane, applied perpendicularly to its edges, 

 and of sufficient magnitude to render the plane form unstable. 

 The problem now considered is that of a sheet of plating of 

 indefinite extent supported on equidistant parallel rib^-, or on 

 a rectangular framework formed by two such sets of ribs cross- 

 ing each other, and which is compressed by thrusts applied in 

 any direction not necessarily perpendicular or parallel to the 

 ribs. Let the plating be supported on parallel ribs at distances 

 h apart, and let it be compressed by a thrust P (per unit length 

 measured in the plane of the plate) in a direction making an 

 angle a with the ribs. Then using C to denote the cylindrical 

 rigidity of the surface, the conditions of instability may be 

 summed up as follows : — 



(i) If a < 30°, the plane form will become unstable when 



P> 



47r-C 



and wrinkles will then appear on the surface. These wrinkles 

 will run in directions perpendicular to the direction of P {i.e. 

 at an angle 90° + a with the ribs, and will consist of alternate 

 elevations and depressions, the lines separating which will be 

 at distances l> apart. In other words, the wrinkles with the 

 ribs will divide the plate into rhombi, in which the displace- 

 ments will be alternately to one side and to the other of the 

 plane form. 



(2) If a < 30°, the same form will become unstable if 



P > '^'^,- 

 /'- sin- a 



and the plating will then buckle into simple corrugations run- 

 ning parallel to the ribs, the displaced form of the plate being a 

 cylindrical surface, of which the section perpendicular to the 

 ribs is a curve of sines. The corresponding results are also 

 worked out for a plate supported on a rectangular framework. 

 A simple rough-and-ready illustration of these results is afforded 

 when a sheet of paper is thrown mto wrinkles. — On the motion 

 of paired vortices with a common axis, by Mr. A. E. H. Love. 

 One of the difficulties of the application of the vortex atom 

 theory to problems of radiation lies in the great frequency of 

 all the modes of oscillation of a single ring. The periods are 

 all of the order of magnitude of the time taken by the ring to 

 move over a distance equal to its diameter, and theories of 

 radiation appear to require the existence of very much longer 

 periods. It is not unlikely that such periods may depend on 

 the relative motions of the constituents of a molecule or mole- 

 cular group consisting of several ring atoms. The simplest case 

 is that of two rings on the same axis passing through each other 

 alternately. The period of this motion when the rings have 

 very different diameters would be very difficult to determine, 

 but it is probable that its order of magnitude can be obtained by 

 considering the corresponding problem in two dimensions. A 

 pair of cylindrical vortices of equal and opposite strengths moves 

 perpendicularly to the plane joining the vortices, and thus 

 behaves like a single ring. Two such pairs with their planes 

 parallel can pass alternately through each other. The case 

 considered is that in which all the vortices are of equal strength 

 (disregarding sign). It is proved that the relative path is 

 always such that, at some instant, the four vortices are in a 

 straight line at right angles to the axis of symmetry, or one pair 

 is passing through the other. It is proved that the relative 

 motion is periodic provided the ratio of the breadth of the wider 

 to that of the more contracted pair, at the instant when one is 

 passing through the other, is less than 3-1-2 >J2. The curves 

 described by either vortex of one pair relative to the homologous 



NO. 1273, VOL. 49] 



vortex of the other pair are found. These curves are very 

 nearly ellipses, with their major axes parallel to the axis of 

 symmetry, and they tend to become very elongated when the 

 condition for the motion to be non-periodic is nearly fulfilled, 

 but they are very nearly circular when the ratio of the breadihs 

 of the pairs at the instant when one is passing throu ^h the other 

 is as great as 2 This result seems to have some bearing on the 

 theoretical conditions of chemical combination. The length of 



the period is proved to be 4^^-^' + Al^ (E -K/c'), where m 

 m /c' ( I - K ) 



is the strength of one of the vortices, 2<r the mean breadth of 

 the two pairs, E and K are complete elliptic integral-; of the 

 second and first kinds of a certain molulus «•, and k is the com- 

 plementary modulus. The modulus k' is (6R;- - R- - r'-)/(R -f- r)'^, 

 where 2R and ir are the breadths of the pairs at the instant 

 when one is passing through the other. The expression for the 

 period is discussed in particular cases, and it is shown that if the 

 order of magnitude of the corresponding period for two vortex 

 rings is the same as that for two vortex pairs, it is in fact long 

 compared with any period of oscillation of a single ring. — On 

 the existence of a root of a rational integral equation, by Prof. 

