scholarly journals II. On the mathematical theory of the stability of earth-work and masonry

1857 ◽  
Vol 8 ◽  
pp. 60-61 ◽  
Keyword(s):  
Compressive Stress ◽  
Royal Society ◽  
Mathematical Theory ◽  
Natural Slope ◽  
The Earth ◽  
The Subject ◽  
The Difference ◽  
The Stability

In the preparation of my course of lectures, I have found it necessary to re-investigate much of the above-named branch of mechanics, and I have now a paper in preparation on the subject, which I propose to offer to the Royal Society when it is ready. In the meanwhile, it appears to me that the two fundamental principles on which my researches are based are of such a nature, that they may very properly be communicated to the Royal Society at once. They are as follows:― I. Principle o f the Stability of Earth . At each point in a mass of earth the directions of greatest and least compressive stress are at right angles to each other; and the condition of stability is, that at each point the ratio of the difference of those stresses to their sum shall not exceed the sine of the angle of natural slope of the earth.

scholarly journals XXXIII. On the figure of the earth

1826 ◽  
Vol 116 ◽  
pp. 548-578 ◽  
Keyword(s):  
Present State ◽  
Royal Society ◽  
Mathematical Theory ◽  
Second Order ◽  
The Earth ◽  
First Approximation ◽  
Figure Of The Earth ◽  
The Subject ◽  
The Difference

The ellipticity of the earth, deduced by Captain Sabine from a series of pendulum experiments the most extensive, and apparently the most deserving of confidence, that has ever been made, differs considerably from that which, as is generally believed, is indicated by geodetic measures. The difference can only be explained by errors of observation, by peculiarities of local circumstances, or by some defect in the theory which connects the figure of the earth with the variation of gravity on its surface: under the last head may be placed defects in the mathematical part of the theory, and errors in the assumptions of the original constitution and present state of the earth. It was with a view to ascertain the sufficiency of the mathematical theory, that I undertook the investigations contained in this paper. The celebrated proposition called Clairaut's theorem, by which the earth's ellipticity is inferred from the variation of gravity on its surface, is obtained only by the rejection of the squares and higher powers of the ellipticity. It is by the same rejection that the figure of the earth, supposed a heterogeneous fluid, is proved to be an elliptic spheroid. It appeared therefore probable, that a more accurate theory might introduce some modification into Clairaut's theorem, and might also show he figure of the earth to differ from an ellipsoid ; and there was no reason to think that the first approximation to that figure was more accurate, than the first approximation to the motion of the moon’s perigee. The result of my investigation does not at all serve to reconcile the pendulum observations made by Captain Sabine with the measures of degrees : and with respect to one object, which I hoped to obtain, I am therefore completely unsuccessful. The theory shows, however, that the earth’s figure, on the usual suppositions as to its constitution, is not an elliptic spheroid; and the formulæ which I have obtained will give the means of determining very exactly the figure of the earth, when the experiments on the variation of gravity, or the measures of arcs on the earth’s surface, shall be thought sufficiently accurate. As the subject is one whose interest is not confined to the present time, I have ventured to offer my investigations to the Royal Society. The first part of the following sheets contains the theory of the heterogeneous earth, pushed so far as to include all the terms of the second order: it is succeeded by a comparison of this theory with Captain Sabine’s results, and with the best arcs of the meridian that have been measured and in the conclusion, I have offered some suggestions on the propriety of repeating some of these measures.

III. On the figure, dimensions, and mean specific gravity of the Earth, as derived from the ordnance trigonometrical survey of Great Britain and Ireland

1857 ◽  
Vol 8 ◽  
pp. 111-116 ◽  
Keyword(s):  
United Kingdom ◽  
Great Britain ◽  
Specific Gravity ◽  
Royal Society ◽  
The United Kingdom ◽  
The Earth ◽  
The Difference ◽  
The Government

The Trigonometrical Survey of the United Kingdom commenced in the year 1784, under the immediate auspices of the Royal Society; the first base was traced by General Roy on the 16th of April of that year, on Hounslow Heath, in presence of Sir Joseph Banks, then President of the Society, and some of its most distinguished Fellows. The principal object which the Government had then in view, was the connexion of the Observatories of Paris and Greenwich by means of a triangulation, for the purpose of determining the difference of longitude between the two observatories.

scholarly journals XX. On new compounds of carbon and hydrogen, and on certain other products obtained during the decomposition of oil by heat

1825 ◽  
Vol 115 ◽  
pp. 440-466 ◽  
Keyword(s):  
High Temperatures ◽  
Liquid State ◽  
Royal Society ◽  
The Subject ◽  
The Difference ◽  
New Compounds ◽  
Oil Gas

