Proceedings of The Royal Society of London

We unearth the interconnection between various analytical methods which are widely used in the current literature to identify integrable nonlinear dynamical systems described by third-order nonlinear ordinary differentiable equations (ODEs). We establish an important interconnection between extended Prelle-Singer procedure and {\lambda}-symmetries approach applicable to third-order ODEs to bring out the various linkages associated with these different techniques. By establishing this interconnection we demonstrate that given any one of the quantities as a starting point in the family consisting of Jacobi last multipliers, Darboux polynomials, Lie point symmetries, adjoint-symmetries, {\lambda}-symmetries, integrating factors and null forms one can derive the rest of the quantities in this family in a straightforward and unambiguous manner. We also illustrate our findings with three specific examples.
Variation of the precession angle δφ as a function of ω0. 
The light deflection angle ∆φ (in arcseconds) as a function of the parameter ω0. 
Variation of the time delay ∆tRD as a function of ω0. 
In the present paper we consider the possibility of observationally testing Horava gravity at the scale of the Solar System, by considering the classical tests of general relativity (perihelion precession of the planet Mercury, deflection of light by the Sun and the radar echo delay) for the Kehagias-Sfetsos asymptotically flat black hole solution of Horava-Lifshitz gravity. All these gravitational effects can be fully explained in the framework of the vacuum solution of Horava gravity, and it is shown that the analysis of the classical general relativistic tests severely constrain the free parameter of the solution. Comment: 7 pages, 3 figures; talk presented at the II Workshop on Black Holes, Instituto Superior Tecnico, Lisbon, 21-22 December 2009
Rotating waves are periodic solutions in SO(2) equivariant dynamical systems. Their precession frequency changes with parameters and it may change sign, passing through zero. When this happens, the dynamical system is very sensitive to imperfections that break the SO(2) symmetry and the waves may become trapped by the imperfections, resulting in steady solutions that exist in a finite region in parameter space. This is the so-called pinning phenomenon. In this study, we analyze the breaking of the SO(2) symmetry in a dynamical system close to a Hopf bifurcation whose frequency changes sign along a curve in parameter space. The problem is very complex, as it involves the complete unfolding of high codimension. A detailed analysis of different types of imperfections indicates that a pinning region surrounded by infinite-period bifurcation curves appears in all cases. Complex bifurcational processes, strongly dependent on the specifics of the symmetry breaking, appear very close to the intersection of the Hopf bifurcation and the pinning region. Scaling laws of the pinning region width, and partial breaking of SO(2) to Zm, are also considered. Previous and new experimental and numerical studies of pinned rotating waves are reviewed in light of the new theoretical results.
In the present paper are given the results of observations, made with the greatest possible accuracy and care, of the muscular anatomy of thirty-four subjects, chiefly of the male sex, with an especial view to the study of the combinations of these abnormalities, and the directions in which they chiefly tend. To enable the reader more readily to comprehend these results, the author has tabulated them in the sheet appended to the paper. In the Table the names of the muscles placed at the head of each column refer to those in which more than one variety has been observed in the session. They will be found to correspond very closely with those given in the former papers by the author. In columns 21, and 27 are placed those of which only one example has been met with. Some of these, however, are of much importance. To explain the nature of the abnormality more precisely than could be done in the Table, a word or two will be necessary on such of the specimens as may be considered novel or typical.
It is well known that the number of facts which seem to prove that an accidentally produced affection may be transmitted by parents to their offspring is still small, and that serious objections have been raised against most, if not all, the facts of this kind. The following observations seem to show peremptorily that, at least in one species of animals, this kind of transmission may occur. I have shown that certain injuries to the spinal cord, in Guinea-pigs and other Mammals, are followed, after a few weeks, by a convulsive disease, very much like epilepsy. For several years it has been frequently observed that the young of a number of those epileptic animals, which I kept in my laboratory, were at times attacked with epileptiform convulsions. For many months I have made regular observations on this curious subject, and I have ascertained, by careful watching, that six young guinea-pigs which had frequent attacks of convulsions, were the offspring of one male and two female guinea-pigs rendered epileptic in consequence of an injury to the spinal cord.