 Elliott, F.R.S. 



Dublin. 



Royal Dublin Society, February 21. — Prof. Arthur A. 

 Rambaut, Astronomer Royal for Ireland, in the chair. — Mr. 

 W. E Adeney read a paper on the reduction of manganese 

 peroxide in sewage. The author stated that freshly precipitated 

 peroxide of manganese, when mixed with sewage matters, and' 

 allowed to air-dry slowly, becomes gradually decomposed into- 

 manganous carbonate. He gave an analysis of some manganous 

 carbonate, formed in this way, showing that the reduction of the 

 peroxide is complete when it is exposed in small heaps to the 

 air in the course of about three months. — A paper on eozoonal 

 structure of the ejected blocks of Monte Somma, by Dr. J. W. 

 Gregory and Prof. H. J. Johnston- Lavis, was communicated to 

 the Society by Prof. G. A. J. Cole. The authors show that 

 the limestone-blocks of Mesozoic age in Monte Somma have 

 frequently become metamorphosed into crystalline masses con- 

 sisting of alternating bands of calcite and various silicates. The 

 authors regard the silica, magnesia, &c. as derived from the 

 igneous rock by chemical interpenetration and interaction. 

 Where the silicate, as often happens, is olivine (montecellite), 

 or a pyroxene, a complete simulation of the structure of 

 Eozoon canadense is produced. The layers of silicates occur 

 parallel to the surfaces of any igneous vein that may have in- 

 truded into the limestone, and they become closer to one 

 another in the areas farther removed from contact. The " proper 

 wall," the "stolons," and in places the "canal system" of 

 eozoon are recognisable under the microscope ; and the 

 authors adduce evidence to show that the typical eozoonal lime- 

 stone of Canada may have arisen similarly as a product of con- 

 tact metamorphism. — Prof. Cole then presented a paper upon 

 derived crystals in basaltic andesite of Glasdrumman Port, 

 CO. Down. The author described a large composite dyke 

 showing at this point a band of andesite on each side of it, 

 from 4 to 17 feet wide, and a more recent dyke of eurite in the 

 centre. 36 feet across. The eurite includes numerous blocks of 

 andesite, and sends oft" veins into it ; but the pyroxene and glass- 

 of the latter rock have become remelted at the contact, a deli- 

 cate interpenetration of the two magmas has occurred, and the 

 porphyritic crystals of quartz and pink felspar from the eurite are 

 found completely surrounded by the dark andesite. Thus a 

 pre-existing rock comes to include crystals derived from one 

 that has subsequently invaded it, and hand specimens, apart 

 from study in the field, would be of a most misleading character. 

 — Sir Howard Grubb read a paper on a new form of equatorial 

 mounting for monster reflecting telescopes, observing that as our 

 neighbours in France inten(i constructing a 3-metre reflector for 

 the Paris Exhibition of 1900, this may not be an inappropriate 

 time to discuss the question of mounting reflecting telescopes of 

 monster sizes, i.e. of 8 or 10 feet diameter. The problem to be 

 solved is that of mounting, on an equatorial movement, a tele- 

 scope of, say, 80 or lOO tons weight, so perfectly equipoised and 

 relieved of friction that it can be conveniently manipulated and 

 carried by clock-work, or some motive power, to follow a celestial 

 object with such accuracy t hat it will not at any moment vary from 

 its correct position by a quantity equal to the apparent motion 

 of that object in a space of one-tenth or one-twentieth part of a 

 second. To effect this the author proposes to develop further a 