The object of the paper which I have the honour of sub­mitting at this time to the attention of the Royal Society, is to describe particularly two new compounds of carbon and hydrogen, and generally, other products obtained during the decomposition of oil by heat. My attention was first called to the substances formed in oil at moderate and at high temperatures, in the year 1820; and since then I have endea­voured to lay hold of every opportunity for obtaining information on the subject. A particularly favourable one has been afforded me lately through the kindness of Mr. Gordon, who has furnished me with considerable quantities of a fluid obtained during the compression of oil gas, of which I had some years since possessed small portions, sufficient to excite great interest, but not to satisfy it. It is now generally known, that in the operations of the Portable Gas Company, when the oil gas used is compressed in the vessels, a fluid is deposited, which may be drawn off and preserved in the liquid state., The pressure applied amounts to 30 atmospheres; and in the operation, the gas previously contained in a gasometer over water, first passes into a large strong receiver, and from it, by pipes, into the portable vessels. It is in the receiver that the condensation principally takes place; and it is from that vessel that the liquid I have worked with has been taken. The fluid is drawn off at the bottom by opening a conical valve: at first a portion of water generally comes out, and then the liquid. It effervesces as it issues forth; and by the difference of re-­fractive power it may be seen, that a dense transparent vapour is descending through the air from the aperture. The effervescence immediately ceases; and the liquid may be readily retained in ordinary stoppered, or even corked bottles; a thin phial being sufficiently strong to confine it. I understand that 1000 cubical feet of good gas yield nearly one gallon of the fluid.

Royal fossils: The Royal Society and progress in palaeontology

2001 ◽  
Vol 55 (1) ◽  
pp. 51-67
Author(s):  
G. E. Budd
Keyword(s):  
Royal Society ◽  
Earth Science ◽  
Evolutionary Morphology ◽  
The Earth ◽  
Conflicting Demands ◽  
Past Life ◽  
Evolutionary Radiations ◽  
The Subject ◽  
Science Interests ◽  
The 19Th Century

The study of the remains of past life is a relatively young discipline, and one that has been defined partly by conflicting demands placed on it by both the life and Earth sciences. Fellows of The Royal Society have made critical contributions both to the growth of material knowledge of the subject and to the expansion of its theoretical basis, especially in the formative decades at the beginning of the 19th century. In particular, British palaeontologists and stratigraphers were pre-eminent in the shift away from viewing the Earth as a young creation conforming to the account in Genesis and towards the modern view of it as an ancient and dynamic system with a distinct history. Despite these early Earth science interests, palaeobiological subjects were also soon a topic of research, ranging from the reconstruction of ancient ecologies to the description of extinct organisms such as the dinosaurs. Nevertheless, palaeontology has notoriously failed to make signal contributions to evolutionary theory and the recent development of areas where palaeontology does have a unique imput to make, such as the global patterns of biodiversity through time and the controversy over mass extinction, has largely been a North American concern. British palaeontologists have, however, made fundamental contributions to the study of major evolutionary radiations, and this tradition is well represented in the current research interests of extant Fellows. Palaeontology remains a poorly defined discipline with little sense of an overarching paradigm, but one important future prospect probably lies with the revival of evolutionary morphology and development as neontological subjects.

scholarly journals XXII. An improved solution of a problem in physical astronomy; by which, swiftly converging series are obtained, which are useful in computing the perturbations of the motions of the Earth, Mars, and Venus, by their mutual attraction. To which is added an appendix, containing an easy method of obtaining the sums of many slowly converging series which arise in taking the fluents of binominal surds, &c. In a letter to the Rev. Nevil Maskelyne, D. D. F. R. S. and Astronomer Royal

1798 ◽  
Vol 88 ◽  
pp. 527-566
Keyword(s):  
Royal Society ◽  
Easy Method ◽  
Strong Argument ◽  
Mutual Attraction ◽  
The Earth ◽  
Royal Observatory ◽  
The Subject ◽  
The Many ◽  
Nevil Maskelyne

Reverend Sir, Such is the subject of the inclosed paper, and such the repu­tation for skill and industry, which the many valuable papers you have communicated to the Royal Society, and your other learned works, have justly procured to you, that it could not with more propriety be submitted to the judgment of any other person than yourself, even if the writer of it were a stranger to you. But there are circumstances which render my presenting it to you, in some measure, a duty. I had the advantage of being, for some years, your Assistant in the Royal Observatory at Greenwich; during which time, you made the important observations on the mountain Schehallien , in Scotland, which afford an ocular demonstration of the attraction of that mountain, and a strong argument for the general attraction of matter, a subject nearly connected with that of the following pages; and it was from you that I received the problem of which you will here find an improved solution.

