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The following Table is supplementary to those accompanying the paper “On the Mathematical Theory of Suspension Bridges,” printed in the Philosophical Transactions for 1826. It is deduced from the first Table there given, by the plain operations of common arithmetic; but this admits of a far more ready application than the former, to all cases of practical investigation. The first column contains the deflections or versed sines of the curve, expressed in fractional parts of the double ordinate or Span. It is therefore 2 y divided by x , and their reciprocals are added under each.

The principle of applying diagonal frame-work to ships of war was first partially and successfully adopted in the Kent, of 74 guns, in the year 1805, and since that period has been successfully employed in the construction of thirty-eight sail of the line and thirty frigates. These circumstances might be deemed conclusive as to the advantages of the new system; but as the Royal Society have already published this author’s account of it at a very early period of its adoption, he is induced to offer the result of a new experiment in proof of the correctness of the principles before laid down, which, as far as his knowledge extends, has never been previously applied, nor ever suggested by any continental writer, though, says the author, it has been pretty broadly insinuated that the hint was borrowed from the French. In the early part of the present year, the Justitia, an old 74, was ordered to be broken up; when Mr. Seppings, notwithstanding her shattered condition, determined to apply the trussing principle. Prior to her being taken into dock, sights were placed in the lower and upper gun-deck, to ascertain, when she had grounded on the blocks, how much she deviated from her state afloat. She was then partially trussed, as described by reference to an annexed drawing, and floated out into the basin. After lying one hour, it was found, by the sights placed on the gun-deck, that she had come down in the mid-ship 1 foot; and by those on the upper-deck, 1 foot 2⅝ inches. In twenty-four hours she further hogged 2⅝ inches, and then appeared stationary. The trusses in the hold were then removed, and she further hogged 6 inches, and 3½ inches in removing those in the ports.

The experiments of M. Arago having excited much interest, the authors of this communication were induced to erect an apparatus for their verification; and after a few trials they succeeded in causing a compass to deviate from the magnetic meridian, by setting in rotation under it plates of copper, zinc, lead, &c. To obtain more visible and regular effects, however, they found it necessary to reverse the experiment, by setting in rotation a powerful horse-shoe magnet, and suspending over it the various metals and other substances to be examined, which were found to follow with various degrees of readiness the motion of the magnet. The substances in which they succeeded in developing signs of magnetism were, copper, zinc, silver, tin, lead, antimony, mercury, gold, bismuth, and carbon, in that peculiar metalloidal state in which it is precipitated from carburetted hydrogen in gas-works. In the case of mercury the rigorous absence of iron was secured. In other bodies, such as sulphuric acid, resin, glass, and other non-conductors, or imperfect conductors of electricity, no positive evidence of magnetism was obtained.

In this paper the author states that his attention was first directed to a consideration of suspension bridges, when the plan for the Menai Bridge was submitted to the Commissioners of Roads and Bridges. It then appeared to him that the proposed depth of curvature was insufficient for insuring a due degree of strength; and this opinion was confirmed by some investigations, which are printed in the Quarterly Journal of Science. In consequence of this, the interval between the road-way and the points of support has been augmented to 50 feet, and its strength now appears sufficient. The object of this paper is the expansion of the formulae, from which the above-mentioned approximation was derived, into tables adapted to general use; and the derivation of other formulae and tables for the catenary of equal strength; a curve not merely of speculative curiosity, but of practical use when bridges of very wide span are to be constructed. The author first remarks, that as all catenaries, like circles, parabolas, &c., are similar curves; tables constructed for one value of the parameter apply to all by simple proportion.

The author begins this paper by an enumeration of the various works on the subject extant in our language, and a general mention of the writings of foreign mathematicians, which he considers as leaving room for further inquiry and simplification. He then states the method employed in his experiments for determining the refractive and relative dispersive powers of his glasses, the former of which is that generally known and practised;—of measuring the radii and focal length of a lens, and thence deriving the refractive index; with some refinements in its practical application, consisting chiefly in using the lens as the object-glass of a telescope, and adapting to it a positive eye-piece and cross-wires, which are brought precisely to the true focus by the criterion of the evanescence of parallax arising from a motion of the eye, as is practised in adjusting the stops of astronomical instruments. The only source of error it involves is in the measurement of radii of the tools which it was found could always be performed within 1/500th of their whole values. The dispersive ratio of two glasses was determined by over-correcting the dispersion of a convex lens of the less dispersive glass by a concave of the greater, and then withdrawing the latter from the former till the achromaticity is perfect, or as nearly so as the materials will admit, and measuring the interval between the lenses and their foci, from which data the ratio of their dispersive powers is easily obtained. The refractive indices and dispersive ratio thus determined, the next step is to find the radii of curvature so as to destroy spherical -aberration. In this investigation, the author does not consider it as necessary to limit the indeterminate problem by any further condition, as others before him have done, but regarding it as a matter of great convenience to avoid contact of the interior surfaces in the centre of the glasses, leaves it open to the optician to make a choice within certain limits, thus avoiding what he considers as an intricate equation arising out of the fourth condition. He proceeds, therefore, to express analytically the aberrations of the glasses, and to deduce the equation expressive of its destruction, which of course involves one indeterminate quantity; this may be either of the radii, or any combination of them. The author chooses the ratio of the radii of the interior and exterior surfaces of his flint lens for this indeterminate, which he assumes, as well as may be, to satisfy the condition of the absence of contact and near equi-curvature of the adjacent surfaces; thence deduces, first, the radii of both of the surfaces of the flint lens; next, its aberration to be corrected; and thence, by the solution of a quadratic, or by the use of a table containing its solutions registered in various states of the data, the ratio of the radii of the convex, whence the radii themselves are easily deduced.