The results which are shortly stated in the following paragraphs relate to (1) the order and duration of the rhythmical and excitatory motions of the heart of the frog; (2) the normal electrical condition of the surface of the heart and the influence thereon of mechanical, chemical, and thermal injuries; and (3) the characters of the normal and of the excitatory electrical variation, and the modifications of those characters which are induced by injuries of the surface, and under the temporary influence of radiant heat. Section I.— Order and Duration of the Motions of the Heart . 1. Duration of the Ventricular Systole .—In the rhythmically contracting excised heart, i. e ., in the heart removed by cutting across the sinus, which will in this paper be called “the entire heart,” the frequency of the contractions is usually, in winter frogs, a little over 30 per minute. The systole of the ventricle lasts about one second. The contraction attains its maximum in a little more than half a second after its commencement, declining at first gradually, afterwards more suddenly. The sadden relaxation occurs between 0".7 and 0".9 after the commencement. At the close of this period the ventricle does not become entirely flaccid, for a lever resting upon it continues to descend for about a third of a second.
Notwithstanding all the work that has been done on the subject of the coagulation of the blood, the definite results which have been obtained as to intravascular clotting are extremely scanty. I think most physiologists will agree with me in the statement, that no method is known by which one can, at will, produce a complete fibrinous coagulation in the vessels of a living animal. I have found such a method, and one which appears to be infallible in its action.
The first 4 terms of the sequence Am for the Hénon map.  
log |fn| for the Hénon map.  
Acceleration of convergence for the sequenceãnsequence˜sequenceãn. +, ˜ a 4k , k = 1,. .. , 7; ×, ˜ a 4k − c3γ 4k ; , the exponential fit given by λ1 + c3γ n. giving the new sequence
In a previous paper (Aston, P. J. & Dellnitz, M. 1999 Comput. Meth. Appl. Mech. Engng 170, 223-237) we introduced a new method for computing the dominant Lyapunov exponent of a chaotic map by using spatial integration involving a matrix norm. We conjectured that this sequence of integrals decayed proportional to 1/n. We now prove this conjecture and derive a bound on the next term in the asymptotic expansion of the terms in the sequence. The Hénon map and a system of coupled Duffing oscillators are explored in detail in the light of these theoretical results.
From a comparison of the different accounts of “Hemiopsia,” “Halfvision,” or “Half-blindness,” given by Dr. Wollaston (Phil. Trans. 1824, p. 222), M. Arago (Annales de Chimie et de Physique, tom. xxvii. p. 102), Sir David Brewster (Phil. Mag. 1865, vol. i. p. 503, and Transactions of Royal Society of Edinburgh, vol. xxiv. part 1), the Astronomer Royal (Phil. Mag. July 1865, vol. ii. p. 19), Professor Dufour (in a letter to the Astronomer Royal), Sir John Hersehel (Familiar Lectures on Scientific Subjects, p. 406, Lecture IX., and private letters), Sir CharlesWlieatstone (in a private letter), Mr. Tyrrell (On the Diseases of the Eye, 1840, vol. ii. p. 231), and the author of this paper, it is plain that there are different forms of transient Hemiopsia, irrespective of the wide primary distinction between the transient and permanent forms, which have all been included under the same name Hemiopia or Hemiopsia. It seems that Wollaston, Arago, Brewster, and Tyrrell are describing one form of the transient affection, while Sir John Herschel, Sir Charles Wheatstone, the Astronomer Royal, Professor Dufour, and the author agree in describing another.
The ‘ Comptes Rendus ’ for August 28 (p. 434) contains a communi­cation from Professor Dewar to M. Henri Moissan, “ relative à la solidification de l’hydrogène.” It concludes with the following sentence, which may be easily overlooked:—“ Des graines refroidies dans de l’hydrogène liquide conservent toute la propriété de germer."
That the presence of free oxygen is one of the essential conditions of protoplasmic movements has long been recognised. Further than this however the subject has not hitherto been investigated. The following are the results of a long series of experiments made to ascertain the minimum pressure of oxygen necessary to restore the streaming, amœboid and ciliary movements of protoplasm after they have come to rest in the absence of that gas. The object experimented upon was in each case placed in a hanging drop of water and exposed to an indifferent gas such as hydrogen or nitrogen, or else put into connexion with the exhausted receiver of an air-pump.
1. When the opposite ends of a living leaf of Dionæa are placed on non-polarizable electrodes in metallic connexion with each other, and a Thomson’s reflecting galvanometer of high resistance is introduced into the circuit thus formed, a deflection is observed which indicates the existence of a current from the proximal to the distal end of the leaf. This current I call the normal leaf-current . If, instead of the leaf, the leaf-stalk is placed on the electrodes (the leaf remaining united to it) in such a way that the extreme end of the stalk rests on one electrode and a part of the stalk at a certain distance from the leaf on the other, a current is indicated which is opposed to that in the leaf. This I call the stalk-current .