scholarly journals On the influence of the method of approximation of an unknown function on the stability of numerical methods for solving the anomalous diffusion equation

2019 ◽  
pp. 23-29
Author(s):  
Vladimir Andreevich Litvinov
Keyword(s):  
Diffusion Equation ◽  
Numerical Solution ◽  
Anomalous Diffusion ◽  
Caputo Derivative ◽  
Numerical Algorithms ◽  
Difference Approximation ◽  
Liouville Derivative ◽  
The Subject ◽  
The Difference ◽  
The Stability

The subject of the research is numerical algorithms for solving fractional partial differential equations. The object of the study is the stability of several algorithms for the numerical solution of the anomalous diffusion equation. Algorithms based on the difference representation of the fractional Riemann-Liuville derivative and the Caputo derivative for various orders of accuracy are considered. A comparison is made of the results of numerical calculations using the analyzed algorithms for a model problem with the exact solution of the anomalous diffusion equation for various orders of the fractional derivative with respect to the spatial coordinate. The results of the work were obtained on the basis of the analysis of the constructed difference schemes for stability, the conducted numerical experiments and a comparative analysis of the data obtained. The main conclusions of the study are the advantage of using the approximation of the fractional Caputo derivative compared to using the difference scheme for the fractional Riemann-Liouville derivative in the numerical solution of the anomalous diffusion equation. The paper also indicates the importance of choosing the method of difference approximation of the second derivative, which is a derivative of the Caputo.

scholarly journals III. Photochemical researches.—Part V. On the measurement of the chemical action of direct and diffuse sunlight

1863 ◽  
Vol 12 ◽  
pp. 306-312 ◽  
Keyword(s):  
Royal Society ◽  
Chemical Action ◽  
The Earth ◽  
The Subject ◽  
Methods Of Measurement

In one of the four communications which the authors have already had the honour of presenting to the Royal Society on the subject of the measurement of the chemical action of light, the attempt was made to determine experimentally the laws regulating the distribution of the chemical action of the sunlight and diffuse daylight on the surface of the earth when the sky is perfectly unclouded and the atmosphere clear. The methods of measurement there employed do not, unfortunately, apply to the much more usually occurring case of cloudy skies and hazy atmosphere.

XVI. The Bakerian Lecture.— On the radiation of heat from the moon, the law of its absorption by our atmosphere, and of its variation in amount with her phases

1873 ◽  
Vol 163 ◽  
pp. 587-627 ◽  
Keyword(s):  
Royal Society ◽  
Radiant Heat ◽  
The Moon ◽  
Short Series ◽  
The Earth ◽  
Series Of Experiments ◽  
The Subject ◽  
The Law

In the years 1869 and 1870 I communicated to the Royal Society the results of a series of experiments made with the view of determining, if possible, the amount of radiant heat coming to the earth from the moon in various conditions of phase, and the nature of that heat as regards the average refrangibility of the rays. Though more successful than I had at first been led to expect, the imperfect accordance between many of the observations still left much to be desired, and the novelty and importance of the subject appeared sufficient to render it advisable to pursue the investigation with greater care and closer attention to details than had hitherto been deemed necessary. Since the conclusion of the series of observations which form the subject of the second paper above referred to, nothing (with the exception of a short series of observations in August and October 1870, of which mention is made towards the end of this paper) was done towards pursuing the subject till the spring of the following year (1871), when the series of observations which form the subject of the present paper were commenced, the same apparatus (only slightly modified) being used and the same method of observation adopted; but, with the view of obtaining an approximate value of the absorption of the moon’s heat in its passage through our atmosphere, and of rendering possible the satisfactory comparison of observations made at different zenith-distances of the moon, the observations were in many cases carried on at intervals at all possible zenith- distances on the same night, and the most favourable opportunities for observing the moon at very different zenith-distances in various conditions of the atmosphere were not lost.

scholarly journals XXIV. On the Indian arc of meridian

1861 ◽  
Vol 151 ◽  
pp. 579-594 ◽  
Keyword(s):  
Royal Society ◽  
A Priori ◽  
Central India ◽  
Negative Sign ◽  
Great Care ◽  
Present Communication ◽  
Direct Process ◽  
Resultant Effect ◽  
The Subject ◽  
The Difference

