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straight-line

The latter gives values of the constants a and b for different samples of iron and steel, some of which are shown in the following table :- K=a+bH For most samples of steel the straight-line law was found to hold approximately up to H=3; in the case of iron and of soft steel the approximation was less close.

32Lower your body toward the floor, maintaining your body in a straight-line from head to heel.

32His lips thinned to a straight line.

10He paused only long enough to locate her, and then made a straight line for her.

10There are other arrangements of bars giving straight-line motions, and these arrangements together with ths general properties of mechanisms of this kind are discussed in How to Draw a Straight Line by A.

12His lips thinned into a straight line as he focused on the food in his plate.

00in a straight line broken only by the mouths of the Don-Nai and Mekong.

00Its greatest length in a straight line along the mainland is from N.W.

00This is most clearly marked on the side of the Apennines, where the great Aemilian Way, which has been the high road from the time of the Romans to our own, preserves an unbroken straight line from Rimini to Piacenza, a distance of more than 150 m., during which the underfalls of the mountains continually approach it on the left, without once crossing the line of road.

00The Via Flaminia was the earliest and most important road to the north; and it was soon extended (in 187 B.C.) by the Via Aemilia running through Bononia as far as Placentia, in an almost absolutely straight line between the plain of the P0 and the foot of the Apennines.

00In all, there is a wonderful amount of specialization, though perhaps in a very straight line from generalized forms; but the affinity to Australian or Polynesian types is in many cases clearly traceable, and it cannot be supposed but that these last are of cognate origin with those of New Zealand.

00Napoleon, in making the road over the Simplon, deviated from the straight line in order to leave it standing.

00In the Orthorrhapha, in the pupae of which the appendages of the perfect insect are usually visible, the pupa-case generally splits in a straight line down the back near the cephalic end; in front of this longitudinal cleft there may be a small transverse one, the two together forming a T-shaped fissure.

00Indeed, he never shook off the erroneous ideas of his time regarding the paths of projectiles, further than to see that no part of them could be a straight line.

00GAYAL, a domesticated ox allied to the Gaur, but distinguished, among other features, by the more conical and straighter horns, and the straight line between them.

00The straightness of a straight line and the planeness of a plane require consideration.

00representing only 47 in a straight line.

00Stations which are placed in a straight line across a sea are then connected and " sections " are made.

00This correction may be indicated in the diagram by a straight line drawn from o through the point at which the line of I = moo intersects that of H = o 28 (Rayleigh, Phil.

00The curve thus constructed should be a straight line inclined to the horizontal axis at an angle 0, the tangent of which is 1.6.

00Rowland, believing that the curve would continue to fall in a straight line meeting the horizontal axis, inferred that the induction corresponding to the point B-about 17,500-was the highest I Phil.

0024 was converted into an almost perfectly straight line passing through the origin, and lying below the horizontal axis; while the permeability of the metal was greatly diminished by the operation.

00in a straight line from source to mouth.

00in a straight line S.S.E.

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.

00the contraction along a given straight line will in general have different values in any two neighbouring crystals, and the crystals consequently become slightly detached from one another.

00For the desulphurization of zinc blende where it is not intended to collect and save the sulphur there are many mechanical kilns, generally classified as straight-line, horse-shoe, turret and shaft kilns; all of these may be made to do good work on moderately clean ores which do not melt at the temperature of desulphurization.

00Beyond the fort are various public buildings leading to Otoo Street, the main thoroughfare, which runs two miles in a straight line to Christiansborg.

00This line has been twice modified by treaties between Bolivia and Brazil, but without the consent of Peru, which claimed all the territory eastward to the Madeira between the above-mentioned line and the Beni-Madidi rivers, the line of demarcation following the Pablo-bamba, a small tributary of the Madidi, to its source, and thence in a straight line to the village of Conima, on Lake Titicaca.

00The line adopted starts from Lake Suches, the source of a small river of that name flowing into the north of Lake Titicaca, crosses the Cordillera by the Palomani to the Tambopata river, follows that stream to the mouth of the Lanza, thence crosses to the source of the Heath river, which forms the dividing line down to its junction with the Madre de Dios, descends that river to the mouth of the Torosmonas, thence in a straight line north-westerly to the intersection of the Tahu.amanu river by the 69th meridian, and thence north on that meridian to the Brazilian frontier.

00The vapour tension may approximate to a linear function of the composition, and the curve will then be practically a straight line.