In a memoir published some years ago by Helmholtz (Crelle, Bd. lvii.) it was proved that if a uniform frictionless gaseous medium be thrown into vibration by a simple source of sound of given period and intensity, the variation of pressure is the same at any point B when the source of sound is at A as it would have been at A had the source of sound been situated at B, and that this law is not interfered with by the presence of any number of fixed solid obstacles on which the sound may impinge. A simple source of sound is a point at which the condition of continuity of the fluid is broken by an alternate introduction and abstraction of fluid, given in amount and periodic according to the harmonic law.
Two platinum wires were attached to the ends of a small bar of ellurium, about 1 inch in length, by heating the wires to a bright red leaf and bringing them suddenly in contact, one with each end of the bar. The platinum wires melted a small portion of the tellurium, and became imbedded in it. The resistance of the bar and wires was about half an ohm. The tellurium was placed in a box, and its resistance balanced; then it was exposed to the light of a paraffin-lamp, just as in he experiments with selenium. At first the light seemed to have no effect; but in consequence of the heat from the lamp, the resistance of I the tellurium was increased. On placing a rectangular vessel of water between the lamp and the tellurium and then exposing as before, there was no change of resistance in the tellurium, showing that if there was any diminution in the resistance due to the action of light it was entirely balanced by the increase in the resistance due to heating by the current and by the residual portion of the radiant heat.
The action of cutting tools has not often been treated from a theoretical point of view; in fact I only know of two papers on the subject, one by Professor Willis and the other by Mr. Babbage. Of these Professor Willis’s paper is purely geometrical, showing what angles the edges of tools may make with one another if the cutting angles are to be such as experience shows to answer best. Mr. Babbage, on the other hand, does not enter at all on the question of the shape of the tool, but by making certain assumptions as to the relation between the dimension of the shaving removed by a tool and the work required to remove it, he deduces some results showing how to remove a given amount of material most economically. His conclusions cannot be considered correct, nor do they agree with experience (see Note 1). I do not attempt in the following paper to give any dynamical investigation of the action of tools, in fact it would be almost impossible to do so without a more extended knowledge of the laws which govern the strains in bodies subjected to large forces, but merely to classify the various actions which observation shows to be caused by the progress of the tool, and to quantify approximately the work expended in each. For this purpose, shavings from a great variety of substances were examined both in the course of their formation (by a microscope attached to the toolholder) and after they were removed. Among the substances examined may be mentioned four or five samples of wrought iron, and as many of steel, cast iron, gun metal, brass, copper, lead, zinc, hard paraffin, soap, and clay.
In the following memoir the truth will be verified in a particular instance, of a statistical law of heredity that appears to be universally applicable to bisexual descent. 1 stated it briefly and with hesitation in my book ‘Natural Inheritance’ (Macmillan, 1889; page 134), because it was then unsupported by sufficient evidence. Its exist­ence was originally suggested by general considerations, and it might, as will be shown, have been inferred from them with considerable assurance. Consequently, as it is now found to hold good in a special case, there are strong grounds for believing it to be a general law of heredity.
“Co-relation or correlation of structure” is a phrase much used in biology, and not least in that branch of it which refers to heredity, and the idea is even more frequently present than the phrase; but I am not aware of any previous attempt to define it clearly, to trace its mode of action in detail, or to show how to measure its degree. Two variable organs are said to be co-related when the variation of the one is accompanied on the average by more or less variation of the other, and in the same direction. Thus the length of the arm is said to be co-related with that of the leg, because a person with a long arm has usually a long leg, and conversely.
1. Let M Θ be the coefficient of mutual induction of a circle and a portion of a coaxial helix, beginning in the plane of the circle and of helical angle Θ. Then if M is the coefficient of mutual induction of the circle, and any portion of the helix for which the extreme points are determined by helical angles Θ 1 and Θ 2 , we have M=M Θ 2 –M Θ 1 . It will therefore be sufficient to show how to calculate M Θ for all values of Θ.
The experiments here described, which were made during April and May of the present year (1888), to determine the constant of viscosity of water, may be of some interest on account of the newness of the method employed, and also as being on rather a larger scale than other experiments which have been made with the same object. Fig. 1 gives a section of the apparatus used. A and B are two coaxial cylinders; of these A is mounted on the vertical axis E, and can be made to rotate by a belt passing over the wheel F. B is suspended by a long fine wire C, and the annular space between A and B is filled with water or any other fluid to be experimented on.
