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foci

The excitable foci of the cerebral cortex are well myelinated long before the unexcitable are so.

118The excitable foci of the cerebral cortex are well myelinated long before the unexcitable are so.

118Larger and thicker in the rabbit, when excited it gives rise in that animal to movements of the eyes and of the fore-limbs and neck; but it is only in much higher types, such as the dog, that the cortex yields, under experimental excitation, definitely localized foci, whence can be evoked movements of the fore-limb, hind-limb, neck, eyes, ears and face.

65Larger and thicker in the rabbit, when excited it gives rise in that animal to movements of the eyes and of the fore-limbs and neck; but it is only in much higher types, such as the dog, that the cortex yields, under experimental excitation, definitely localized foci, whence can be evoked movements of the fore-limb, hind-limb, neck, eyes, ears and face.

65F2' =objectand image-side foci of eyepiece.

52F2' =objectand image-side foci of eyepiece.

52F 1 ' =objectand image-side foci of objective.

41F 1 ' =objectand image-side foci of objective.

41Metrical relations between the axes, eccentricity, distance between the foci, and between these quantities and the co-ordinates of points on the curve (referred to the axes and the centre), and focal distances are readily obtained by the methods of geometrical conics or analytically.

34In that case, however, in the compound microscope a small object may always be represented by means of wider pencils, one of the foci of the objective (not of the collective system) being near it.

34Also the auxiliarly circle is the locus of the feet of the perpendiculars from the foci on any tangent.

36Negative values of n must be interpreted by a streaming motion on a parallel plane at a level slightly different, as on a double Riemann sheet, the stream passing from one sheet to the other across a cut SS' joining the foci S, S'.

21F l, F1' =objectand image-side foci of objec tive.

22According to the laws of optics it is only possible either to portray a small object near one of the foci of the system with wide pencils, or to produce an image from a relatively large object by correspondingly narrow pencils.

23Experiment shows that in the manlike (anthropoid) apes the differentiation of the foci or "centres" of movement in the motor field of the cortex is even more minute.

25Besides streets running east and west, which are named by the letters of the alphabet, and streets running north and south, which are numbered, there are avenues named for various states, which radiate from two foci - the Capitol and the White House - or traverse the city without any fixed plan.

10Johann Kepler had proved by an elaborate series of measurements that each planet revolves in an elliptical orbit round the sun, whose centre occupies one of the foci of the orbit, that the radius vector of each planet drawn from the sun describes equal areas in equal times, and that the squares of the periodic times of the planets are in the same proportion as the cubes of their mean distances from the sun.

10also several optical problems relating to lenses of various forms and their combinations for telescopic projection, rules for finding foci, &c. He does not, however, mention the camera obscura as an instrument in use, but in John Harris's Lexicon Technicum (1704) we find that the camera obscura with the arrangement called the "scioptric ball," and known as scioptricks, was on sale in London, and after this must have been in common use as a sketching instrument or as a show.

11netaacet Diagram of the Topography of the Main Groups of Foci in the Motor of Chimpanzee.

11The points called foci presented themselves in the theory of the conic, and were well known to the Greek geometers, but the general notion of a focus was first established by Plucker (in the memoir " Uber solche Puncte die bei Curven einer hdheren Ordnung den Brennpuncten der Kegelschnitte entsprechen " (Crelle, t.

11There will be from each circular point X tangents (X, a number depending on the class of the curve and its relation to the line infinity and the circular points, 2 for the general conic, 1 for the parabola, 2 for a circular cubic, or bicircular quartic, &c.); the X tangents from the one circular point and those from the other circular point intersect in X real foci (viz.

11each of these is the only real point on each of the tangents through it), and in X 2 -X imaginary foci; each pair of real foci determines a pair of imaginary foci (the so-called antipoints of the two real foci), and the 2X(X-1) pairs of real foci thus determine the X 2 ---X imaginary foci.

11There are in some cases points termed centres, or singular or multiple foci (the nomenclature is unsettled), which are the intersections of improper tangents from the two circular points respectively; thus, in the circular cubic, the tangents to the curve at the two circular points respectively (or two imaginary asymptotes of the curve) meet in a centre.

11There are in some cases points termed centres, or singular or multiple foci (the nomenclature is unsettled), which are the intersections of improper tangents from the two circular points respectively; thus, in the circular cubic, the tangents to the curve at the two circular points respectively (or two imaginary asymptotes of the curve) meet in a centre.

