This result created a great sensation, and proved that Transatlantic electric wave telegraphy was quite feasible and not inhibited by distance, or by the earth's curvature even over an arc of a great circle 3000 m.
Starting from an observation of Marconi's, a number of interesting facts have been accumulated on the absorbing effect of sunlight on the propagation of long Hertzian waves through space, and on the disturbing effects of atmospheric electricity as well as upon the influence of earth curvature and obstacles of various kinds interposed in the line between the sending and transmitting stations.4 Electric wave telegraphy has revolutionized our means of communication from place to place on the surface of the earth, making it possible to communicate instantly and certainly between places separated by several thousand miles, whilst The Electrician, 1904, 5 2, p. 407, or German Pat.
When a root comes in contact at its tip with scme hard body, such as might impede its progress, a curvature of the growing part is set up, which takes the young tip away from the stone, or what-not, with which it is in contact.
In Great Britain the curvature is defined by stating the length of the radius, expressed in chains (i chain=66 ft.), in America by stating the angle subtended by a chord ioo ft.
The amount of superelevation required to prevent derailment at a curve can be calculated under perfect running conditions, given the radius of curvature, the weight of the vehicle, the height of the centre of gravity, the distance between the rails, and the speed; but great experience 1 See The Times Engineering Supplement (August 22, 1906), p. 265.
In general it is not curvature, but change of curvature, that presents difficulty in the laying-out of a line.
(On the continent of Europe, however, six-wheeled vehicles are to be found much longer than those employed in Great Britain.) This difficulty is avoided by providing the vehicles with four axles (or six in the case of the largest and heaviest), mounted in pairs (or threes) at each end in a bogie or swivel truck, which being pivoted can move relatively to the body and adapt itself to the curvature of the line.
The object, however, can be fully attained only if the scale of the map is sufficiently large, if the horizontal and vertical scales are identical, so that there shall be no exaggeration of the heights, and if regard is had, eventually, to the curvature of the earth's surface.
The adaption of these gores to the curvature of the sphere calls for great care.
- This section of the Atlas, known to the inhabitants of Morocco by its Berber name, Idraren Draren or the " Mountains of Mountains," consists of five distinct ranges, varying in length and height, but disposed more or less parallel to one another in a general direction from south-west to north-east, with a slight curvature towards the Sahara.
(2) A theorem relating to the apparent curvature of the geocentric path of a comet.
If a surface intended to be flat is affected with a slight general curvature, a remedy may be found in an alteration of focus, and the remedy is the less complete as the reflection is more oblique.
In like manner, the term in y 2 corresponds to a general curvature of the lines (fig.
The term in y corresponds to a variation of curvature in crossing the grating (fig.
14); and that in y 3 would be caused by a curvature such that there is a point of inflection at the middle of each line (fig.
A linear error in the spacing, and a general curvature of the lines, are eliminated in the ordinary use of a grating.
(22); and for the curvature, Cornu remarks that this equation suffices to determine the general character of the curve.
The cartesian equation referred to the axis and directrix is y=c cosh (x/c) or y = Zc(e x / c +e x / c); other forms are s = c sinh (x/c) and y 2 =c 2 -1-s 2, being the arc measured from the vertex; the intrinsic equation is s = c tan The radius of curvature and normal are each equal to c sec t '.
If r denotes the radius of curvature of the stream line, so that I dp + dV - dH _ dq 2 q2 (6) p dv dv dv dv - r ' the normal acceleration.
Along the path of a particle, defined by the of (3), _ c) sine 2e, - x 2 + y2 = y a 2 ' (Io) sin B' de' _ 2y-c dy 2 ds ds' on the radius of curvature is 4a 2 /(ylc), which shows that the curve is an Elastica or Lintearia.
(12) Along the stream line xBAPJ, t ' =0, u=ae-" c bl, n; (13) and over the jet surface JPA, where the skin velocity is Q, - q = - Q, u = ae rs Q /m = ae rs lc, (14) ds denoting the arc AP by s, starting at u = a; a ' ch nS2=cos nB= -a' u u - - a b' (15) a l a - b l u - a' a-a' u-b' co > u = ae'" S " c > a, and this gives the intrinsic equation of the jet, and of curvature ds '&1) _ i dw i dw dS2 P= - dO = Q a0 - Q as2 = Q c u-b d (u -a.u -a') _ ?
At any point a sounding line would hang in the line of the radius of curvature of the water surface.
In the shape and curvature of the horns, which at first incline outwards and forwards, and then bend somewhat upwards and inwards, this breed of cattle resembles the aurochs and the (by comparison) dwarfed park-breeds.
The face has the ordinary gazelle-markings; but the rather short horns - which are wanting in the female - have a peculiar upward and forward curvature, unlike that obtaining in the gazelles FIG.
The semi-elliptical shape of the arches, the variation of span, the _ slight curvature of the 26:0'=-----.
Divide the span L into any convenient number n of equal parts of length 1, so that nl = L; compute the radii of curvature R 1, R2, R3 for the several sections.
In very many cases the pollen is carried to the stigma by elongation, curvature or some other movement of the filament, the style or stigma, or corolla or some other part of the flower, or by correlated movements of two or more parts.
But, as originally pointed out by Euler, the difficulty can be turned if we notice that in the ordinary trajectory of practice the quantities i, cos i, and sec i vary so slowly that they may be replaced by their mean values,, t, cos 7 7, and sec r t, especially if the trajectory, when considerable, is divided up in the calculation into arcs of small curvature, the curvature of an arc being defined as the angle between the tangents or normals at the ends of the arc.