00Also the notion that snakes when attacking are able to jump off the ground is quite erroneous; when they strike an object, they dart the fore part of their body, which was retracted in several bends, forwards in a straight line.

00Since the potential rises proportionately to the quantity in the conductor, the ends of these ordinates will lie on a straight line and define a triangle whose base line is a length equal to the total quantity Q and V height a length equal to the final potential V.

00Newton defined the diameter of a curve of any order as the locus of the centres of the mean distances of the points of intersection of a system of parallel chords with the curve; this locus may be shown to be a straight line.

00Thence it crosses that lake in a straight line and afterwards the Ruwenzori to its highest point, Margherita peak, whence it follows the Lamia River to its junction with the Semliki.

00The Avenue Jules Ferry is intersected by a north-to south street running in a straight line over two miles.

00It is also convenient to regard as coming under mensuration the consideration of certain derived magnitudes, such as the moment of a plane figure with regard to a straight line in its plane, the calculation of w]iich involves formulae which are closely related to formulae for determining areas and volumes.

00The rectangle, for instance, has so far been regarded as a plane figure bounded by one pair of parallel straight lines and another pair at right angles to them, so that the conception of " rectangularity " has had reference to boundary rather than to content; analytically, the rectangle must be regarded as the figure generated by an ordinate of constant length moving parallel to itself with one extremity on a straight line perpendicular to it.

00Draw any straight line at right angles to CA and DB (produced if necessary), meeting them in M and N.

00(iii) Take any straight line intersecting or not intersecting the figure, and draw perpendiculars Aa, Bb, Cc, Dd,.

00In the case of a plane area or a plane continuous line the moment with regard to a straight line in the plane is the same as the moment with regard to a perpendicular plane through this line; it is the sum of the products of each element of area or length by its distance from the straight line.

00- The solid or surface generated by the revolution of a plane closed figure or a plane continuous line about a straight line in its plane, not intersecting it, is a solid of revolution or surface of revolution, the straight line being its axis.

00When the value of dyldx is not very small E is no longer constant, but is rather greater in compression and rather less in extension than -yP. This can be seen by considering that the relation between p and is given by a curve and not by a straight line.

00The cylinder is mounted on an axis and turned round, while the style attached to the vibrating body is in light contact with it, and traces therefore a wavy circle, which, on taking off the paper and flattening it, becomes a wavy straight line.

0072 with arcs of the length 1,, l2, l3, &c., and with the radii r1, r 2, &c. (note, for a length 2l 1 at each end the radius will be infinite, and the curve must end with a straight line tangent to the last arc), then let v be the measured deflection of this curve from the straight line, and V the actual deflection of the bridge; we have V = av/b, approximately.

00It imitates the motions made in polishing a speculum by hand by giving both a rectilinear and a lateral motion to the polisher, while the speculum revolves slowly; by shifting two eccentric pins the course of the polisher can be varied at will from a straight line to an ellipse of very small eccentricity, and a true parabolic figure can thus be obtained.

00On the assumption of uniform pressure up the bore, practically realizable in a Zalinski pneumatic dynamite gun, the pressure-curve would be the straight line HK of fig.

00If the pressure falls off uniformly, so that the pressure-curve is a straight line PDF sloping downwards and cutting AM in F, then the energy-curve will be a parabola curving downwards, and the velocity-curve can be represented by an ellipse, or circle with centre F and radius FA; while the time-curve will be a sinusoid.

00But if the pressure-curve is a straight line F'CP sloping upwards, cutting AM behind A in F', the energy-curve will be a parabola curving upwards, and the velocity-curve a hyperbola with center at F'.

00in a straight line S.

00to the IIIth meridian, thence in a straight line (nearly W.N.W.) to a point on the Colorado river 20 m.

00A system of circles is coaxal when the locus of points from which tangents to the circles are equal is a straight line.

00Since the area of a circle equals that of the rectilineal triangle whose base has the same length as the circumference and whose altitude equals the radius (Archimedes, KIKXou A ir, prop.i), it follows that, if a straight line could be drawn equal in length to the circumference, the required square could be found by an ordinary Euclidean construction; also, it is evident that, conversely, if a square equal in area to the circle could be obtained it would be possible to draw a straight line equal to the circumference.

00A given straight line being viewed as equal in length to the circumference of a circle, he sought to find the diameter of the circle.

00The diameter sought is the straight line from A to the limiting position of the series of B's, say the straight line AB co.

