scholarly journals VII.—On the theory of the perturbations of the planets

1832 ◽  
Vol 122 ◽  
pp. 195-228 ◽  
Keyword(s):  
Differential Equations ◽  
General Structure ◽  
Dynamical Problem ◽  
The Body ◽  
The Other ◽  
The Sun ◽  
First Case ◽  
Foreign Countries ◽  
Analytical Formulas ◽  
Pass Through

The perturbations of the planets is the subject of reiterated researches by all the great geometers who have raised up Physical Astronomy to its present elevation. They have been successful in determining the variations which the elements of the orbit of a disturbed planet undergo; and in expressing these variations analytically, in the manner best adapted for computation. But the inquirer who turns his attention to this branch of study will find that it is made to depend upon a theory in mechanics, which is one of considerable analytical intricacy, known by the name of the Variation of the Arbitrary Constants. Considerations similar to those employed in this theory were found necessary in Physical Astronomy from its origin; but the genius of Lagrange imagined and completed the analytical processes of general application. In a dynamical problem which is capable of an exact solution, such as a planet revolving by the central attraction of the sun, the formulas constructed by Lagrange enable us to ascertain the alterations that will be induced on the original motions of the body, if we suppose it urged by new and very small forces, such as the irregular attractions of the other bodies of the planetary system. General views of this nature are very valuable, and contribute greatly to the advancement of science. But their application is sometimes attended with inconvenience. In particular cases, the general structure of the formulas may require a long train of calculation, in order to extricate the values of the quantities sought. It may be necessary for attaining this end to pass through many differential equations, and to submit to much subordinate calculation. The remedy for this inconvenience seems to lie in separating the general principles from the analytical processes by which they are carried into effect. In some important problems, a great advantage, both in brevity and clearness, will be obtained by adapting the investigation to the particular circumstance of the case, and attending solely to the principles of the method in deducing the solution. It may therefore become a question whether it be not possible to simplify physical astronomy by calling in the aid only of the usual principles of dynamics, and by setting aside every formula or equation not absolutely necessary for arriving at the final results. The utility of such an attempt, if successful, can hardly be doubted. By rendering more accessible a subject of great interest and importance, the study of English mathematicians may be recalled to a theory which, although it originated in England, has not received the attention it deserves, and which it has met with in foreign countries. The paper which I have the honour to submit to the Royal Society, contains a complete determination of the variable elements of the elliptic orbit of a disturbed planet, deduced from three differential equations that follow readily from the mechanical conditions of the problem. In applying these equations, the procedure is the same whether a planet is urged by the sole action of the central force of the sun, or is besides disturbed by the attraction of other bodies revolving about that luminary; the only difference being that, in the first case, the elements of the orbit are all constant, whereas in the other case they are all variable. The success of the method here followed is derived from a new differential equation between the time and the area described by the planet in its momentary plane, which greatly shortens the investigation by making it unnecessary to consider the projection of the orbit. But the solution in this paper, although no reference is made to the analytical formulas of the theory of the variation of the arbitrary constants, is no less an application of that method, and an example of its utility and of the necessity of employing it in very complicated problems.

On the theory of the perturbations of the planets

1837 ◽  
Vol 3 ◽  
pp. 98-98
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
The Other ◽  
The Sun ◽  
Constant Force ◽  
First Case ◽  
Complete Determination ◽  
Analytical Formulae ◽  
Sole Action

The methods hitherto employed by mathematicians for determining the variations which the elements of the orbit of a planet undergo in consequence of perturbation, and for expressing these variations analytically in the manner best adapted for computation, are found to depend upon a theory in mechanics, of considerable intricacy, known by the name of the Variation of the Arbitrary Constants . In seeking the means for abridging the severe labour of the calculations, we must separate the general principles on which they are founded from the analytical processes by which they are carried into effect; and in some important problems great advantage is obtained by adapting the investigation to the particular circumstance of the case, and attending solely to the principles of the method in deducing the solution. The author suggests the possibility of simplifying physical astronomy by calling in the aid of only the usual principles of Dynamics, and by setting aside every formula or equation not absolutely necessary for arriving at the final results. The present paper contains a complete determination of the variable elements of the elliptic orbit of a disturbed planet, deduced from three differential equations, that follow readily from the mechanical conditions of the problem. In applying these equations the author observes, the procedure is the same whether a planet is urged by the sole action of the constant force of the sun, or is besides disturbed by the attraction of other bodies revolving round the luminary; the only difference being that, in the first case, the elements of the orbit are all constant, whereas in the other case they are all variable. The success of the method followed by the author is derived from a new differential equation between the time and the area described by the planet in its momentary plane, which greatly shortens the investigation by rendering it unnecessary to consider the projection of the orbit. But the solution given in the present paper, although it makes no reference to the analytical formulæ of the theory of the Variations of the Arbitrary Constants , is no less an application of that method and an example of its utility, and of the necessity of employing it in very complicated problems.