Based on the Location Quotient (LQ) method, this paper selected datas of Statistical Yearbook from 2001 to 2008, and calculated the LQ of all sectors of industry in Xinjiang, finding three industries has the phenomenon of clustering, namely Extraction of Petroleum and Natural Gas industry, Oil Processing, Coking and Nuclear Fuel Processing industry and Processing of Ferrous Metals Ores industry. The cluster degree of all sectors has also been calculated, sorted and analyzed. In addition, changes of cluster degree from 2001 to 2008 in clustered industrial sectors was described and reasons for, and some suggestions on the industrial cluster development has been put forward of this region.

The table here communicated is supplementary to those accom­panying the paper “On the Mathematical Theory of Suspension Bridges,” which was published in the Philosophical Transactions for 1826, and is deduced from the first of the tables there given; but admits of a far more ready application than the former to all cases of practical investigation. It consists of five columns, exhibiting respectively the deflections or versed sines of the curve; the lengths of the chains; the tension at the middle points, or apices of the curve; the tensions at the extremities; and the angles made by the chains with the horizon at the extremities.

Dr. Davy complains that Mr. Faraday has, in the paper referred to, made certain statements with respect to the opinions of Sir Humphry Davy relative to the conducting powers of dry nitre, and caustic potash and soda, when in fusion by heat, and also with regard to other matters connected with voltaic electricity, wdiich are not correct; and vindicates Sir Humphry Davy from the charge of want of perspicuity in the statement of his views of these subjects. A Note by Mr. Faraday on the preceding Remarks by Dr. Davy was then read, in which he replies to the charges there brought forward, and justifies those statements, the accuracy of which had been impugned by Dr. Davy.

The author states, that it has been his object, in this series of investigations, to perfect the methods of electrical measurement, whether relating to the quantity of electricity, intensity, inductive power, or any other element requiring an exact numerical value, and by operating with large statical forces both attractive and repulsive, to avoid many sources of error inseparable from the employment of extremely small quantities of electricity, such as those affecting the delicate balance used by Coulomb. He then describes some improvements in his hydrostatic electrometer, an instrument already mentioned in his first paper, which, although not available for the measurement of such minute forces as those to which the balance of torsion is applicable, is still peculiarly delicate and well adapted to researches in statical electricity. Its indications depending on the force between two opposed planes operating on each other under given conditions, are reducible to simple laws, and are hence invariable and certain; the attractive force between the discs is not subject to any oblique action, is referable to any given distance, and may be estimated in terms of a known standard of weight. The author next proceeds to the further consideration of the subject of his former papers, viz. the elementary laws of electrical action. He proves, by the following experiments, that induction invariably precedes, or at least accompanies attraction and repulsion. A circular disc of gilded wood, about six inches in diameter, is suspended by an insulating thread of varnished silk from a delicate balance; a delicate electroscope is attached to this disc, and the whole is counterpoised by a weight. A similar disc insulated on a glass rod, and having also an electroscope attached to it, is placed at any convenient distance immediately under the former. One of the lower discs being charged with either electricity and the other remaining insulated and neutral, the electroscope of the neutral disc begins to rise, whilst that of the charged disc, already in a state of divergence, tends to collapse: when these respective effects ensue, the suspended disc descends the charged disc. Two inductive actions are indicated in this experiment, the one the author considers to be a direct induction, the other a reflected induction.

By reflecting on certain facts connected with the respiratory movements, and which seem to derive no explanation from our actual knowledge of the structure of the spinal chord, I was induced to undertake a series of observations with the view of determining, if possible, the relations which appear to subsist between the spinal nerves and the respiratory nervous centres. These observations, however, led me into a more extended inquiry than I at first contemplated, the results of which I now venture to lay before the Royal Society. It is needless to point out the difficulties which attend, not only the minute investigation, but a clear and connected description, of a structure so intricate and delicate as that of the spinal chord. It may be proper however to state, with regard to the contents of this paper, that those facts only which were verified by cautious and repeated examination have been brought forward with confidence; while in cases where the results of my observations were less satisfactory, I have expressed myself with corresponding reserve. Yet, no labour has been spared in order to arrive at correct conclusions. My observations were made, by means of one of Mr. Ross’s finest microscopes, on many thousand preparations of the spinal chord of Man, of the Calf, Sheep, Pig, Dog, Cat, Rabbit, Guinea Pig and Frog, and occupied a period of more than two years.

This paper is written in continuation of a series of papers, of which six sections have already been published in the Transactions of the Royal Society of Edinburgh.It commences with some articles supplementary to the first six sections, and intended to apply to the theoretical principles contained in them to the extensive and precise experimental data which have been obtained in the course of the last two years.

The object of the following communication is to describe a method by which every variety of visible colour may be exhibited to the eye in such a form as to admit of accurate comparison; to show how experiments so made may be registered numerically; and to deduce from these numerical results certain laws of vision.The different tints are produced by means of a combination of discs of paper, painted with the pigments commonly used in the arts, and arranged round an axis, so that a sector of any required angular magnitude of each colour may be exposed. When this system of discs is set in rapid rotation, the sectors of the different colours become indistinguishable, and the whole appears of one uniform tint. The resultant tints of two different combinations of colours may be compared by using a second set of discs of a smaller size, and placing these over the centre of the first set, so as to leave the outer portion of the larger discs exposed. The resultant tint of the first combination will then appear in a ring round that of the second, and may be very carefully compared with it.