00For in such a construction every point of the figure is obtained by the intersection of two straight lines, a straight line and a circle, or two circles; and as this implies that, when a unit of length is introduced, numbers employed, and the problem transformed into one of algebraic geometry, the equations to be solved can only be of the first or second degree, it follows that the equation to which we must be finally led is a rational equation of even degree.

00De Rationis Sectione had for its subject the resolution of the following problem: Given two straight lines and a point in each, to draw through a third given point a straight line cutting the two fixed lines, so that the parts intercepted between the given points in them and the points of intersection with this third line may have a given ratio.

00De Inclinationibus had for its object to insert a straight line of a given length, tending towards a given point, between two given (straight or circular) lines.

00Following Euclid, a right angle is formed by a straight line standing upon another straight line so as to make the adjacent angles equal; any angle less than a right angle is termed an acute angle, and any angle greater than a right angle an obtuse angle.

00Galileo proceeded to measure the motion of a body on a smooth, fixed, inclined plane, and found that the law of constant acceleration along the line of slope of the plane still held, the acceleration decreasing in magnitude as the angle of inclination was reduced; and he inferred that a body, moving on a smooth horizontal plane, would move with uniform velocity in a straight line if the resistance of the air, and friction due to contact with the plane, could be eliminated.

00Newton assumed the possibility of choosing a base such that, relatively to it, the motion of any particle would have only such divergence from uniform velocity in a straight line as could be expressed by laws of acceleration dependent on its relation to other bodies.

00The south side, running nearly due east and west, is about equally long, if measured from the end of the west wall to the point which the east wall would touch when produced due south in a straight line from the place at which it was demolished to make way for " Nero's house."

00from Ochamps to Anseremme in a straight line.

00A straight line of latitude runs through all of these.

00The Suez Canal runs in a straight line for 20 m.

00The error of flatness of the joints from a straight line and a true square is but thth in.

00Turkey claimed that the peninsula of Sinai consisted only of the territory south of a straight line from Akaba to Suez, and that Egyptian territory north of that line was traced from Rafa to Suez.

00an approximately straight line as far as a point on the gulf of Akaba at least 3 m.

00Peaucellier's discovery of the straight line link motion associated with his name, and he also invented the skew pentagraph.

00A joint commission was appointed, which marked out the boundary from Rafah, about midway between Gaza and El-Arish, in an almost straight line S.S.W.

00Between the debouchment of the Upper Murghab from the Firozkhoi uplands into the comparatively low level of the valley above Bala Murghab, extending eastwards in a nearly straight line to the upper sources of the Shibarghan stream, the Band-i-Turkestan range forms the northern ridge between the plateau and the sand formations of the Chul.

00Deduction is analysis when it is regressive from consequence to real ground, as when we start from the proposition that the angles of a triangle are equal to two right angles and deduce analytically that therefore (i) they are equal to equal angles made by a straight line standing on another straight line, and (2) such equal angles are two right angles.

00in a straight line and attains a maximum width N.

00The light reflected from the fixed mirror traces a straight line on the paper, serving as a base line from which the variations in declination are measured.

00It is therefore adequately represented, for mathematical purposes, by a straight line AB drawn in the direction in question, of length proportional (on any convenient scale) to the magnitude of the force.

00If funiculars be drawn for two positions 0,0 of the pole in the force-diagram, their corresponding sides will intersect on a straight line parallel to 00.

00When the given forces are all parallel, the force-polygon consists of a series of segments of a straight line.

00For diagrammatic purposes each member is sufficiently represented by a straight line terminating at the two joints; these lines will be referred to as the bars of the frame.

00The co-ordinates of any point on (13) may be written x=rcosO, y=rsrnO, z=csin2O; (14) hence if we imagine a curve of sines to be traced on a circular cylinder so that the circumference just includes two complete undulations, a straight line cutting the axis of the cylinder at right angles and From Sir Robert S.

00Again, any plane w is the locus of a system of null-lines meeting in a point, called the null-point of c. If a plane revolve about a fixed straight line p in it, its ntill-point describes another straight line p, which is called the conjugate line of p. We have seen that the wrench may be replaced by two forces, one of which may act in any arbitrary line p. It is now evident that the second force must act in the conjugate line p, since every line meeting p, p is a null-line.

00P,, we draw any system of parallel planes meeting a straight line OX in the points Mi, M2,

00The curve of positions corresponding to (4) is a parabola, and that of velocities is a straight line.