scholarly journals On the Geodetic Rotation of the Major Planets, the Moon and the Sun

2009 ◽  
Vol 44 (2) ◽  
pp. 43-52
Author(s):  
G. Eroshkin ◽  
V. Pashkevich
Keyword(s):  
Angular Velocity ◽  
Reference Frame ◽  
Velocity Vector ◽  
Previous Investigation ◽  
The Body ◽  
The Other ◽  
The Sun ◽  
The Moon ◽  
Angular Velocity Vector

On the Geodetic Rotation of the Major Planets, the Moon and the SunThe problem of the geodetic (relativistic) rotation of the major planets, the Moon and the Sun was studied in the paper by Eroshkin and Pashkevich (2007) only for the components of the angular velocity vectors of the geodetic rotation, which are orthogonal to the plane of the fixed ecliptic J2000. This research represents an extension of the previous investigation to all the other components of the angular velocity vector of the geodetic rotation, with respect to the body-centric reference frame from Seidelmann et al. (2005).

I. Researches on the foraminifera

1859 ◽  
Vol 149 ◽  
pp. 1-41 ◽  
Keyword(s):  
General Structure ◽  
Detailed Comparison ◽  
The Body ◽  
The Other ◽  
General Plan ◽  
Wide Range ◽  
Preceding Case ◽  
Adjacent Segments ◽  
Comparative Inquiry ◽  
Range Of Variation

119. In my preceding memoirs, I have shown that two very dissimilar types of structure present themselves among the Foraminifera; one characterized by its simplicity, the other by its complexity. In the former, of which Orbitolites , Orbiculina , and Alveolina are typical examples, the calcareous skeleton does not present any definite indications of organization, but seems to have been formed by the simple calcification of a portion of the homogeneous sarcode-body of the animal; that the sarcode-body is but very imperfectly divided into segments, the communications between the cavities occupied by these segments being very free and irregular; the form of the segments themselves, and the mode of their connexion, are alike inconsistent; and even the plan of growth, on which the character of the organism as a whole depends, though preserving a general uniformity, is by no means invariable maintained. In the latter, to which Cycloclypeus and Heterostegina belong, we find the calcareous skeleton presenting a very definite and elaborate organization; the several segments of the body are so completely separated from each other, that they remain connected only by delicate threads of sarcode; each segment thus isolated has its own proper calcareous envelope, which seems to be moulded (as it were) upon it, and this envelope or shell is perforated with minute parallel tubuli, closely resembling those of dentine except in the absence of bifurcation or ramification; the partition-walls between adjacent segments are consequently double, and are strengthened by an intermediate calcareous deposit, which is traversed by a system of inosculating passages that seems properly to belong to it. The form of the segments, their mode of communication, and consequently the general plan of growth, have a very considerable degree of constancy; and altogether the tendency is strongly manifested in this type, to the greater individualization of the parts of the composite body, which in the preceding must be looked upon rather as constituting one aggregate whole. 120. I purpose in the present memoir to carry on this contrast, by presenting a detailed comparison of the structure of two generic forms, which, whilst they so far agree in general plan of growth as not only to have been ranked by M. d'Orbigny side bv side in his order Hélicostègues , but to have been placed by other systematists in close apposition, differ in the most marked manner as to all the particulars just enumerated. Both these types are of peculiar interest:- the first, Peneroplis , on account of the very wide range of variation it presents, which has led to the establishment of three genera , apparently distinguishable by well-marked differences in conformation, upon what I feel satisfied will prove to be but individual modifications of one and the same specific type ;— the second, Operculina , as being the nearest existing representative of Nummulites , and consequently as affording not merely the key to the elucidation of the structure, but also the basis for the determination of the value of the reputed species, of that genus, by the study of the range of variation which it presents; this range being, though more restricted than in the preceding case, still quite sufficient to justify a large multiplication of species, in the estimation of those who do not practise that extended method of comparative inquiry, on the importance of which I have dwelt in a former Memoir (74). With the latter of these genera, as also with Nummulites , I shall prove that the genus Amphistegina is closely allied; although M. d’Orbigny, misled by the marked want of symmetry and by the alternation in the disposition of the chambers, which are exhibited by certain forms of that type, has placed it in a different order, Entomostègues . For I shall have to show that a gradational variety in this respect, ending in complete symmetry, may coincide with such a uniformity in general structure, that even a very decided departure from symmetry must be regarded as a character of little value in classification, compared with agreement in the organization of the shell and in those peculiarities in the conformation of the animal which are indicated by it; and further, that a most marked difference in degree of organization exists between two species of Amphistegina , which so closely resemble each other externally that the young of one may easily be mistaken for the adult of the other.