A near-regular texture (NRT) is a geometric and photometric deformation from its regular origin--a congruent wallpaper pattern formed by 2D translations of a single tile. A dynamic NRT is an NRT under motion. Although NRTs are pervasive in man-made and natural environments, effective computational algorithms for NRTs are few. This paper addresses specific computational challenges in modeling and tracking dynamic NRTs, including ambiguous correspondences, occlusions, and drastic illumination and appearance variations. We propose a lattice-based Markov-Random-Field (MRF) model for dynamic NRTs in a 3D spatiotemporal space. Our model consists of a global lattice structure that characterizes the topological constraint among multiple textons and an image observation model that handles local geometry and appearance variations. Based on the proposed MRF model, we develop a tracking algorithm that utilizes belief propagation and particle filtering to effectively handle the special challenges of the dynamic NRT tracking without any assumption on the motion types or lighting conditions. We provide quantitative evaluations of the proposed method against existing tracking algorithms and demonstrate its applications in video editing.

The aim of this paper is to introduce a novel phase-based feature representation for robust speech recognition. This method consists of four main parts: autoregressive (AR) model extraction, group delay function (GDF) computation, compression, and scale information augmentation. Coupling GDF with an AR model results in a high-resolution estimate of the power spectrum with low frequency leakage. The compression step includes two stages similar to MFCC without taking a logarithm of the output energies. The fourth part augments the phase-based feature vector with scale information which is based on the Hilbert transform relations and complements the phase spectrum information. In the presence of additive and convolutional noises, the proposed method has led to 15% and 12% reductions in the averaged error rates, respectively (SNR ranging from 0 to 20 dB), compared to the standard MFCCs.

In a paper read before this Society on the 29th of April, 1861, and contained in the ninth vol. of the Journal, there is given a table showing the probability of living a year at each age, as evidenced by the males of the families of the peerage existing within the last half century; and it appeared to me that it would be worth while, if only as a matter of curiosity, to put the information there given into a form better adapted to ordinary calculation.

My attention was first directed to this subject by reading a report of Professor Stokes’s very excellent lecture at the Royal Institution, Friday, March 4th, 1864. It immediately occurred to me that a spectroscope might be combined with a microscope, and employed to distinguish coloured minerals in thin sections of rocks and meteorites. I was soon led to examine many other coloured substances, and found that the instrument is ore useful in connexion with qualitative analysis, when only very small quantities of material can be obtained. At first I employed the imperfect apparatus described in my Paper in the ‘Quarterly Journal of Science’, not afterwards, along with Mr. Browning, I constructed that described in my Paper in the ‘Popular Science Review’. For general purposes I do at think this could be much improved; but for chemical testing it is much less fatiguing to use a binocular instrument. There were many difficulties to contend with, but at length I constructed one which appears to answer all the requirements of the case.

When a solid figure is brought too near the object-glass of a camera obscura, the difference of focus for its various planes is comparatively so great, that it is impossible that all the images should be equally well defined. Hence, in the case of photographic portraiture, there is a want on harmony in the representation of the various parts; some are too sharply delineated, and some others are confused in proportion as they are more and more distant from the plane in focus. But there is another defect which is the consequence of the difference of distance of the various planes bearing too great a proportion to the distance of the whole, which is that the nearest parts of the figure are too much enlarged, and the furthest too much reduced. In a paper I read at the British Association at Nottingham in 1866, proposed a plan to obviate these defects, which consisted in bringing all the planes consecutively into focus, by moving, during the exposure, that tube of the lens or the back frame of the camera; the consequence of which was, of course, that the planes were also during that movement brought out of focus; so that a sharp image of every plane was impressed upon a confused image; but they were all in the same degree in that mixed state, and the result was an equality of effect producing harmony in the whole, and that kind of softness in the picture so much approved by artists, as resembling, more than the sharpest photographs, the effect that they aim at producing.

In this paper an attempt is made to supply, at least in part, what the author has long felt as a want in the beautiful system of quaternions, so far as it has yet been developed. To apply it to general inquiries connected with electricity, fluid motion, &c, we require to have means of comparing quaternion-integrals taken over a closed surface with others extended through the enclosed space—and of comparing integrals taken over a non-closed surface with others extended round its boundary.

In the previous paper on this subject in August Transactions is outlined a method of investigation, in which the volume or weight of each member of a skeleton girder is expressed in terms of the vo...

In the year 1849 the great paper of Stokes "On the Dynamical Theory of Diffraction " was read before the Cambridge Philosophical Society, and this has remained until the present day the standard upon this important subject. The method of Stokes was based upon the old elastic solid theory of light, and gave the following conclusions: First. That when the incident light was plane polarized, the diffracted light from a small orifice was also plane polarized in such a manner that the displacement was in the same plane as that of the medium at the orifice. So that if a sphere was drawn with the orifice as a center and meridians drawn on the sphere with the axis in the direction of the vibration at the orifice, then these meridians represented the direction of displacement in the diffracted light. Second. The intensity of the polarized light was represented as follows: Let 3 represent the angle between the incidenlt ray prolonged and the diffracted ray, and let q be the angle between the diffracted ray and the direction of the displacement at the orifice. Then the intensity of the diffracted light around a very small orifice will be proportional to