It is with pleasure that I request the attention of the Royal Society to the present com­munication, in continuation and completion of my former papers, because I think that the anomalies which the Indian Arc has appeared to present are here traced to the true causes. 1. I will explain what those anomalies were. On completing a laborious and wellexecuted survey of the two northern portions of the Indian Arc of Meridian, between Kaliana (29° 30' 48") and Kalianpur (24° 7' 11"), and Kalianpur and Damargida (18° 3' 15"), Colonel Everest found that their astronomical and geodetical amplitudes differed considerably; in the higher arc the geodetic amplitude he found to be in excess by 5"·236, in the lower of the two ares in defect by 3"·791. The three stations had been selected with great care, and were finally chosen as being apparently free from all disturbing causes. Indeed, a fourth station which had been at one time adopted, Takal Khera in Central India, was rejected by Colonel Everest because a neighbouring hillrange was discovered on calculation to produce a deflection of about 5". Kaliana had been chosen nearly sixty miles from the lower hills at the foot of the Himmalaya Moun­tains, in the full conviction that it would be free from mountain influence. The surprise was therefore great when, on the completion of the survey of the two arcs in question, these two errors were brought to light. The first was attributed to the influence of the Himmalayas, but without any calculation; but the second, with its negative sign, received no interpretation. At this stage I devised a method of calculating the effect of the Himmalayas by a direct process; and found that the deflections produced are far greater than the errors which had to be explained, and the negative sign was left alto­gether unaccounted for. Thus the perplexity was increased. It next occurred to me that the vast Ocean to the south of India might have some influence on the plumb-line. On making the necessary calculations the effect of this cause was found, as the moun­tain attraction had been, to be far greater than had been anticipated; the negative sign was still unexplained, and the difficulties were not cleared up. No other cause of dis­turbance was apparent at the surface. But I showed by calculation that in the crust below one might exist sufficient to reduce the large deflections occasioned by the Moun­tains and the Ocean, and make them accord with the results deduced by Colonel Everest from the arcs themselves. But, being hidden from our sight, neither the magnitude nor indeed the existence of this cause could be à priori ascertained, much less reduced to calculation. Whether, moreover, the errors brought to light by Colonel Everest arose solely from local attraction, or from local attraction combined with some local peculiarity in the curvature of the Indian Arc, was not apparent; so that the subject of local attrac­tion and its influence on geodetic operations in this country, was still involved in obscu­rity, and the anomalies of the Indian Arc remained unexplained in the papers which I have hitherto forwarded to the Society. In the present communication I think ambi­guity is removed. It is demonstrated that no peculiarity in the curvature of the arc can produce any part of the errors brought to light by Colonel Everest; that those errors arise solely from local attraction; that they are in fact the exact measure of the difference of the resultant local attraction at the two extremities of each arc, from what­ ever causes the attraction may arise—mountains, ocean, or crust; lastly, it is proved that there are hidden causes in the crust below the Indian Arc, and the differences of their resultant effect upon the stations of the arc are computed. An inference from these results is, that the relative position of places in a Map, laid down from geodetic operations, is accurate, being altogether unaffected by local attraction; though the position of the Map itself on the terrestrial spheroid will be dependent upon the observed latitude of some one station in it, and that observed latitude will be affected by the local attraction at that place. To determine the absolute latitude in some one station connected with the geodetic operations is still a desideratum.

‘But where shall my soul repose?’: Nonconformity, Science and the Geography of the Afterlife, c. 1660–1720

2009 ◽  
Vol 45 ◽  
pp. 268-279
Author(s):  
Andrew Cambers
Keyword(s):  
Seventeenth Century ◽  
Religious Belief ◽  
Scientific Inquiry ◽  
Royal Society ◽  
Scientific Revolution ◽  
Science And Religion ◽  
The Earth ◽  
The Subject ◽  
Religious Cultures ◽  
Henry More

Life, the afterlife, and life beyond the Earth are matters of scientific inquiry as well as religious belief. As we might expect, in the wake of the scientific revolution of the seventeenth century, the afterlife was subjected to new scrutiny. Such scrutiny, notably the demonology of Joseph Glanvill and Henry More, both fellows of the Royal Society, was undoubtedly scientific and serious, even if it has rarely been treated as such by scholars preferring to treat belief in witchcraft as a hangover from an earlier age. Far from being opposed, or necessarily pulling in opposite directions, the conjunction of science and religion in this era breathed new life into old problems and opened up new questions for debate. One such area, with a long history as a philosophical conundrum, was the possibility of life beyond Earth. It is this question, its place within religious cultures, and its relation to traditional ideas about the afterlife, that is the subject of this essay.

Sign in / Sign up

Export Citation Format

Share Document