Search

n/a

1. The hypothesis by which the figures of the heavenly bodies are theoretically explained has long engaged the attention of geologists and geometers, without having acquired any important improvements. Great as have been the discoveries which have originated from this hypothesis, it remains in nearly the same philosophical position as that to which it had arrived when Clairaut published his Theory of the Figure of the Earth. During the period of more than a century which has elapsed since the appearance of that immortal work, the improvements which have been made in the theory of the figures of the planets, appear to consist chiefly in discoveries connected with the attractions of bodies, and in some important generalizations of the equili­brium and motions of fluids. Comparatively few positive discoveries have however been as yet made in geology as deductions from the hypothesis of the primitive fluidity of the earth. In explana­tion of this circumstance several causes may be assigned, one of which appears to be the limited nature of the hypothesis. It has not been considered sufficient to suppose that the earth was originally a mass of heterogeneous matter in a fluid state; an additional supposition has been made, in support of which I am not aware that any evidence has been ever adduced. The supposition alluded to is, that the volume of the entire mass and the law of density of the fluid have not been changed by the soli­dification of a part of that fluid, no matter how far the solidification may have pro­ceeded; or in other words, that the distribution of the molecules composing the earth is the same in the present state of our planet as that which they had when the mass was fluid. Although no precise evidence can be brought forward for the exami­nation of this portion of the hypothesis, it appears not to be entirely consistent with what is known respecting the solidification of fluids. It is thus defective from appear­ing to involve an unproved and improbable physical law. Its exclusion from the hypothesis will make the latter more general and more applicable to the explanation of certain cosmical phenomena. Making the simplified hypothesis the basis of my investigations, it shall be their object further to generalize the theory of the figure of the earth, and to examine the nature and the energy of the physical and mechanical actions which may have been exerted upon its surface during its different geological transformations.

n/a

(1858). XXVI. On the distribution of heat over islands, and especially over the British Isles. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Vol. 16, No. 107, pp. 241-257.

(1880). XVIII. On the figure of the planet Mars. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Vol. 10, No. 60, pp. 119-122.

Eighty years have elapsed since Dr. Thomas Young published a theorem which has since found a place in most of the scientific treatises on mechanism. This theorem states that in order to obtain a given value or velocity ratio by a train of toothed wheels and pinions of which all the pairs are equal, the ratio of the number of teeth in each wheel to the number in each pinion should be as 359 to 100, when the total number of teeth in the train is the least possible. The late Professor Willis has remarked that the rule deduced from this theorem seemed not to have much practical utility, but he illustrates his remarks by referring to the trains of wheels and pinions employed in clockwork.

n/a

In that division of hydromechanics which is devoted to the investigation of the flow of liquids through pipes and open channels, the resistance due to the friction of the contained liquid against the sides of the pipes or channels has led to expressions for the velocity as a function of the dimensions and shape of the cross-section commonly designated as the hydraulic mean depth. This quantity is defined as the quotient of the area of the cross-section of the liquid by that part of its perimeter in contact with the pipe or channel. In a full pipe this perimeter is identical with that of the pipe’s cross-section, and in practice this is generally a circle.

My dear Sir,—In your work on 'Pendulum Experiments,’ and subsequently in a paper printed in the ‘Philosophical Magazine’ for April 1846, you have directed attention to the influence of the Gulf-stream on the winters of the British Islands. You have been led to attribute the remarkably mild winters which we sometimes experience, to an abnormal extension of the warm waters of that stream towards our latitudes. In this view I entirely concur, and beg to submit the following additional proof of its correctness. An abnormal extension of the Gulf-stream in the direction of the British Isles necessarily implies that the waters bathing our coasts acquire a temperature which exceeds their mean temperature for the season of the year at which the extension takes place. The temperature of the air over the sea, and finally of the air over the islands, becomes sensibly increased. The entire temperature at any point will thus depend chiefly on what it gains from sunshine, and from the warm sea-air, and on what it loses by radiation. If the excess of what it gains from sunshine over its losses by radiation be considerable compared to its gain from the influence of the sea, the temperature will depend principally on the latitude. If, on the contrary, the thermal influence of the sea be very considerable, places at different latitudes may possess nearly equal temperatures. It follows that during cold winters we should expect a greater difference between the temperatures of the southern coasts of Great Britain and Ireland, and the remainder of their coasts, than during mild winters. It also follows, that during warm winters the difference of temperature between stations situated on coast and inland stations having nearly the same latitude, should be greater than during cold winters.