1. In the first part of this paper we have considered merely the contours of curves, that is, contour points, and the method of obtaining the various physical diagrams. In this part we shall consider chiefly the contours of surfaces; that is, contour lines. If any curve be cut by planes parallel to that of ( x, y ) and if the various points of intersection be projected on any one of these planes, say z = 0, the contour points so obtained will evidently lie on a definite line, and the line will be more accurately indicated in proportion as the number of intersecting planes is greater and their mutual distance is less. It will be given without any break in continuity by projecting every point of the curve upon the plane z = 0. But such a line may be regarded as the intersection, by the plane z = 0, (see fig. 48) of a cylindrical surface whose generating lines are parallel to the z -axis and are drawn from the given curve to meet that plane. We have here then the intersection of a given surface by a surface over which z is constant. But this satisfies our definition of a contour line. This case of a cylindrical surface supplies the simplest system of contour lines by giving z different values. The contours are all superposed in the diagram, but are not in general conterminous. The only case in which they would be conterminous is that in which the same values of the x and y co-ordinates of a point on the curve correspond to different values of the z -co-ordinate.

This paper deals with 3D shape reconstruction based on a structured-light projector and two cameras using Evolutionary Algorithms (EAs). Two main problems are solved: first, the correspondence problem (also called the stereo matching problem) which allows the matching of different views of a same point in the two images, and second, the camera calibration which takes into account the camera parameters and the camera relative locations through a fundamental matrix. Concerning the correspondence problem, the main issue is the detection of the points to be matched, i.e. the points of interest (POIs). In this paper we propose a structured pattern to be projected on the object to analyse. The structured pattern is composed of triangles with different colors and different orientations. The POIs to be matched are the vertices of the triangles. Then we define an encoding method allowing the recovery of all the POIs that are detected in both images. In previous work, we showed that EAs can be used to obtain the fundamental matrix, thus providing an uncalibrated 3D reconstruction approach. However the method processed too small a number of POIs. The proposed acquisition system allows a high number of POIs to be obtained. The initial EAs are improved to use the new set of POIs. The experiments show that the proposed encoding method allows an efficient matching. In addition, accurate 3D reconstruction results are obtained and the process converges correctly.

I much regret it has not been possible for me, during this summer, experimentally to determine the best forms and sizes of the details in the construction of the C screen; nor have I been able to keep a continuous record of its readings. Only a few observations have been made at intervals with it, as originally constructed, and shown in fig. 1 of this paper, and with the Stevenson screens. The result of all these trials is to confirm the conclusions already arrived at. The C screen always gave the lowest readings when there was any radiation.

In our first paper on this subject we have shown how the luminosity of the spectra of various sources of light can be measured; and the present paper is an extension of the subject, dealing with the measurement of the light reflected from bodies in terms of the colours of the spectrum of the light illuminating them. By the method which we adopted in the first part of "Colour Photometry” this can be effected, and, indeed, we carried that out in several instances. The method then employed was very simple. If we wished to measure the illuminating value of the spectrum of light reflected from a metal, we placed it at an angle in front of the slit of the spectroscope, so as to reflect the light from the crater of the positive pole of the electric light through the photometer, and measured the luminosity of each part of the spectrum thus formed by the method we indicated in our paper. Again, in experimenting with Gorham’s discs, such as Maxwell employed, where it became necessary to determine the light reflected from the different coloured papers or cards used in the discs, the plan first adopted was to replace the receiving shadow screen of zinc oxide (see § VI) by the coloured papers, and again to make a luminosity measurement. This plan answered its purpose, but it was rather laborious. When two or three colours are combined by rotation to form a grey, and black and white sectors are combined to match that grey, in order to ascertain the total luminosity of each colour, the angular value of the sectors being known, it is necessary to refer the luminosity to that of some standard reflecting surface, which is naturally a white one. As the comparison light is coloured by falling on coloured paper, the value of the spectrum reflected from such paper could not by this first method be directly compared with that reflected from the white screen. In the case of a coloured screen, the curve of spectrum luminosity would therefore have to be reduced to that in which the comparison light was white. This difficulty was surmounted by making half the receiving screen white and half of the colour whose luminosity was to be measured, illuminating the shadow of the rod thrown on the coloured paper by the spectrum colour, and that thrown on the white card by the white light reflected from the surface of the first prism (§ XXVI). This did away with any reduction or calculation; but still an objection remained, as, for definite comparison, it was almost necessary that the same observer should always make the measurement.

As a space-filling method, Voronoi Treemaps are used for showcasing hierarchies. Previously presented algorithms are limited to visualize nonspatial data. The approach of spatial Voronoi Treemaps is proposed in this paper to eliminate these problems by enabling the subdivisions for points, lines, and polygons with spatial coordinates and references. The digital distance transformation is recursively used to generate nested raster Voronoi polygons while the raster to vector conversion is used to create a vector-based Treemap visualization in a GIS (geographic information system) environment. The objective is to establish a spatial data model to better visualize and understand the hierarchies in the geographic field.

1. It has been thought advisable to reserve an account of the general aims and scope of the following paper till a few preliminary matters have been disposed of. 2. Consider the following statement, of the truth of which probably no one will doubt. If a body on being moved from a position A to a position B were found thereby to have lost a charge of electricity, physicists would not be content to explain the circumstance on the mere ground that it had left its charge behind. They would hold that processes had gone on, precisely similar to such as would have been required to divest it of its charge, had it remained in its first position A.

This paper studies two-person repeated games with imperfect monitoring without discounting through perceptrons, which are feedforward artificial neural networks. Under a fairly standard informational condition, we establish the folk theorem through perceptrons with at most three linear classifiers. The maximum number of linear classifiers is independent of the number of actions in the component game or the target payoff vector. In particular, the perceptron dictates that each player monitor the opponent's action by computing the ordinary least-square estimator of the opponent's expected payoff. Journal of Economic Literature Classification Number: C72.