Let us now endeavour to ascertain under what circumstance a linear differential equation admits a solution of the form P log e Q, where P and Q are rational functions of ( x ).
If the bulb of an ordinary thermometer be coated chemically with silver, and then electrically with a metallic deposit, the mercury will traverse some portion of the scale, and finally take up a definite posi­tion, independently of temperature. To this phenomenon I have given the name electrostriction . Of the metals hitherto worked with, copper, silver, iron, and nickel constrict the bulb; zinc and cadmium distend it. The general conditions under which the experiments were made were as follow:—A thermometer coated with silver by immersion in a solution of ammoniacal argentic tartrate was placed vertically near a bare ther­mometer at one side of a depositing cell; the anode stood at a distance of 11 centimetres. The bulbs of the thermometers were about their own depth below the surface of the electrolyte; the covered one was turned half round at every comparison. The source of electricity was a pint Daniell’s cell, having a porous diaphragm, and the circuit included a galvanoscope. Observations were made at definite intervals of time, imme­diately after stirring the liquid; and the difference between the two scales, after suitable reduction, was registered as electrostrictive effect. The temperature was in all cases the unrestricted temperature of the labo­ratory.
We were requested a few months ago by Dr. W. Roberts to verify a statement, recently made by Musculus and De Méring, that maltose is a product of the action of an aqueous extract of pancreas upon starch-paste. During the prosecution of the inquiry, and while following up certain lines of experiment which suggested themselves from time to time, we have, besides fully confirming the results of the above mentioned observers, ascertained certain facts which we believe are of some physiological importance in elucidating the still very obscure processes of animal digestion and nutrition. I. Hydrolytic Action of the Pancreas . The first observation upon the amylolytic action of the pancreatic secretion appears to have been made by Bouchardat and Sandras in the year 1845. The general functions of the gland were more fully studied in 1856 by Claude Bernard, and a few years later by Cohnheim (“Virchow’s Archiv,” 28, 241, 1863). Danilewski in 1862, and Hiifner (“ Journ. f. Prakt. Chem.” [2], 5, 1872, 396), ten years later, isolated a soluble amylolytic ferment from the pancreas, the former observer by acidifying the aqueous infusion with phosphoric acid and precipitating with lime; the latter by the glycerine method first described by Wittich.
Octonions is a name adopted for various reasons in place of Clifford’s Bi- quaternions . Formal quaternions are symbols which formally obey all the laws of the quaternion symbols , q (quaternion), x (scalar), ρ (vector) ϕ (linear function in both its ordinary meanings), ϕ' (conjugate of ϕ ), i, j, k, ζ , K q , S q , T q , U q , V q . Octonions are in this sense formal quaternions. Each octonion symbol, however, requires for its specification just double the number of scalars required for the corresponding quaternion symbol. Thus, of every quaternion formula involving the above symbols there is a geometrical interpretation more general than the ordinary quaternion one, an octonion interpretation.
This paper attempts to examine the well-known difficulties in connection with the partition of energy in the molecules of a gas. A definite dynamical system is first considered, an ideal gas in which the molecules are loaded spheres, that is, spheres of radius a , of which the centre of mass is at a small distance, r , from the geometrical centre. It shown by direct methods that the energy will, after an infinite ne, distribute itself equally between the five degrees of freedom, it when a wave of sound is passed through the gas, the energy will ver have sufficient time to attain to its equilibrium distribution. It shown that sounds of different period will be propagated with appreably different velocities, except in the extreme case in which the ratio: r to a is almost, but not necessarily quite, zero. In this case, the tio of the two specific heats, as determined from indirect experiments the velocity of sound, would be 1 2/3, while direct experiments might ve any value from 1 2/3 to 1 2/3, the value varying with the duration of experiment.
These investigations were made in order to learn how the temperature of the body comports itself in health; since to every one it must be obvious that without such knowledge it is impossible to determine with any approach to certainty what variations in the temperature are to be accepted as indications of disease. It is necessary to state here some particulars of the manner these investigations were conducted, and of the precautions taken to avoid error.