scholarly journals Deadly injuries through recoilless anti-tank weapons while military shooting practice—two case studies from Germany and Switzerland

2020 ◽  
Vol 134 (6) ◽  
pp. 2199-2204
Author(s):  
Katharina Jellinghaus ◽  
Charlotte Scherer ◽  
Edouard Stauffer ◽  
Petra Urban ◽  
Michael Bohnert ◽  
...  
Keyword(s):  
High Speed ◽  
Causes Of Death ◽  
The Body ◽  
The Other ◽  
Gas Jet ◽  
Severe Injuries ◽  
First Case ◽  
Wound Morphology ◽  
Very High ◽  
Case Versus

Abstract In this casuistry, two accidents from Germany and Switzerland are presented that happened during the shot of recoilless anti-tank weapons. In both cases, the injuries led to the death of two soldiers: A 22-year-old soldier in Germany was struck by the counter mass of a so-called Davis gun which had been fired by a comrade during a firing exercise; he died from his severe injuries, especially in the abdominal part of the body. As a peculiarity of the wound morphology, it was found to be a thick-layered, metallic, gray material in the wound cavity, which corresponded to the material of the counter mass that was ejected opposite to the shooting direction. The other case took place in Switzerland, where a 24-year-old soldier was seriously injured during an exercise with portable anti-tank rockets. At the time the shot was fired, he stood behind the launcher and was hit by the propulsion jet of the rocket motor. He died as well from his severe injuries, which were located at the chest done by the gas jet and by the very high pressure. In both cases, two different causes of death were present: massive blunt violence in the first case versus a jet of hot gases of very high speed and temperature in the second case.

scholarly journals Me and My Body: The Relevance of the Distinction for the Difference between Withdrawing Life Support and Euthanasia

2011 ◽  
Vol 39 (4) ◽  
pp. 671-677 ◽  
Author(s):  
Andrew McGee
Keyword(s):  
Lung Cancer ◽  
Life Support ◽  
Terminally Ill ◽  
The Body ◽  
The Other ◽  
First Case ◽  
Lethal Injection ◽  
The Law ◽  
The Difference ◽  
The One

In a paper that has recently attracted discussion, David Shaw has attempted to criticize the distinction the law has drawn between withdrawing and withholding life-sustaining measures on the one hand, and euthanasia on the other, by claiming that the body of a terminally ill patient should be seen as akin to life support. Shaw compares two cases that we might, at least at first, regard as distinct, and argues that they are not. In the first case, Adam, who is dying of lung cancer, is connected to a ventilator and requests to be disconnected. In the second case, Brian, also dying of cancer, is not connected to anything, and so he requests his doctor to provide him with a lethal injection. In the first case, Shaw contends, Adam is being kept alive by a ventilator. In the second case, Brian is being kept alive by his body.