Accurate estimation of noise and signal power is of fundamental interest in a wide variety of vision applications as it is critical to thresholding and decision processes. This paper proposes two methods for the estimation of nonstationary noise based upon models of image structure which locally separate signal from noise. The resulting algorithms are noniterative and thereby fast. The accuracy of the proposed and existing methods is compared, first separately and then in application to two common image processing tasks: edge and corner detection. It is demonstrated that the proposed model can be used to improve the stability of both, in the presence of contrast change and nonstationary noise.

Discriminant Analysis is utilised in working out which specific classification, a data pertains to on the basis of its needed features. Linear Discriminant Analysis(LDA) achieves the maximum class separability by projecting high-dimensional data onto a lower dimensional space. However, LDA suffers from small sample size(SSS) problem where the dimensionality of feature vector is very large compared to the number of available training samples. Regularized Discriminant Analysis(RDA) handles SSS problem of LDA with an introduction of regularization parameter(λ) and has the ability to reduce the variance. One important issue of RDA is how to automatically estimate an appropriate regularization parameter. In this paper, we propose a new algorithm to enhance the performance of RDA by effectively estimating an appropriate regularization parameter in order to reduce training time and error rate. Experiments are done using various benchmark datasets to verify the effectiveness of our proposed method with the state-of-the-art-algorithm.

In three papers, published in the ‘Proceedings' of the Society, in 1877 and 1882, I had the honour to communicate to the Society the results of experiments on various classes of impact with a liquid surface which may all be conveniently referred to as “splashes.” The splashes studied were those produced (i.) by a liquid sphere falling on a horizontal solid plate, (ii.) by a liquid sphere falling into a liquid, (iii.) by a solid sphere falling into a liquid. The phenomena were examined by means of an electric flash of very short duration, which by a suitable mechanism could be so timed as to illuminate the splash at any stage which it was desired to observe, within three or four thousandths of a second. After a sufficient number of repetitions to secure accuracy, a drawing was made of the configuration thus revealed, and when one stage had been sufficiently studied, the observer passed on to a later stage. Since, however, each drawing was made from a separate, though similar splash, it was not possible to obtain accurate information about those details which were at once too minute to be seized in such single, momentary glimpses, and too unstable to be capable of exact reproduction in another splash.

In “Colour Photometry,” Part III. (‘Phil. Trans.,' A, 1892), a description was given of the apparatus employed for estimating the intensity of light of any colours which just failed to cause any sensation on the retina. In the following research a modified form of apparatus has been employed, and experience has shown it to be equally as accurate as and more convenient in many ways than that formerly used. When rotating sectors are employed with less than 4° of aperture, small errors in the reading of the graduated arc cause appreciable errors in the result. Hence, the more nearly the zero reading is approached, the less trustworthy are the determinations of the diminution of the total intensity, and this uncertainty affects all observations in which the light is reduced below 1/40 of its initial amount. The sectors have also the disadvantage of not being noiseless, and of requiring an electro or other motor to work them.

In a previous paper (‘Philosophical Transactions,’ A, 1897, vol. 189, p. 137) we have drawn attention to the fact that the disturbance set up in a liquid by the impact of a rough sphere falling into it, differs in a very remarkable manner from that which follows the entry of a smooth sphere. In the present paper we describe further experiments, made with the object of ascertaining the reason of this difference, and give the conclusions reached. It appeared desirable, in the first place, to take instantaneous photographs of the disturbed liquid below the water-line. These were easily obtained by letting the splash take place in an approximately parallel-sided thin glass vessel (an inverted clock-shade) illuminated from behind. The liquid surface when undisturbed was about level with the middle of the camera-lens, which was focussed for the sphere when under water. The general arrangement of the optical apparatus will be suffi­ciently understood from the accompanying cut (fig. 1). The method of timing the illumination was that already described ( loc. cit. ).

This paper examines methods for formally proving the security of cryptographic schemes. We show that, despite many years of active research and dozens of significant results, there are fundamental problems which have yet to be solved. We also present a new approach to one of the more controversial aspects of provable security, the random oracle model.

In a previous paper the author pointed out the advantages of a three circle form of goniometer in the determination of the morphological characters of crystals ; the crystal is adjusted once for all, and measurements may be made in any desired zone. A description was added of such an instrument, which had resulted from the addition of a two-circle apparatus to an ordinary Fuess goniometer with a single horizontal circle. This instrument has been in almost daily use since the end of June, 1899, and the author is, therefore, in a position to appreciate the ease and celerity with which crystals, however small, may be in this manner measured. As was remarked in the paper quoted above, the adapted instrument has the disadvantage that measurements can only be made through little more than a right angle from the pole in which the zone to be measured and the zone of reference intersect, and, therefore, only half a zone can be measured without readjustment of the circles B and C.