11That in man the excitable foci of the motor field are islanded in excitable surface similarly and even more extensively, was a natural inference, but it had its chief basis in the observations on the orang, now known to be erroneous.

12Both these preparations should only be used in cases where it is possible to exclude any tuberculous foci, or by their action in breaking down protective fibrous tissues they may cause a quiescent lesion to become active.

12The magnifying power of the telescope is = Ff /ex, where F and f are respectively the focal lengths of the large and the small mirror, e the focal length of the eye-piece, and x the distance between the principal foci of the two mirrors (=Ff in the diagram) when the instrument is in adjustment for viewing distant objects.

12A line became continuous, returning into itself by way of infinity; two parallel lines intersect in a point at infinity; all circles pass through two fixed points at infinity (the circular points); two spheres intersect in a fixed circle at infinity; an asymptote became a tangent at infinity; the foci of a conic became the intersections of the tangents from the circular points at infinity; the centre of a conic the pole of the line at infinity, &c. In analytical geometry the line at infinity plays an important part in trilinear co-ordinates.

12This theory he founded on 2 Kings xxii.; and ever since, this chapter has been one of the recognized foci of Biblical criticism.

12Of the properties of a tangent it may be noticed that the tangent at any point is equally inclined to the focal distances of that point; that the feet of the perpendiculars from the foci on any tangent always lie on the auxiliary circle, and the product of these perpendiculars is constant, and equal to the product of the distances of a focus from the two vertices.

12From any point without the curve two, and only two, tangents can be drawn; if OP, OP' be two tangents from 0, and S, S' the foci, then the angles OSP, OSP' are equal and also SOP, S'OP'.

12Of practical importance are the following constructions: - (I) Given the axes; (2) given the major axis and the foci; (3) given the focus, eccentricity and directrix; (4) to construct an ellipse (approximately) by means of circular arcs.

12(2) If the major axis and foci be given, there is a convenient mechanical construction based on the property that the sum of the focal distances of any point is constant and equal to the major axis.

12If one of the foci be at infinity, the conics are confocal parabolas, which may also be regarded as parabolas having a common focus and axis.

12Both these preparations should only be used in cases where it is possible to exclude any tuberculous foci, or by their action in breaking down protective fibrous tissues they may cause a quiescent lesion to become active.

12In the monkey the proportions it assumes are still greater, and the number of foci, for distinct movements of this and that member, indeed for the individual joints of each limb, are much more numerous, and together occupy a more extensive surface, though relatively to the total surface of the brain a smaller one.

13Earthquakes are frequent all over the peninsula, but especially in the south-east and west, where the Maeander valley and the Gulf of Smyrna are notorious seismic foci.

00Hence the locus of J relative to AB, and the locus relative to CD are equal ellipses of which A, B and C, D are respectively the foci.

00The notions of distance and of lines at right angles are connected with the circular points; and almost every construction of a curve by means of lines of a determinate length, or at right angles to each other, and (as such) mechanical constructions by means of linkwork, give rise to curves passing the same definite number of times through the two circular points respectively, or say to circular curves, and in which the fixed centres of the construction present themselves as ordinary, or as singular, foci.

00Roberts) of the triple generation of the curve by means of the three several pairs of singular foci.

00The orbit of the moon around the earth, though not a fixed curve of any class, is elliptical in form, and may be represented by an ellipse which is constantly changing its form and position, and has the earth in one of its foci.

00eccentricity less than unity: this involves the notion of one directrix and one focus; (2) the ellipse is the locus of a point the sum of whose distances from two fixed points is constant: this involves the notion of two foci.

00Let AA' be the axis and S, S' the foci.

00Take a piece of thread of length AA', and fix it at its extremities by means of pins at the foci.

00Confocal conics are conics having the same foci.

00It has stronger anticonvulsant properties than most other barbiturates, and may be preferentially concentrated in metabolically active epileptic foci.

00basal lamina along the base of the cells was damaged at several foci.

00diminished concentrically with distance from the two major commercial foci of the metropolis.

00focusse can then become the foci of the ensuing paragraphs.

00The basal lamina along the base of the cells was damaged at several foci.

00The right kidney parenchyma was thinned and irregular and contained low attenuation areas and tiny foci of calcification.

00Chronic epileptic foci in vitro in hippocampal slices from rats with the tetanus toxin epileptic syndrome.

00typical of the kinds of changes found in the broader range of chronic epileptic foci.