Adiabatic demagnetization experiments were carried out on a spherical ; single crystal of cerium ethyl sulfate. The absolute temperature scale was ; determined down to 0.02 deg K as a function of the entropy. Measurements were ; also made of the adiabatic susceptibility in the antiferromagnetic state which ; sets in at 0.05 deg K and by extrapolation the magnetization at T = 0 deg K could ; be estimated to a fair accuracy. The co-operative phenomena are discussed in ; terms of the theory of electric quadrupole-quadrupole interaction by Finkelstein. ; (auth);
The Declination and the Horizontal Force are deduced from hourly readings of the photographic curves, and so are corrected for thediurnal variation. The results in the following tables, Nos. I, II, III, I"V, are deduced from the magnetograph curves, which have been standardised byobservations of deflection and vibration. These were made with the Collimator Magnet, marked 6 6 a , and the Declinometer Magnet, marked 66c, in the Unifilar Magnetometer No. 66, by Elliott Brothers, of London. The temperature correction (which is probably very small) has not been applied.
Former communications on the influence of altitude on respiration have appeared in the “Proceedings of the Royal Society” for 1878 and 1879. I have continued the inquiry; and my present object is to give an account of my latest investigations on that subject. I must beg leave to premise that a work of this kind is not free from difficulties; some of these are of a physiological nature, and refer to the task of taking into account the different circumstances bearing on the state of the body at the time of the experiment; respiration is, if I may so express it, so delicately balanced in its relations with the other functions, that any one of them becoming either quiescent or in a state of activity reacts immediately upon it.
By exposing the eye for a sufficient length of time to bright sun light in the focus of a burning glass behind suitably chosen transparent screens, it is possible to induce over the whole retina at condition of temporary colour-blindness
“Of all the important results from the discussions of the British Colonial Observatory, the discovery of the direct action of the sun on the magnetism of the earth is certainly a fact of the highest interest, in opening quite a new field for investigation; and few modern discoveries in this branch of science have interested me more than yours of the annual variation of the diurnal variation of declination. It seems that M. Secchi of Rome has nearly touched at the same discovery, and I am indeed glad that the enormous quantity of calculations, which you are superintending, did not prevent you from publishing your results before the ripening fruit was plucked by another.
The method by which integral (227) was obtained may be thus extended. Suppose it was required to obtain.
In the paper referred to above, it was stated that the markings or dots upon the valves of the Diatomaceæ, are the optical expressions of depressions existing upon the valves. All those authors who have paid special attention to the Diatomaceæ, have considered the markings to denote cells; among these we find Ehrenberg, Kützing, Ralfs, Smith, and Quekett.
On the 24th February, 1875 *, we had the honour of communicating to the Society, in conjunction with our friend Mr. Spottiswoode, an account of some experiments to ascertain the cause of stratification in electrical discharges in vacuo . These experiments were made with a battery of 1080 cells of powder chloride of silver, which was described; we have now in action 3240 such cells, and have recently completed 2400 rod-chloride-of-silver cells t , making our total force 5640 cells in action. To these will be shortly added another unit of 1080 cells powder chloride, and two other units of 1200 rod chloride, making a total of 9120 cells. We have more recently made a verbal communication to the Society of Telegraph Engineers, and also in October last a written one to the Académie des Sciences of Paris *, wherein we have stated that the length of the spark in air appears to be in the direct ratio of the square of the number of cells.
Dear General Sabine,—I have ventured to think that a word of my proceedings may be acceptable to you, though I have been much more tardy in getting into observing order than I had expected. It is indeed only now that I am able to make observations without finding some one part or other of my apparatus capable of improvement. At length, however, I find my hopes exceeded in the perfection, precision, and facility with which my colossal equatorial is directed and carried on: the driving motion is indeed as perfect and uniform, I believe, as that of any telescope with which I am acquainted.
Sir,—I have the honour to report that we left Stanley Harbour in East-Falkland Island for Monte Video on the afternoon of the 6th of February, and on the 8th we sounded in lat. 48° 37' S., long. 55° 17' W., about 200 miles to the N. E. of Stanley, in a depth of 1035 fathoms. The trawl was lowered, but it was unfortunately carried away, after the weights, which were at a distance of 300 fathoms in advance of the trawl, had been brought in board. The rope looked much chafed, as if it had been ground against rocks. The sounding-machine brought up no sample of the bottom; but a tow-net attached to the dredge-rope at the weights con­tained a little gravel and one or two small organisms. The bottom-temperature was 1°·7 C. The following day was fine, with light uncertain winds; on the 10th it was blowing half a gale and the sea was running too high for sounding-operations. On the 11th the weather was fine, the wind becoming more moderate towards noon; at 10 a.m. we sounded and put down the trawl in 2040 fathoms, with a bottom of bluish mud containing many Globigerinæ ,and a bottom-temperature of +0°·3 C. The position of the sounding was lat. 42° 32' S., long. 56° 27' W., about 200 miles to the eastward of Valdes Peninsula. Temperature-soundings were taken down to 1500 fathoms (Curve 318, Plate 27). This sounding gives a singularly rapid fall from 14º·2 on the surface to 2° C. at 125 fathoms; the edge of the Ant­arctic indraught appeared to be pushed up against the American shore by the western border of the southern branch of the reflux of the equa­torial current, as the Labrador current is banked up by its northern branch, the result being no doubt increased in both cases by the flinging up of the polar water against the western land-barrier on account of its low initial velocity.