00If two masses m1, nil moving in the same straight line impinge, with the result that the velocities are changed from u1, u2, to ui, ui, then, since the impulses on the two bodies must be equal and opposite, the total momentum is unchanged, i.e.

00(I) A parallel projection of a straight line is a straight line.

00(3) A parallel projection of a straight line or a plane surface divided in a given ratio is a straight line or a plane surface divided in the same ratio.

00For the condition of equilibrium of forces not parallel is that they shall be represented in direction and magnitude by the sides and diagonals of certain parallelograms, and of parallel forces that they shall divide certain straight lines in certain ratios; and the parallel projection of a parallelogram is a parallelogram, and that of a straight line divided in a given ratio is a straight line divided in the same ratio.

00The most common forms for the paths of the points of a piece of mechanism, whose motion is simple shifting, are the straight line and the circle.

00Shifting in a straight line is regulated either by straight fixed guides, in contact with which the moving piece slides, or by combinations of link-work, called parallel motions, which will be described in the sequel.

00Shifting in a straight line is usually reciprocating; that is to say, the piece, after shifting through a certain distance, returns to its original position by reversing its motion.

00That for a pair of turning pieces with parallel axes, and for a turning piece and a shifting piece, the line of contact is straight, and parallel to the axes or axis; and hence that the rolling surfaces are either plane or cylindrical (the term cylindrical including all surfaces generated by the motion of a straight line parallel tO itself).

00That for a pair of turning pieces with intersecting axes the line of contact is also straight, and traverses the~ point of intersection of the axes; and hence that the rolling surfaces are conical, with a common apex (the term conical including all surfaces generated by the motion of a straight line which traverses a fixed point).

00In a pair of pieces in rolling contact every straight line traversing the line of contact is a line of connection.

00To work with a wheel of any other figure, its section must be a rolling curve, subject to the condition that the perpendicular distance from the pole or centre of the wheel to a straight line parallel to the direction of the motion of the rack shall be constant.

00Let r1 be the radiusvector of a point of contact on the wheel, Xi the ordinate from the straight line before mentioned to the corresponding point of contact on the rack.

00It also determines the forms of the teeth of straight racks, if one of the centres be removed, and a straight line EIE, parallel to the direction of motion of the rack, and perpendicular to CilCi, be substituted for a pitch-circle.

00Let C1, C1 be the centres of two wheels, B~IB1, B2IB1 their pitch-circles, I the pitch-point; let the obliquity of action of the teeth be constant, so that the same straight line P1 I?z shall represent at once the constant line of connection of teeth and the path of contact.

00Teeth for a given Path of Contact: Sangs Method.In the preceding section the form of the teeth is found by assuming a figure for the path of contact, viz, the straight line.

00where perpendicular to the straight line TI; so FIG.

00The figure of the path of con tact is that traced on a fixed plane by the tracing-point, when the rolling curve is rotated in such a manner as always to touch a fixed straight line EIE (or EIE, as the case may be) at a fixed point I (or I).

00The teeth of a rack, of the same, set, are traced by rolling the rolling curve on both sides of a straight line.

00Teeth of Skew-Bevel Wheels.The crests of the teeth of a skew-bevel wheel are parallel to the generating straight line of the hyperboloidal pitch-surface; and the transverse sections of the teeth at a given pitch-circle are similar to those of the teeth of a bevelwheel whose pitch surface is a cone touching the hyperboloidal surface at the given circle.

00If the axes of the ~ shafts are in the same straight line, the coupling consists in so connecting their the same straight line combinations of contiguous ends that they shall rotate as one piece; but if the axes are not in C

00Oldhams coupling may be used with advantage where the axes of the shafts are intended to be as nearly in the same straight line as is possible, but where there is some doubt as to the practibility I or nermanency of their exact continuity.

00Then, if the two ends of the stroke be in one straight line with the axis of the crank, S=2R; (37)

00and if these ends be not in one straight line with that axis, then S, L R, and L+R, are the three sides of a triangle, having the angle opposite S at that axis; so that, if 0 be the supplement of the arc between the dead-points, Si=2(L2+Ri)_2(Li_R~ cos0,)

00Draw BE perpendicular to CB, cutting CD produced in E, then E is the instantaneous axis of the bar ADB; and the direction of motion of A is at every instant perpendicular to EAthat is, along the straight line ACa.

0078.* An example of an approximate straight-line motion composed of three bars fixed to a frame is shown in fig.

00If the respective lengths are made in the proportions AC: CD: DB = I: 1.3: o4 the middle point P of DB will describe an approximately straight line parallel to AC within limits of length about equal to AC. C. N.