In the application of Siacci's method to the calculation of a trajectory in high angle fire by successive arcs of small curvature, starting at the beginning of an arc at an angle 4) with velocity v4), the curvature of the arc 4-8 is first settled upon, and now (80) n=1(0+0) is a good first approximation for n.
In the long range high angle fire the shot ascends to such a height that the correction for the tenuity of the air becomes important, and the curvature 4)-8 of an arc should be so chosen that 4)y 0, the height ascended, should be limited to about moo ft., equivalent to a fall of I inch in the barometer or 3% diminution in the tenuity factor T.
The horns of the bucks are heavy, and have a peculiar forward curvature at the tips; the colour of the coat is red-fawn, with a broad brown band down the back.
(See River -HoG.) The recently discovered Hylochoerus of the equatorial forestdistricts of Africa comes nearest to the under-mentioned warthogs, but the skull is of a much less specialized type, while the upper tusks are much smaller although they have the same general curvature and direction, and the cheek-teeth lack the peculiar characteristics of those of Phacochoerus, although they present a certain approximation thereto.
Apollonius' genius takes its highest flight in Book v., where he treats of normals as minimum and maximum straight lines drawn from given points to the curve (independently of tangent properties), discusses how many normals can be drawn from particular points, finds their feet by construction, and gives propositions determining the centre of curvature at any point and leading at once to the Cartesian equation of the evolute of any conic.
The under surface of the left lobe is concave for the interior surface of the stomach (see Alimentary Canal: Stomach Chamber), while a convexity, known as the tuber omentale, fits into the lesser curvature of that organ.
Proposition 30 describes the construction of a curve of double curvature called by Pappus the helix on a sphere; it is described by a point moving uniformly along the arc of a great circle, which itself turns about its diameter uniformly, the point describing a quadrant and the great circle a complete revolution in the same time.
De Paris, 1781), which, while giving a remarkably elegant investigation in regard to the problem 3f earth-work referred to in the title, establishes in connexion with it his capital discovery of the curves of curvature of a surface.
Leonhard Euler, in his paper on curvature in the Berlin Memoirs for 1760, had considered, not the normals of the surface, but the normals of the plane sections through a particular normal, so that the question of the intersection of successive normals of the surface had never presented itself to him.
Monge's memoir just referred to gives the ordinary differential equation of the curves of curvature, and establishes the general theory in a very satisfactory manner; but the application to the interesting particular case of the ellipsoid was first made by him in a later paper in 1795.
Crystals of blende are of very common occurrence, but owing to twinning and distortion and curvature of the faces, they are often rather complex and difficult to decipher.
Duced by euclidian methods from the definition include the following: the tangent at any point bisects the angle between the focal distance and the perpendicular on the directrix and is equally inclined to the focal distance and the axis; tangents at the extremities of a focal chord intersect at right angles on the directrix, and as a corollary we have that the locus of the intersection of tangents at right angles is the directrix; the circumcircle of a triangle circumscribing a parabola passes through the focus; the subtangent is equal to twice the abscissa of the point of contact; the subnormal is constant and equals the semilatus rectum; and the radius of curvature at a point P is 2 (FP) 4 /a 2 where a is the semilatus rectum and FP the focal distance of P.
He was well aware of the failures of all attempts to perfect telescopes by employing lenses of various forms of curvature, and accordingly proposed the form of reflecting telescope which bears his name.
Moreover the greater depths of the curves (or "curvature powers") in itself neutralize more or less the advantages obtained from the reduced irrationality of dispersion.
Let it be supposed that two positive lenses of equal curvature powers are made out of these two glasses, then in order to represent the combined dispersion of the two together the two 0µ's for each spectral region may be added together to form 0'µ as in the line below, and then, on again expressing the partial z'µ in terms of L'µ (C to F) we get the new figures in the bottom row beneath the asterisks.
Hence it is clear that if the two positive lenses of equal curvature power of o 60 and 0.102 respectively are combined with a negative lens of light flint o 569, then a triple objective, having no secondary spectrum (at any rate with respect to the blue rays), may be obtained.
Since the curvature powers of the positive lenses are equal, the partial dispersions of the two glasses may be simply added together, and we then have: [0.543 +0.3741 The proportions given on the lower line may now be compared with the corresponding proportional dispersions for borosilicate flint glass 0.658, closely resembling the type 0.164 of Schott's list, viz.: [0.658 (A D = I.546) 50' 11 A slight increase in the relative power of the first lens of 0.543 would bring about a still closer correspondence in the rationality, but with the curves required to produce an object-glass of this type of 6 in.
21 (d); in this case a convex mirror of different curvature is employed, the equivalent focus of the combination being 80 ft.
By directing the telescope to a distant object, or to the intersection of the webs of a fixed collimating telescope (see Transit Circle), it is easy to measure the effect of a small change of zenith distance of the axis of the telescope in terms both of the level and of the micrometer screw, and thus, if the levels are perfectly sensitive and uniform in curvature and graduation, to determine the value of one division of each level in terms of the micrometer screw.
R, Radius of curvature, formula (1).
Where p, p are the radii of curvature of the two curves at J, 4~ is the inclination of the common tangent at J to the horizontal, and h is the height of G above J.
Suppose, for example, that we have a light string stretched over a smooth curve; and let Rs denote the normal pressure (outwards from the centre of curvature) on bs.