Helmholtz's attention was directed to the subjects to be discussed in this paper while very young. Even while attending the gymnasium and reading Cicero and Virgil, for which he had little taste, Helmholtz was pondering on various problems in optics not met with in text-books, and which served as a basis some years later for the construction of the ophthalmoscope. The mathematics of physical problems always came easy to him, not that he seems to have had any special love for pure mathematics for its own sake, but only as a means of solving the questions which interested him. His mathematical ability was of a very high order, and this fact seems all the more remarkable when it is noted that he never had any systematic training in this branch of science, as have most other eminent mathematical physicists. His knowledge in the more advanced departments of mathematics was acquired

In this paper a kernel-based nonlinear spectral matched filter is introduced for target detection in hyperspectral imagery, which is implemented by using the ideas in kernel-based learning theory. A spectral matched filter is defined in a feature space of high dimensionality, which is implicitly generated by a nonlinear mapping associated with a kernel function. A kernel version of the matched filter is derived by expressing the spectral matched filter in terms of the vector dot products form and replacing each dot product with a kernel function using the so called kernel trick property of the Mercer kernels. The proposed kernel spectral matched filter is equivalent to a nonlinear matched filter in the original input space, which is capable of generating nonlinear decision boundaries. The kernel version of the linear spectral matched filter is implemented and simulation results on hyperspectral imagery show that the kernel spectral matched filter outperforms the conventional linear matched filter.

The investigation of development described in a previous communication was extended by the application of microscopic methods. The fact that both the silver haloid and the resulting silver are distributed through the film in the form of particles of minute but measurable size, allows us in this way to detect finer qualitative differences in, and to draw independent deductions on the processes of exposure and development. The size of the grain is important, both from the practical point of view and from the theoretical: in the one case as bearing on spectroscopical and astronomical photography, in the other on account of the great importance of the degree of surface-extension for heterogeneous systems. The method has been used previously by Abney, Abegg, Kaiserling, Ebert, and others, but by far the most systematic and important inquiry is that of K. Schaum and V. Bellach.

In the course of a series of experiments carried on by the Massachusetts State Board of Health it became necessary to devise a method for separating and determining quantitatively small amounts of copper in water; such a method has been worked out and is published in detail in the "Standard Methods of Water Analysis" of the Laboratory Section of this Association.1 It is the purpose of this short paper to give a brief outline of the method, together with some experimental results, and to call attention to certain statements that have appeared in print regarding the total disappearance of the copper in a few hours when applied to a water supply, and the impossibility of detecting it in the water by chemical tests. The chemical test in general use for detecting copper in solution in small quantities is that mentioned by Moore and Kellerman in Bulletin 64 of the Bureau of Plaftt Industry, and consists of adding potassium ferrocyanide to the solution to be tested, acidified by acetic acid. The sensitiveness of this test is shown by the following figures.

It is well known that when light is propagated in an absorbing medium, the dynamical equations and the boundary conditions are of exactly the same form as for a transparent medium. From a mathematical point of view the only difference between the two cases is that μ , the refractive index in a transparent medium, is replaced in the absorbing medium by a complex quantity μ — ia where μ is the “refractive index” of the medium, i. e. , the ratio of the velocity of light in air to that in the medium, and a is the coefficient of absorption. When dealing with the problem of reflection we shall take the plane of xy as that of incidence, and x = 0 as the surface of separation of the two media; the vectors representing the displacements will then be of the forms e ipt-i ( x cos ϕ + y sin ϕ )/V in the incident, and re ipt+i ( x cos ϕ - y sin ϕ )/V in the reflected wave. Here ϕ is the angle of incidence for the frequency, and V the velocity of propagation in the first medium. The incident wave is of unit amplitude, and if r = Re iθ , then R and θ represent the amplitude and change of phase in the reflected wave.

It has been shown in former papers that wood has the property of acting in the dark on a photographic plate, when placed in contact or in proximity to it. Not only does wood act in this way, but leaves, seeds, roots, bulbs, and, in fact, with only few exceptions, all vegetable substances act in a similar way. The more important bodies which are without this property are starch, cellulose, gum, sugar, pith, and pollen. To obtain this action on a plate it is necessary that the body used be tolerably dry, or else the moisture contained in it will act on the gelatine of the photographic plate and destroy the picture. The time necessary for the exposure to the plate varies from a few minutes to 18 hours or more. To quicken the action, heat may be applied, but the temperature must not be above 55º C., nor the time of exposure, under ordinary circumstances, longer than 18 hours, or the photographic film will be injured. Any ordinary rapid photographic plate may be used, and its development is exactly the same as that of an ordinary picture. The best and most general method of drying vegetable substances before exposing them to the photographic plate is to place them between pure white blotting paper and subject them to considerable pressure, say from 1 to 5 or 6 tons per square inch. This process has also the advantage of giving a second picture, for it is found that the liquid which has been expressed and absorbed by the blotting paper is capable of acting on a photographic plate, and that it gives a good representation of the plant from which it came (Plate 19, fig. 1, an oak leaf). Since different woods are capable of acting on a photographic plate it was to be expected that leaves, stems, flowers would do the same. This has been found to be the case, and the action has been traced from its commencement in the sprouting embryo of a plant till after its death. Postponing for the present the full discussion of the cause of this activity of vegetable matter on a photographic plate, it may be assumed as a working hypothesis that the active substance is hydrogen peroxide. As far as the activity of a plant goes, it is comparable with that of hydrogen peroxide. For instance, if one part of pure peroxide be dissolved in one million parts of water it is sufficient to enable the solution in 24 hours at ordinary temperatures, even when the plate is 1/8 inch above the liquid, to give a marked action on the plate; and, on the other hand, a seed leaf of a runner bean weighing only0·02 gramme can give a similar effect.

IN NATURE of September 20 (vol. lxxiv., p. 526) I find mention of a paper read before Section B at the recent meeting of the British Association by Mr. W. Popplewell Bloxam, on a new method of determining indigotin. It is stated that “the author concludes that the present process of manufacture is a wasteful one, the highest efficiency attained not reaching 50 per cent., whilst on the average only 25 per cent of the indigotin in the leaves is extracted.”