00Thus it has a real centre, two foci, two directrices and two vertices; the transverse axis, joining the vertices, corresponds to the major axis of the ellipse, and the line through the centre and perpendicular to this axis is called the conjugate axis, and corresponds to the minor axis of the ellipse; about these axes the curve is symmetrical.

00Calling the foci S, S', the real vertices A, A', the extremities of the conjugate axis B, B' and the centre C, the positions of B, B' are given by AB = AB' = CS.

00Also the auxiliarly circle is the locus of the feet of the perpendiculars from the foci on any tangent.

00(casale) the rustici were grouped in families (foci): the tenants paid from 4 to a of the crop, besides a poll-tax and labour-dues.

00If the law of attraction is that of gravitation, the orbit is a conic section - ellipse, parabola or hyperbola - having the centre of attraction in one of its foci; and the motion takes place in accordance with Kepler's laws (see Astronomy).

002 " In the same way we may conclude that in flat gratings any departure from a straight line has the effect of causing the dust in the slit and the spectrum to have different foci - a fact sometimes observed " (Rowland, " On Concave Gratings for Optical Purposes," Phil.

00If "=4), the term of the first order vanishes, and the reduction of the difference of path via P and via A to a term of the fourth order proves not only that Q and Q' are conjugate foci, but also that the foci are exempt from the most important term in the aberration.

00Since we have now to integrate for the whole illumination at a particular point 0 due to all the components which have their foci in its neighbourhood, we may conveniently regard 0 as origin.

00By embolism is meant the more or less sudden stoppage of a vessel by a plug of solid matter carried thither by the current of the blood; be it a little clot from the heart or, what is far more pernicious, an infective fragment from some focus of infection in the body, by which messengers new foci of infection may be scattered about the body.

00Negative values of n must be interpreted by a streaming motion on a parallel plane at a level slightly different, as on a double Riemann sheet, the stream passing from one sheet to the other across a cut SS' joining the foci S, S'.

00also several optical problems relating to lenses of various forms and their combinations for telescopic projection, rules for finding foci, &c. He does not, however, mention the camera obscura as an instrument in use, but in John Harris's Lexicon Technicum (1704) we find that the camera obscura with the arrangement called the "scioptric ball," and known as scioptricks, was on sale in London, and after this must have been in common use as a sketching instrument or as a show.

00It is important to note that although sleeping sickness (of which the chief foci are at present the Congo Free State and Uganda) has hitherto been associated with one particular species of Glossina, it has been shown experi mentally both that other tsetse-flies are able to transmit the parasite of the disease, and that G.

00The castles of these great lords were the foci of the social and political life of their respective provinces.

00In the monkey the proportions it assumes are still greater, and the number of foci, for distinct movements of this and that member, indeed for the individual joints of each limb, are much more numerous, and together occupy a more extensive surface, though relatively to the total surface of the brain a smaller one.

00Experiment shows that in the manlike (anthropoid) apes the differentiation of the foci or "centres" of movement in the motor field of the cortex is even more minute.

00The accompanying simple figure indicates better than any verbal description the topography of the main groups of foci in the motor field of a manlike ape (chimpanzee).

00netaacet Diagram of the Topography of the Main Groups of Foci in the Motor of Chimpanzee.

00The motor field, therefore, though absolutely larger, forms a smaller fraction of the whole cortex of the brain than in the lower forms. The statement that in the anthropoid (orang-outan) brain the groups of foci in the motor fields of the cortex are themselves separated one from another by surrounding inexcitable cortex, has been made and was one of great interest, but has not been confirmed by subsequent observat'on.

00That in man the excitable foci of the motor field are islanded in excitable surface similarly and even more extensively, was a natural inference, but it had its chief basis in the observations on the orang, now known to be erroneous.

00It will be seen, then, that the visual and photographic foci are now merged in one, and the image is practically as achromatic as that yielded by a reflector.

00The extension of the image away from the axis or size of field available for covering a photographic plate with fair definition is a function in the first place of the ratio between focal length and aperture, the longer focus having the greater relative or angular covering power, and in the second a function of the curvatures of the lenses, in the sense that the objective must be free from coma at the foci of oblique pencils or must fulfil the sine condition (see Aberration).

00The earlier arrangement of two lenses of the Huygenian eye-piece (see Microscope) having foci with ratio of 3 to I, gives a fairly large flat field of view approximately free from distortion of tangential lines and from coma, while the Mittenzw ?