In the first part of these researches, I have endeavoured, by generalizing the hypothesis on which is usually founded the theory of the earth’s figure, not only to improve that theory, but also to establish a secure basis for researches into the changes which may have taken place within and at the surface of the earth during the epochs of its geological history. Although I stated that no precise physical evidence could be adduced for the examination of the assumption that the molecules of the primitive fluid, supposed to have constituted the earth, retained their positions after solidification, it yet appears that such evidence exists, if we may be permitted to draw any conclusions relative to the physical properties of substances in the earth’s interior, from the observed physical properties of substances at its surface. Professor Bischof of Bonn, has shown that Granite contracts in volume in passing from the fluid to the solid crystalline state, from 1 to ⋅7481, Trachyte from 1 to ⋅8187, and Basalt from 1 to ⋅8960. The first of these rocks appears, as far as can be observed, to constitute the greater part of the earth; hence the assumption alluded to must be considered not only as superfluous, but as erroneous. In this Part it is my object to discover relations between the interior structure of the earth and phenomena observed at its surface, and also the effects of the reaction of the fluid nucleus, described in Article 6, Part I., upon the solid crust. I divide this Part into sections, each containing a distinct investigation, the order of arrangement of these sections being determined according to their fundamental importance. The statement of the geological results capable of being deduced from these investigations is, for greater clearness, reserved for the end. Such of these results as chiefly depend on the validity of the reasonings used in Section III. are presented with some diffidence, owing to the imperfect experimental knowledge we possess respecting the subjects discussed in that section. The diminution of the earth’s mean radius by refrigeration is neglected all through, except where the contrary is specially mentioned.

In this communication the author states that, having in Part I. (read to the Society in December 1846) endeavoured, by generalizing the hypothesis on which is usually founded the theory of the earth’s figure, not only to improve that theory, but also to establish a secure basis for researches into the changes which may have taken place, within and at the surface of the earth, during the epochs of its geological history, his object here is to discover relations between the interior structure of the earth and phenomena observed at its surface, and also the effects of the reaction of the fluid nucleus, described in Part I., upon the solid crust. This memoir is divided into sections, each containing a distinct investigation; and the statement of the geological results is given at the end. I. The Pressures of the Shell and Nucleus at their surface of contact . In the investigation of these pressures the earth is supposed to consist of a nucleus of fluid matter inclosed in a solid shell, the inner and outer surfaces of which are spheroidal, but nearly spherical; and both shell and nucleus are supposed to consist of strata varying in density according to some unknown inverse law of the radii. The pressure at the inner surface of the shell is conceived to be due to a constant pressure, which is the same for every point, and a variable pressure, arising from the difference in form of the surface of the nucleus and inner surface of the shell. On these suppositions, simple expressions for the pressure on any stratum of the nucleus and on the shell’s inner surface are deduced.

n/a

The principal object of this memoir is to develope the laws of the distribution of temperature in the portion of the atmosphere in contact with the earth, and to point out the connexion between the phenomena of aërial temperature and those of soil and oceanic temperature. The author maintains that hitherto no perfect physical representation of the distribution of heat over the earth’s surface has been obtained.

In the paper on “Hydraulic Problems on the Cross-sections of Pipes and Channels,” it was shown that the greatest hydraulic mean depth was that for a channel formed by a segment of a circle, and bounded by an arc of 257° 27'. It is easy to find by a similar process the wetted perimeter of a circular pipe corresponding to the maximum discharge when the velocity of the liquid is due only to the inclination of the pipe.

n/a

n/a

n/a

ARCHDEACON PRATT'S letter in NATURE for June 22 calls for some remarks on my part. He communicates a few marginal notes written by Mr. Hopkins on a copy of the second part of my “Researches in Terrestrial Physics,” which appeared in the “Philosophical Transactions,” and seems seriously to regard these curt expressions as judicial utterances beyond which there can be no appeal.

n/a

THE question of the solidification of the crust of the earth from the fluid interior nucleus, as referred to by Mr. Mathieu Williams, in NATURE, vol. xv. p. 5, is one which has been long since fully discussed in my papers in the Philosophical Transactions, the Atlantis, vol. i., and in a paper of which an abstract appears in the Report of the British Association for 1856. As far as I am aware, no person has controverted my conclusions as to the process of solidification of the earth. The results are, in the main, somewhat similar to those so admirably illustrated and enforced by Mr. Robert Mallet, and also such as Mr. Williams upholds in this journal.

IN the report of the proceedings of the Academy of Sciences at Paris for October 22 (NATURE, vol. xviii. p. 712), with reference to a communication from me relative to the flattening of the planet Mars, it is stated that I confirm M. Amigues' conclusions from independent calculations. Allow me to say that the communication referred to, has clearly established by reference to dates of publication, that the calculations I had been the first to make were confirmed by the subsequent results of M. Amigues. A formula presented by me in February, 1870, in which the mean density, surface density, and velocity of rotation of Mars are expressed in connection with its ellipticity, was reproduced by apparently identical methods by M. Amigues, in the Comptes Rendus for June, 1874. The conclusions drawn from this formula by M. Amigues were, that in order to account for the high amount of ellipticity assigned to Mars by many astronomers its mean density must be less than its surface density. My conclusion was, on the contrary, that the high ellipticity alluded to was improbable and that the values given by Bessel, Oudemanns, Johnson, and other astronomers, whereby Mars would have an ellipticity nearly the same as that of the earth, should be adopted until the subject was cleared up by fresh observations.