The volume presents new developments in data analysis and classification, and gives a state of the art impression of these scientific fields at the turn of the Millenium. Areas that receive considerable attention in this book are Cluster Analysis, Data Mining, Multidimensional and Symbolic Data Analysis, Decision and Regression Trees. The volume contains a refereed selection of original papers, overview papers, and innovative applications presented at the 7th Conference of the International Federation of Classification Societies (IFCS-2000), with contributions from eminent scientists all over the world. The reader finds introductory material into various areas and kaleidoscopic views of recent technical and methodological developments in widely different areas within data analysis and classification. The presence of a large number of application papers demonstrates the usefulness of the recently developed techniques.

The desirability of a clinical method for determining the alkalinity of blood—that is to say, the OH and H ionization—has long been recognized. The recent determinations of this ionization by Friedenthal, 1 Hober, 2 Fraenkel, 3 Farkas 4 and Tangl and his pupils 5 have shown that the alkalinity is very slight and subject to very little variation. Accordingly a clinical method has seemed difficult to seek. The recent study of indicators by Salm, 6 however, characterizing with the greatest accuracy a whole series of indicators, has suggested the possibility of devising a method at once certain, accurate and easy of application. The present paper is concerned with experiments to this end. There are two general methods by which the reaction of a fluid may be quantitatively measured: 1. Titration to an end point. 2. Determination of the H and OH ionization. The former yields information concerning the amount

In the usual theory of gratings, upon the lines laid down by Fresnel, the various parts of the primary wave-front after undergoing influences, whether affecting the phase or the amplitude, are conceived to pursue their course as if they still formed the fronts of waves of large area. This supposition, justifiable as an approximation when the grating interval is large, tends to fail altogether when the interval is reduced so as to be comparable with the wave-length. A simple example will best explain the nature of the failure. Consider a grating of perfectly reflecting material whose alternate parts are flat and parallel and equally wide, but so disposed as to form a groove of depth equal to a quarter wave-length, and upon this let light be incident perpendicularly. Upon Fresnel’s principles the central regularly reflected image must vanish, being constituted by the combination of equal and opposite vibrations. If the grating interval be large enough, this conclusion is approximately correct and could be verified by experiment. But now suppose that the grating interval is reduced until it is less than the wavelength of the light. The conclusion is now entirely wide of the mark. Under the circumstances supposed there are no lateral spectra and the whole of the incident energy is necessarily thrown into the regular reflection, which is accordingly total instead of evanescent. A closer consideration shows that the recesses in this case act as resonators in a manner not covered by Fresnel’s investigations, and illustrates the need of a theory more strictly dynamical. The present investigation, of which the interest is mainly optical, may be regarded as an extension of that given in ‘Theory of Sound,’* where plane waves were supposed to be incident perpendicularly upon a regularly corrugated surface, whose form was limited by a certain condition of symmetry. Moreover, attention was there principally fixed upon the case where the wave-length of the corrugations was long in comparison with that of the waves themselves, so that in the optical application there would be a large number of spectra. It is proposed now to dispense with these restrictions. On the other hand, it will be supposed that the depth of the corrugations is small in comparison with the length (λ) of the waves.

The determination of the efficiency of various forms of illuminants, and of the power expended in light production, does not appear to have received the attention it deserves in this country, nor have the labours of workers in Germany and in the United States as yet sufficed to permit of definite values being adopted for luminous efficiencies, or for the mechanical equivalent of light. In what follows, an account of some observations made by Mr. A. C. Jolley and the writer, with the object of determining the mechanical equivalent of light, will be given. For this purpose an attempt was first made to find the luminous efficiencies and total consumption of some of the newer highly incandescent electric lamps; and this was followed by a direct determination by a bolometer in the spectrum.

In this paper, a novel construction algorithm called imbalanced Takagi–Sugeno–Kang fuzzy classifier (IB-TSK-FC) for the TSK fuzzy classifier is presented to improve the classification performance and rule-based interpretability for imbalanced datasets. IB-TSK-FC consists of two components: 1) a cross-class Bayesian fuzzy clustering algorithm (BF3C) and 2) an imbalance learning algorithm. In order to achieve high interpretability, BF3C is developed to determine an appropriate number of fuzzy rules and identify antecedent parameters of fuzzy rules from the perspective of the probabilistic model. In addition to inheriting the distinctive advantage of Bayesian fuzzy clustering that the number of clusters can be estimated in the framework of Bayesian inference, BF3C considers repulsion forces between cluster centers belonging to different classes, and uses an alternating iterative strategy to obtain more interpretable antecedent parameters for imbalanced datasets. In order to improve the classification performance for imbalanced datasets, an imbalance learning algorithm is derived to estimate consequent parameters of fuzzy rules on the basis of the weighted average misclassification error. Comprehensive experiments on synthetic and UCI datasets demonstrate the effectiveness of the proposed IB-TSK-FC algorithm.