00Peaucellier, a French engineer officer, was the first, in 1864, to invent a linkwoik with which an exact straight line could be drawn.

00It can be proved that the point C always moves in a straight line at right angles to the line EF.

00116), he fixed at any one point a in any one of the links produced in either direction, and if any straight line be drawn from this point to cut the links in the points b and a, then the points a, b, c a b 0

00will be in a straight line for - - - - .

00The combination of the parallelogram with a straight-line motion, for guiding one of the points in a straight line, is illustrated in Watts parallel motion for steam-engines.

00Adding the centres corresponding to these several axes to the figure, it will be seen that there are six centres in connection with the four-bar chain of which four are permanent and two are instantaneous or virtual centres; and, further, that whatever be the configuration of the chain these centres group themselves into three sets of three, each set lying on a straight line.

00Now let PT be a tangent to the curve at P, cutting OX in T; PT=PYXsecant obliquity, and this is to be a constant quantity; hence the curve is that known as the tractory of the straight line OX, in which PT = OR = constant, This curve is described by having a fixed straight edge parallel to OX, along which slides a slider carrying a pin whose centre is T.

00Originally nomads (hunters and fishers), all the Finnic people except the Lapps and Ostyaks have long yielded to the influence of civilization, and now everywhere lead settled lives as herdsmen, agriculturists, traders, &c. Physically the Finns (here to be distinguished from the Swedish-speaking population, who retain their Scandinavian qualities) are a strong, hardy race, of low stature, with almost round head, low forehead, flat features, prominent cheek bones, eyes mostly grey and oblique (inclining inwards), short and flat nose, protruding mouth, thick lips, neck very full and strong, so that the occiput seems flat and almost in a straight line with the nape; beard weak and sparse, hair no doubt originally black, but, owing to mixture with other races, now brown, red and even fair; complexion also somewhat brown.

00on that parallel to its intersection with the 111th meridian of longitude west of Greenwich, from that point of intersection in a straight line to the Colorado river, 20 m.

00Single and two-reel machines are generally constructed on the " straight line " principle, i.e.

00The distance from Mt Ararat to Serrakhs in a straight line is about 930 m.

00in a straight line.

00The treaty gave to Portugal all lands which might be discovered east of a straight line drawn from the Arctic Pole to the Antarctic, at a distance of 370 leagues west of Cape Verde.

0010 20' S., and designated a straight line to the source of the Javary as the frontier, which gave to Brazil a large area of territory; but when the valuable rubber forests of the upper Purus became known the Brazilians invaded them and demanded another modification of the boundary line.

00north of Fort Olimpo and run south-west in a straight line to an intersection with the Pilcomayo in long.

00The new boundary line starts from the summit of the Sapaleri (or Zapalegui), where the Argentine, Bolivian and Chilean boundaries converge, and runs west to Licancaur, thence north to the most southern source of Lake Ascotan which it follows to and across this lake in the direction of the Oyahua volcano, and thence in a straight line to the Tua volcano, on the frontier of the province of Tarapaca.

00When the ellipse becomes a circle, the meridian line becomes a straight line parallel to the axis, and the film passes into the form of a cylinder of revolution.

00At first the tension will diminish, but if the process be continued the tension will reach a minimum value and will afterwards increase to infinity as the chain between A and B approaches to the form of a straight line.

00in a straight line N.E.

00In a straight line the two towns are only 80 m..

00' The total length of the Passaic is about 100 m., but its course is so irregular that the distance in a straight line from its source to its mouth is only about 15 m.

00Schizodentalium: ventral border of posterior aperture with a series of small holes in a straight line.

00Seen from the valley, this straight line of lofty heights, culminating in Crossfell, presents the nearest approach in England to the appearance of a mountain range.

00The low island of Anglesey, which is built tip of the fundamental Archaean rocks, is important as a link in the main line of communication with Ireland, because it is separated from the mainland by a channel narrow enough to be bridged, and lies not far out of the straight line joining London and Dublin.

00The simplest instance of a caustic by refraction (or diacaustic) is when luminous rays issuing from a point are refracted at a straight line.

