(2) A theorem relating to the apparent curvature of the geocentric path of a comet.
At any point a sounding line would hang in the line of the radius of curvature of the water surface.
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.
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.
If w is the weight of a locomotive in tons, r the radius of curvature of the track, v the velocity in feet per sec.; then the horizontal force exerted on the bridge is wv 2 /gr tons.
In general it is not curvature, but change of curvature, that presents difficulty in the laying-out of a line.
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.
He determined the "elastic curve," which is formed by an elastic plate or rod fixed at one end and bent by a weight applied to the other, and which he showed to be the same as the curvature of an impervious sail filled with a liquid (lintearia).
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.
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.
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.
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.
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.
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.
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.
The curve must be a geodesic, and that the normal pressure per unit length must vary as the principal curvature of the curve.
The above problem is identical with that of the oscillation of a particle in a smooth spherical bowl, in the neighborhood of the lowest point, If the bowl has any other shape, the axes Ox, Oy may, ..--7 be taken tangential to the lines tof curvature ~ / at the lowest point 0; the equations of small A motion then are dix xdiy (II) c where P1, P2, are the principal radii of curvature at 0.
Where p is the radius of curvature of the path at P, the tangential and normal accelerations are also expressed by v dv/ds and v1/p, respectively.
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.
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.
Curvature of the primary focal line having a very injurious effect upon definition, it may be inferred from the excellent performance of these gratings that y is in fact small.
The same method of representation is applicable to spherical waves, issuing from a point, if the radius of curvature be large; for, although there is variation of phase along the length of the infinitesimal strip, the whole effect depends practically upon that of the central parts where the phase is sensibly constant.'
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.
Arabica, in which the horns have a somewhat S-shaped curvature in profile.
He suggests that the propagation of earthquake disturbances is probably affected by the curvature of the surface of the globe, which may act like a whispering gallery.
The semi-elliptical shape of the arches, the variation of span, the _ slight curvature of the 26:0'=-----.
Then the deflection at the centre is the value of y for x = a, and is _ 5 wa4 S - 14 EI' The radius of curvature of the beam at D is given by the relation R=EI/M.
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.
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.
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.
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.
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.
- 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.
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.
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.
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.
A linear error in the spacing, and a general curvature of the lines, are eliminated in the ordinary use of a grating.