The lack of precision of measurements with alternate currents, as compared with those using direct currents, is mainly due to the relative sensitiveness of the instruments available for such tests. The fact that the turning moment acting on the moving system depends in one case on the square of the current and in the other on the first power of the current, readily explains the high ratio between the currents needed to cause the minimum measurable deflection in the two cases, but this ratio is, nevertheless, most striking when a numerical comparison is actually made on some fair basis. The only likely way at present of improving alternate current instruments is to use iron cored electromagnets to increase the strength of the magnetic field. I have found that the difficulties due to varying permeability and hysteresis of the iron can be avoided by exciting the electromagnet in shunt. It proves possible, with careful design, to construct an electromagnet whose flux is connected with the exciting voltage by a strict mathematical law involving no variable physical properties like permeability, etc. Such an electromagnet is eminently suited for measuring purposes. The theoretical and experimental study of instruments constructed on this principle has brought out certain novel points which are set forth in the present paper. The first part discusses the mathematical relations of cyclic quantities having a common fundamental period, and constitutes a development of a method already published. This method is the only one known to me which is independent of assumptions in regard to the wave form of the quantities dealt with. The usual methods, which are based on the erroneous assumptions of sine law wave form, are not any simpler in working, and are most unsatisfactory when the accuracy of new results has to be critically examined. All alternate current measurements refer to mean squares or to mean products, and the natural method of obtaining the connections between such squares and products is to study the properties of quadratic functions of the variables. The earliest instance of this in alternate current theory was in connection with the “three voltmeter method.” Such processes lead to a very simple form of calculus appropriate to cyclic quantities.

The new method described in Mr. King's recent paper, “On the Construction of Mortality Tables from Census Returns and Records of Deaths”, marks such a great advance on that employed in the construction of the official English Life Table, that it occurred to me that it might be worth examining whether the numerical application could not be further simplified by the use of central differences. Everett's formula (J.I.A., xxxv, 452) lends itself admirably to the construction of tables by subdivision of intervals. It involves only even central differences of each of the two middle terms of the series between which the interpolation has to be made, and, as was pointed out by the author in communicating his formula to the Journal, “each sum of three terms does double duty, serving both for “the preceding and the succeeding interval. In an extended “computation, the number of ‘sums of three terms’ to be “calculated is accordingly practically identical with the number “of intervals, and the labour of calculation is only about half “what it appears to be on the face of the formula.”The problem before us is that of fitting between consecutive pairs of a series of points a series of partial interpolation curves, which shall have the same slope and curvature at their points of junction. In what follows, the central difference notation is that introduced by Dr. W. F. Sheppard in his paper on “Central Difference Formulæ” (Proceedings of the London Mathematical Society, xxxi, 449).

In the half century that elapsed from the time when Cauchy published is memoirs on dispersion, the only measurements of refractive indices that ere available for the test of any theory were confined to the neighbourhood of the visible spectrum. They extended from somewhat beyond 0·2 µ to bout 0·8 µ , i. e. over a range of two octaves. In this range the variation of refractive index for most substances is small, and it is not surprising that, by a proper adjustment of constants, a variety of different formulæ may be lade to fit the experimental facts. More recently, however, the range of observations has been immensely extended, so that we now have a large umber of determinations of refractive indices for various wave-lengths extending from less than 0·2 µ to 22·3 µ . With a knowledge extending ever this range of about seven octaves, there is more hope of testing the herits of different dispersion formulæ. Accordingly, when, in 1879, Mouton lade the first considerable extension in the direction of great wave-lengths, e found that, with the same number of constants, the formula of Briot represented the facts much better than did the older one of Cauchy, and the same result was reached by Langley in 1884 and 1886. The still more extended observations of Paschen, Rubens, E. F. Nichols, and A. Trowbridge, published at various dates from 1892 to 1897, have shown that Sellmeier’s forrmula n 2 = K + c 1 /(λ 2 —λ 1 2 +... is the only one of those that have been tried that is in thorough accord with the observed values of the refractive indices over the whole range of the experiments.

In a communication published in the ‘Proceedings,’ Mr. Marconi has given the results observed when a straight horizontal conductor is substituted for the usual vertical conductor employed as a transmitter or receiver at a wireless telegraph station. The object of the following note is to consider the theory of such an arrangement, or at any rate one aspect of it. The receiver, as being the more important, will be considered first. Let AB (fig. 1) represent the horizontal receiver, consisting of a straight conductor having the end A connected to a spark-gap CC 1 or other wave-detector. The electric oscillations in AB can be represented by a distribution of Hertzian oscillators along AB, and, if L denotes the current strength at any point of AB, it must satisfy the conditions L= 0 at B, the free end, and d L/ ds = 0 at A, since the electric force perpendicular to AB at A must vanish. If the distance of AB from the earth is not too small, the effect of the oscillations belonging to the image in the earth of AB on those in AB may be neglected, the radiation from the free end B will be approximately symmetrical with respect to AB, and the oscillations in AB are then approximately the same as if BA formed part .of a semi-infinite straight conductor in which a system of oscillations is being maintained, B being the free end and A. the first node from the free end; the wave-length of these oscillations is very approximately five times the length of AB, and therefore the receiver is of maximum efficiency when its length is one-fifth of the length of the transmitted wave, a result observed by Marconi. When the distance of AB from the earth is so small that the effect of the oscillations in the image of AB in the earth on the oscillations in AB is not negligible, the radiation from the free end B will not be symmetrical with respect to AB, but may be taken as being approximately symmetrical with respect to some line through B making an angle with BA; the wave-length of the oscillations in AB is therefore equal to the wave-length of the oscillations in a bent conductor joining AB; that is greater than five times the length of AB, and, therefore, in this case the receiving conductor has its maximum efficiency when its Length is somewhat less than one-fifth of the length of the transmitted wave, result also observed by Marconi. To examine the effect of the orientation of the receiver, consider a straight conductor BAB' twice the length of AB (fig. 2) and its image B 1 A 1 B 1 ' in the horizontal plane, A and A 1 being their middle points respectively.