00showed that, if the large mirror were a segment of a paraboloid of revolution whose focus is F, and the small mirror an ellipsoid of revolution whose foci are F and P respectively, the resulting image will be plane and undistorted.

00The magnifying power of the telescope is = Ff /ex, where F and f are respectively the focal lengths of the large and the small mirror, e the focal length of the eye-piece, and x the distance between the principal foci of the two mirrors (=Ff in the diagram) when the instrument is in adjustment for viewing distant objects.

00Earthquakes are frequent all over the peninsula, but especially in the south-east and west, where the Maeander valley and the Gulf of Smyrna are notorious seismic foci.

00Besides streets running east and west, which are named by the letters of the alphabet, and streets running north and south, which are numbered, there are avenues named for various states, which radiate from two foci - the Capitol and the White House - or traverse the city without any fixed plan.

00Hence the locus of J relative to AB, and the locus relative to CD are equal ellipses of which A, B and C, D are respectively the foci.

00As the ellipse degenerates into the straight line joining its foci, the contracted parts of the unduloid become narrower, till at last the figure becomes a series of spheres in contact.

00The effects produced by bacteria may be considered under the following heads: (I) tissue changes produced in the vicinity of the bacteria, either at the primary or secondary foci; (2) tissue changes produced at a distance by absorption of their toxins; (3) symptoms. The changes in the vicinity of bacteria are to be regarded partly as the direct result of the action of toxins on living cells, and partly as indicating a reaction on the part of the tissues.

00Johann Kepler had proved by an elaborate series of measurements that each planet revolves in an elliptical orbit round the sun, whose centre occupies one of the foci of the orbit, that the radius vector of each planet drawn from the sun describes equal areas in equal times, and that the squares of the periodic times of the planets are in the same proportion as the cubes of their mean distances from the sun.

00Similarly any other property might be used as a definition; an ellipse is the locus of a point such that the sum of its distances from two fixed points (the foci) is constant, &c., &c.

00The points called foci presented themselves in the theory of the conic, and were well known to the Greek geometers, but the general notion of a focus was first established by Plucker (in the memoir " Uber solche Puncte die bei Curven einer hdheren Ordnung den Brennpuncten der Kegelschnitte entsprechen " (Crelle, t.

00There will be from each circular point X tangents (X, a number depending on the class of the curve and its relation to the line infinity and the circular points, 2 for the general conic, 1 for the parabola, 2 for a circular cubic, or bicircular quartic, &c.); the X tangents from the one circular point and those from the other circular point intersect in X real foci (viz.

00each of these is the only real point on each of the tangents through it), and in X 2 -X imaginary foci; each pair of real foci determines a pair of imaginary foci (the so-called antipoints of the two real foci), and the 2X(X-1) pairs of real foci thus determine the X 2 ---X imaginary foci.

00The notions of distance and of lines at right angles are connected with the circular points; and almost every construction of a curve by means of lines of a determinate length, or at right angles to each other, and (as such) mechanical constructions by means of linkwork, give rise to curves passing the same definite number of times through the two circular points respectively, or say to circular curves, and in which the fixed centres of the construction present themselves as ordinary, or as singular, foci.

00Roberts) of the triple generation of the curve by means of the three several pairs of singular foci.

00A line became continuous, returning into itself by way of infinity; two parallel lines intersect in a point at infinity; all circles pass through two fixed points at infinity (the circular points); two spheres intersect in a fixed circle at infinity; an asymptote became a tangent at infinity; the foci of a conic became the intersections of the tangents from the circular points at infinity; the centre of a conic the pole of the line at infinity, &c. In analytical geometry the line at infinity plays an important part in trilinear co-ordinates.

00The orbit of the moon around the earth, though not a fixed curve of any class, is elliptical in form, and may be represented by an ellipse which is constantly changing its form and position, and has the earth in one of its foci.

00This theory he founded on 2 Kings xxii.; and ever since, this chapter has been one of the recognized foci of Biblical criticism.

00eccentricity less than unity: this involves the notion of one directrix and one focus; (2) the ellipse is the locus of a point the sum of whose distances from two fixed points is constant: this involves the notion of two foci.

00Metrical relations between the axes, eccentricity, distance between the foci, and between these quantities and the co-ordinates of points on the curve (referred to the axes and the centre), and focal distances are readily obtained by the methods of geometrical conics or analytically.