In a paper which will he found in the “Proceedings of the Royal Society” for June, 1865, I gave methods for expressing the sum of certain series by definite integrals, or in other words, of expressing F( x ) by the form ∫PQ x dθ . As shown in my last paper, this method is immediately connected with the solution of those partial differential equations which have constant coefficients by definite integrals, a circumstance which never crossed my mind till lately. In the present communication I hope to make further extensions in both these directions.
Dear Sir,— In a short Note which I communicated to the Royal Society in December last I gave an account of certain observations relating to the electromotive phenomena of the uninjured gastrocnemius muscle of the frog. In commenting on these results I was led, I need not say unintentionally, to make a serious misstatement of the doctrine taught by Prof, du Bois-Reymond with reference to these phenomena. After comparing the electromotive properties of the muscle-cylinder derive from the gastrocnemius with those of the typical muscle-cylinder, as set forth in the “Law of the Muscle-current,” I stated that the phenomena, as they actually present themselves, had not been correctly described. It is this statement that I desire to correct. Shortly after the publication of my “Note” the magnificent collection of scientific papers in which Prof, du Bois-Reymond has brought together his electrophysiological researches appeared. The work had not long been in my possession before I became much more strongly impressed than I had been before with the extent and completeness of the investigations to which he has devoted the last thirty-five years. My attention was particularly directed to the paper, No. XVII. of the series, “Ueber das Gtesetz des Muskelstromes mit besonderer Berücksichtigung des M. Gastrocnemius vom Frosch.” In this very important research, with which, although it was originally published in 1863, I was, I regret to say, only acquainted at second hand, Du Bois-Reymond not only recognized the electromotive anomalies of the gastrocnemius, but explained them in the most elaborate manner as dependent on its peculiarities of structure.
It follows from the expansion of cos n θ in terms of the cosines of the multiples of θ , that n . n - 1/2. n - 2/3 ... n - r +1/ r = 2 n / π ∫ π 0 cos nθ cos ( n -2 r θdθ , and consequently this theorem can be used in the summation of series involving binomial coefficients. I propose to give a few examples of this.
In a paper, communicated to the Royal Society in March last, I described a series of Balanoglossus larvse, found by me in the Bahama Islands. The series extended from a larva with one pair of gill-slits to a form resembling in many ways a normal Tornaria; but the differences between this larva and the normal European form were so great as to induce me to believe that a process of degeneration was going on, and that the Tornaria-like creature was the oldest, not the youngest, of the series. On seeing my paper, Professor Spengel, whose researches on Balanoglossus are well known, wrote to me, informing me that I was altogether mistaken in my interpretation of the larvae which I had found, and that my series belonged in fact to the normal order of development.
On leaving England for Ascension Island in May 1862, Lieut. Rokeby was supplied by General Sabine with the following instruments for the purpose of making observations of magnetical variation and intensity, viz.:— A portable declinometer and unifilar for absolute observations of declina­tion and horizontal intensity, a Barrow’s dip-circle (No. 24), a differential declinometer, and a differential bifilar. The differential declinometer and the bifilar were erected at George Town, Ascension, in August 1862, and bihorary observations commenced; but in consequence of instability in the supports of the instruments, caused pro­bably by the shifting of the volcanic cinders which formed the ground at the observing-station, the observations made exhibit frequent discrepancies. The whole of the bifilar observations, and all the differential declinometer observations prior to June 1864, have therefore been omitted from the present discussion.
On the 14th of December 1862, a magnetic disturbance occurred about 6 o’clock in the afternoon, and was registered by means of the Kew magnetographs. As usual it was accompanied by an auroral display and by earth-currents, and the latter phenomena were observed at Greenwich by means of a system of telegraphic wires which had recently come into the possession of the Astronomer Royal. By the kindness of Mr. Airy, the Kew Observatory has been favoured with a copy of the curves which represent the earth-currents collected at Greenwich during the progress of this disturbance; and a comparison of these with the Kew magnetograph curves will form the subject of the following paper.
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