La riflessione impossibile e il rispecchiamento nel mondo. Dall’esperienza infantile alla surréflexion

2020 ◽  
Vol 22 ◽  
pp. 135-151
Author(s):  
Prisca Amoroso ◽  
Keyword(s):  
The Body ◽  
The Other ◽  
The Sun ◽  
The Earth ◽  
Way Of Knowing ◽  
The Moment

This essay builds on two questions: the relation of the child with the other and the child’s way of knowing, in which the resistance of the unreflected is not yet problematized. Through a reconstruction of Merleau-Ponty’s critique of Piaget’s idea of the child’s linear intellectual progression toward reflexive abstraction, I highlight the moment of unreflection by taking up the notion of ultra-thing, which Merleau-Ponty borrows from Henry Wallon. These ultra-things are entities with which the child entertains a vague relation and which always remain at the horizon of her perception without yet being possessed in a representation or grasped in a concept. They include, for example, the sun, the sky, the Earth, the body as an object, existence before the birth of the child – uninhabitable dimensions or, to the contrary, ones that are necessarily inhabited. The concept of ultra-thing has not been sufficiently explored in Merleau-Pontian studies and its importance remains underappreciated. This essay thus formulates a hypothesis about the relation between ultra-things and hyper-reflection.

World Ages and the Body Politic

1961 ◽  
Vol 54 (3) ◽  
pp. 131-140
Author(s):  
H. J. Rose
Keyword(s):  
Body Politic ◽  
Early Period ◽  
The Body ◽  
The Other ◽  
Wide Spread ◽  
The Earth ◽  
The World ◽  
Pass Through ◽  
The One ◽  
The Universe

When, at an unknown but manifestly early period, speculation regarding the duration and destiny of the world began, the thinkers of those days had two analogies to guide them, and consequently two divergent conclusions were reached. The first was the recurrent cycle of the seasons; the second, the growth, maturity, decay and death of the human and all other animal bodies. Reasoning from the one, some arrived at the conclusion that the world, at least the earth and mankind, had passed and would always continue to pass through a series of epochs, limited in number, which when they had ended would recommence, and so on indefinitely. From the other datum the result was reached that as a man dies and does not come to life again (for even the fairly wide-spread and early doctrine of reincarnation supposed only that the soul would be given a new earthly body of some kind, not that the whole individual would return), so the earth, or the universe generally, would grow old and die and that would be the end of it. It is the purpose of this paper to examine these two ideas and one or two offshoots of them as they are known to have appeared in the two classical civilizations of Europe, and especially in Greece, and if possible to draw some tentative conclusions as to which, if either, can be found more characteristic of native thought.

The Captain's Widow: Maria Graham and the Independence of South America

1963 ◽  
Vol 20 (2) ◽  
pp. 127-142 ◽  
Author(s):  
Anyda Marchant
Keyword(s):  
South America ◽  
Rio De Janeiro ◽  
The Body ◽  
The Other ◽  
Outward Bound ◽  
The Sun ◽  
The Andes ◽  
The Town ◽  
Maria Graham ◽  
Cape Horn

On April 28, 1822, His Britannic Majesty's ship Doris, outward bound from Portsmouth, by way of Rio de Janeiro, entered the bay of Valparaíso in Chile with her flag halfmast. Aboard was the body of her captain, Thomas Graham, who had died as the vessel rounded Cape Horn. His widow Maria, looking out at the town that Sunday night, wrote in her journal:Many days have passed, and I have been unable and unwilling to resume my journal. To-day, the newness of the place, and all the other circumstances of our arrival, have drawn my thoughts to take some interest in the things around me. I can conceive nothing more glorious than the sight of the Andes this morning, on approaching the land at daybreak; starting, as it were, from the ocean itself, their summits of eternal snow shone in all the majesty of light long before the lower earth was illuminated, when suddenly the sun appeared from behind them and they were lost; and we sailed on for hours before we descried the land.

On the Development of Ascaris lumbricoides Lin. and Ascaris suilla Duj. in the Rat and Mouse

Parasitology ◽  
1917 ◽  
Vol 9 (2) ◽  
pp. 213-227 ◽  
Author(s):  
F. H. Stewart
Keyword(s):  
Pulmonary Artery ◽  
Ascaris Lumbricoides ◽  
Alimentary Canal ◽  
Fatty Degeneration ◽  
The Body ◽  
Blood Capillaries ◽  
Mature Embryos ◽  
First Case ◽  
Lateral Lines ◽  
Pass Through