00Of the properties of a tangent it may be noticed that the tangent at any point is equally inclined to the focal distances of that point; that the feet of the perpendiculars from the foci on any tangent always lie on the auxiliary circle, and the product of these perpendiculars is constant, and equal to the product of the distances of a focus from the two vertices.

00From any point without the curve two, and only two, tangents can be drawn; if OP, OP' be two tangents from 0, and S, S' the foci, then the angles OSP, OSP' are equal and also SOP, S'OP'.

00Of practical importance are the following constructions: - (I) Given the axes; (2) given the major axis and the foci; (3) given the focus, eccentricity and directrix; (4) to construct an ellipse (approximately) by means of circular arcs.

00(2) If the major axis and foci be given, there is a convenient mechanical construction based on the property that the sum of the focal distances of any point is constant and equal to the major axis.

00Let AA' be the axis and S, S' the foci.

00Take a piece of thread of length AA', and fix it at its extremities by means of pins at the foci.

00Confocal conics are conics having the same foci.

00If one of the foci be at infinity, the conics are confocal parabolas, which may also be regarded as parabolas having a common focus and axis.

00By compounding two lenses or lens systems separated by a definite interval, a system is obtained having a focal length considerably less than the focal lengths of the separate systems. If f and f' be the focal lengths of the combination, and f2, f2 the focal lengths of the two components, and A the distance between the inner foci of the components, then f = - f,f2/4, f' =fi f27 0 (see Lens).

00According to the laws of optics it is only possible either to portray a small object near one of the foci of the system with wide pencils, or to produce an image from a relatively large object by correspondingly narrow pencils.

00In that case, however, in the compound microscope a small object may always be represented by means of wider pencils, one of the foci of the objective (not of the collective system) being near it.

00F l, F1' =objectand image-side foci of objec tive.

00The approach could also potentially help eliminate local foci for trypanosomes causing sleeping sickness in humans.

00Chronic epileptic foci in vitro in hippocampal slices from rats with the tetanus toxin epileptic syndrome.

00These foci will be combined with transect survey of the entire area, which we intend to cover with a 12% sample.

00These are typical of the kinds of changes found in the broader range of chronic epileptic foci.

00The motor field, therefore, though absolutely larger, forms a smaller fraction of the whole cortex of the brain than in the lower forms. The statement that in the anthropoid (orang-outan) brain the groups of foci in the motor fields of the cortex are themselves separated one from another by surrounding inexcitable cortex, has been made and was one of great interest, but has not been confirmed by subsequent observat'on.

01It will be seen, then, that the visual and photographic foci are now merged in one, and the image is practically as achromatic as that yielded by a reflector.

01showed that, if the large mirror were a segment of a paraboloid of revolution whose focus is F, and the small mirror an ellipsoid of revolution whose foci are F and P respectively, the resulting image will be plane and undistorted.

01The effects produced by bacteria may be considered under the following heads: (I) tissue changes produced in the vicinity of the bacteria, either at the primary or secondary foci; (2) tissue changes produced at a distance by absorption of their toxins; (3) symptoms. The changes in the vicinity of bacteria are to be regarded partly as the direct result of the action of toxins on living cells, and partly as indicating a reaction on the part of the tissues.

01Similarly any other property might be used as a definition; an ellipse is the locus of a point such that the sum of its distances from two fixed points (the foci) is constant, &c., &c.

01(casale) the rustici were grouped in families (foci): the tenants paid from 4 to a of the crop, besides a poll-tax and labour-dues.

022 " In the same way we may conclude that in flat gratings any departure from a straight line has the effect of causing the dust in the slit and the spectrum to have different foci - a fact sometimes observed " (Rowland, " On Concave Gratings for Optical Purposes," Phil.

02If "=4), the term of the first order vanishes, and the reduction of the difference of path via P and via A to a term of the fourth order proves not only that Q and Q' are conjugate foci, but also that the foci are exempt from the most important term in the aberration.

02It is important to note that although sleeping sickness (of which the chief foci are at present the Congo Free State and Uganda) has hitherto been associated with one particular species of Glossina, it has been shown experi mentally both that other tsetse-flies are able to transmit the parasite of the disease, and that G.

02The accompanying simple figure indicates better than any verbal description the topography of the main groups of foci in the motor field of a manlike ape (chimpanzee).

02The castles of these great lords were the foci of the social and political life of their respective provinces.

07

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