THE relations between weight and mass, gravity and acceleration, are so well defined in all good treatises on dynamics, that it appears superfluous to dwell on these questions. But as it has been stated by Prof. Barrett, vol. xiii., p. 385, that the C. G. S. system of units has been introduced into the course of Mechanics in this College, I may be permitted to say that the system actually employed is not that referred to by your correspondent. I generally employ the kilogramme, metre, and second, and sometimes the foot, pound, and second, to measure a dynam or unit of force. The dynamometers alluded to as about to be exhibited at the Loan Exhibition of Scientific Instruments at South Kensington are suitable to the former system, and I use them for the measurement of dynams in kilogrammetres. One of these dynamometers is graduated for every 200 grammes up to 100 kilogrammes, the other for every 100 grammes up to 10 kilogrammes, and they cannot be depended on for results within the tenth of a kilogramme. Spring dynamometers, though suitable for the large units employed in mechanics, are totally unfit for measuring units on the C. G. S. system. I concur with Prof. Everett, in his book on this system, when he says:—“A spring balance, it is true, gives a direct measurement of force, but its indications are too rough for purposes of accuracy” (p. 8). Spring dynamometers are therefore unsuited to a system where the units are measured by 1/981 of a gramme, or about 1/63 of a grain, as in the C. G. S. system.

The result obtained in the paper on the cell of the honey bee, read November 26, 1885, by which the side of one of the lozenges composing the cell was found to be three times the difference between the two parallel edges forming the sides of one of the trapeziums of the prism, gives a very simple method for constructing the figure as follows. On a straight line take a part AD, and lay off DC equal to twice AD, from D erect a perpendicular, and with radius AC = 3DA cut off DP; AC and AP are sides of the lozenge ACEP, which fulfils the required conditions. It is manifest that from this lozenge the remaining two lozenges and also the six trapeziums can he immediately constructed.

(1844). A meteorological phaenomenon. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Vol. 24, No. 158, pp. 238-239.

If from the intersections of the diagonals of the three lozenges forming the apex of the cell, perpendiculars be erected, these will meet at a point on the cell’s axis, and each of them is manifestly the radius of a sphere tangent to the three lozenges. A plane passing through a radius and the axis passes through the short diagonal, e , of the lozenge whose length is h √(3/2); using the notation and results of the paper above cited. The distance intercepted on the axis by a perpendicular let fall from the middle of the lozenge is equal to x = h /(2√2), and as this perpendicular is manifestly equal to √(¼ e 2 — x 2 ), and as we have evidently— r/√(¼ e 2 — x 2 ) = e /2 x , we obtain r = ½ h √3.

The author refers to a communication to the Geological Society by Sir John Lubbock, in which he appeals, in support of the possibility of a change in the earth’s axis, to the influence of two disturbing causes, which appear to have almost entirely escaped the notice of Laplace and Poisson in their investigations on the stability of the earth’s axis of rotation:—1. The necessary displacement of the earth’s interior strata arising from chemical and physical actions during the process of solidification. 2. The friction of the resisting medium in which the earth is supposed to move.

The well-known problem of the bee s cell occupied the attention of eminent mathematicians early in the last century, and it is still presented as an interesting example of geometrical maxima and minima. In 1743 Maclaurin communicated to the Royal Society a solution of the question, which appears in the “Philosophical Transactions,” and it seems that the comparison between the mathematical results and the actual cells was effected by angular measurements. Long since a simple method occurred to me for the construction of the figure without employing angles, and as I have not been able to find it in any publication, I venture to submit it in this short paper.

The author’s investigations of the figure of the earth proceed on the hypothesis of its having originally been a heterogeneous fluid mass, possessing only such general properties as those which have been established for fluids; and independently of the supposition, with which the theory has generally been complicated, that the vo­lume of the entire mass, and the law of the density of the fluid, have suffered no change in consequence of the solidification of a part of that fluid. Assuming the figure of the mass to be an ellipsoid of revolution, the author obtains general analytical expressions for its ellipticity, and for the variation of gravity at its surface. He gives a general sketch of the consequences that may result from the im­proved hypothesis of the primitive figure of the earth, to physical geology, that is, to the changes occurring upon the external crust of the earth during the process of its solidification, resulting both from calorific and chemical changes taking place among its different parts, and giving rise to a process of circulation throughout the fluid por­tions of the mass. The present memoir is only the first of a series which the author announces it is his intention to communicate to the Society on the same subject.

The results presented in the author’s paper, entitled “ On the Simul­taneous Distribution of Heat throughout the superficial parts of the Earth" , are confirmed and extended in the present communication.