When eggs of Ascaris lumbricoides Lin. or A. suilla Duj. containing mature embryos gain entrance to the alimentary canal of the sewer rat, Mus decumanus, or the mouse, M. musculus, they hatch. It is not possible to say at present in what part of the alimentary canal hatching takes place. (The number of animals suitable for experiment at the disposal of the writer is unfortunately so small that he is unable to devote any of them to the working out of the details of the process.) A certain proportion of the larvae thus liberated escape in the faeces where under suitable circumstances they can live for at least three days. It is, however, probable they ultimately succumb and that this is not a true road of development.The majority of the larvae gain entrance into the body of the host. The exact point of entrance and the time after hatching at which entrance takes place have not been determined. Some animals show signs of illness on the second day after infection. The time elapsing between infection and the entrance of the larvae into the body is therefore probably not more than two days.Larvae are found in the lungs and liver of the host not later than four days after infection and possibly as early as two days. Sections of the tissues show that they are situated in the air vesicles of the lung and in the blood capillaries of the liver close to the interlobular branches of the portal vein.Larvae are not found in the liver after the fifth day from infection. They are found in the bronchi about the seventh day and in the trachea on the eighth day.No larvae are found in any portion of the lung on the ninth day after infection. Dead larvae have been found in the stomach and rectum on the ninth day after the last infection.The route by which the larvae reach these sites is of course not definitely proved but from anatomical considerations it is hardly possible that it can be other than one of the two following (the diameter of the larva is three times that of a red blood corpuscle of the mouse. The larva could therefore not pass through the lumen of an ordinary capillary vessel):(1) Boring through the wall of the stomach or intestine the larva enters a mesenteric venule and is carried to the liver. It is here arrested at the entrance to the hepatic capillary plexus and it is for this reason that so many larvae are found in the capillaries close to the interlobular veins. The liver undergoes extreme and acute fatty degeneration so that the larvae are able to penetrate along the capillaries between the degenerated columns of liver cells to the hepatic venules. Thence they pass in the hepatic vein to the heart and by the pulmonary artery to the lung. They are of course at once arrested by the pulmonary capillary field. Embolism of the smaller branches of the pulmonary artery takes place with haemorrhage around these arterioles. The larvae readily work their way along with the effused blood into the air vesicles and thence into the bronchi and trachea.(2) The larva after hatching in the stomach or duodenum travels up the bile duct and reaches the bile capillaries of the interlobular zone. It here bores its way through the degenerated liver tissues and reaching a hepatic venule continues its course as in the first case.During the residence in the body of the rat or mouse the larvae grow from a length of 0·22 mm. to 1·4 mm. The proportion length of oesophagus/total length diminishes from 1/2·5 to 1/6·1. The ventral line which is the greatest of the longitudinal lines in the embryo is reduced to the same dimensions as the dorsal and lateral lines. The ventral gland (the rudiment of the excretory system) is developed from a cell of the ventral line, enlarges very greatly, acquires the massive nucleus characteristic of Ascaris larvae (Stewart, 1906; Baylis, 1916) and finally develops its duct from the cells of the ventral line. The intestine, anal canal and anus become pervious. The rudiment of the female gonads appears.

scholarly journals Observations on the structure of the tongue ; illustrated by cases in which a portion of that organ has been removed by ligature

1832 ◽  
Vol 1 ◽  
pp. 111-112
Keyword(s):  
Internal Structure ◽  
The Body ◽  
The Other ◽  
Considerable Degree ◽  
First Case ◽  
Glandular Structures

These observations will be allowed to have a considerable degree of importance, when we find that they ultimately lead to a safe and effectual method of removing a portion of the tongue, when that organ has assumed a diseased action or morbid excrescences of a cancerous nature, to which this, as well as many other glandular structures, are known to be liable. In a physiological view they will likewise be found to merit particular attention, as they tend to prove that the internal structure of the tongue is not of that delicate and sensible nature which, from its being the organ of taste, we should be led to imagine. The first case here mentioned, and from which various inferences are derived which lead to a new mode of treating the disorders of the tongue, was that of a gentleman whose tongue had been accidentally bit near the tip, and had hence become completely insensible, insomuch that every article of nourishment he took was equally insipid, and that the tip felt like a bit of wood in his mouth. No degree of inflammation, however, or spasmodic tendency having accompanied these symptoms, Mr. Home inferred that the nerves supplying this, and perhaps the other organs of sense, are not so liable to irritation as those which belong to other parts of the body.

Sign in / Sign up

Export Citation Format

Share Document