00In November 1768, at a general council of the Six Nations with Sir William Johnson and representatives of Pennsylvania and Virginia, held at Fort Stanwix, on the site of the present Rome, New York (q.v.), at which was signed a treaty establishing the boundary line between the English possessions and the territory claimed by the Six Nations, the Indians sold for $io,000 to Thomas Penn (1702-1775) and Richard Penn (1706-1771), respectively, the second and third sons of William Penn - the founder of Pennsylvania - by his second wife, the remaining land in the province of Pennsylvania to which they claimed title, namely the tract lying south of the west branch of the Susquehanna river and of a straight line from the north-west corner of what is now Cambria county to the present Kittanning (in Armstrong county), and all of the territory east of the Allegheny river below Kittanning and south of the Ohio river.

00The new building, the shell of which was completed in 1906, faces the Rettifilo, a new wide street which leads from the Borsa in a straight line to the railway station; at the back it joins the former building, which is at a higher level.

00There are over 120 separate chambers, the caverns extending nearly a mile in a straight line.

00Correspondingly, the straight line a a represents uniformly distributed supply, also cumulatively recorded, of the same quantity of water over the same period.

00Now, in order that a reservoir may enable the varying flow, represented cumulatively by the irregular line, to be discharged in a continuous and uniform flow to satisfy a demand represented cumulatively by the straight line a a, its capacity must be such that it will hold not only the II% surplus of the same year, but that, on June loth, when this surplus has been used to satisfy the demand, it will still contain the water c d-19%stored from a previous year; otherwise between June 10th and August 31st the reservoir will be empty and only the dry weather flow of the stream will be available for supply.

00The reservoir begins to fall at the end of February, and continues to do so with few and short exceptions until the end of August, and it so happens that about the end of August this dotted line, b b representing actual cumulative demand, crosses the straight line a a of uniform demand, so that the excess of demand, represented by the slope from June to September, is balanced by the deficiency of demand, represented by the flatter slope in the first five months, except as regards the small quantity b e near the end of February, which, not having been drawn off during January and February, must overflow before the end of February.

00In the same way we may group in a single diagram any number of consecutive driest years, and either ascertain the reservoir capacity necessary for a given uniform yield (represented cumulatively by a straight line corresponding with a'a', but drawn over all the years instead of one), or conversely, having set up a vertical from the most trying point in the line of cumulative flow (c or c in fig.

003 - representing, in percentage of the total annual flow of the driest year, the capacity of reservoir which it may be convenient to provide) we may draw a straight line a"' a" of uniform yield from the head of that vertical to the previous point of maximum excess of cumulative flow.

0019, the maximum movement from the original straight line being about I ft.

00Aschan (Ber., 1902, 35, p. 33 8 9) depicts these cases by representing the plane of the carbon atoms of the ring as a straight line and denoting the substituted hydrogen atoms by the letters X, Y, Z.

00In June 1696 Bernoulli addressed a letter to the mathematicians of Europe challenging them to solve two problems - (1) to determine the brachistochrone between two given points not in the same vertical line, (2) to determine a curve such that, if a straight line drawn through a fixed point A meet it in two points P 1, P 2, then AP 1 m +AP 2 m will be constant.

00in a straight line from those of the Ucayali.

00It is one of the most crooked streams in the world, and its length in a straight line is less than half that by its curves.

00(The straight line and the point are not for the moment regarded as curves.) Next to the circle we have the conic sections, the invention of them attributed to Plato (who lived 430-347 B.C.); the original definition of them as the sections of a cone was by the Greek geometers who studied them soon replaced by a proper definition in piano like that for the circle, viz.

00and flows almost in a straight line through the heart of the kingdom to the Danube.

00which act upon each other, their motions are so related that the centre of gravity of the entire system moves in a straight line with a constant velocity.

00Rounding the southern end of the island, there is no other inlet save the small bay north of Fort Dauphin, at the southern end of the straight line of coast already mentioned.

00To investigate the form of the curve use may be made of the definition: the ellipse is the locus of a point which moves so that the ratio of its distance from a fixed point (the focus) to its distance from a straight line (the directrix) is constant and is less than unity.

00The straight line and the line through the centre parallel to the chords are named conjugate diameters; each bisects the chords parallel to the other.

00I12), Cistaceae, and most gymnosperms. In such an ovule a straight line drawn from the hilum to the micropyle passes along the axis of the ovule.

00His lips thinned to a straight line.

00He paused only long enough to locate her, and then made a straight line for her.

00His lips thinned into a straight line as he focused on the food in his plate.

00amortisests are amortized on a straight line basis over the time period during which the product is expected to be sold.

00In this case the forward false cast is hit high and continued into a straight line backcast without any water contact.

00The regression coefficient for a straight line through origin is.

00As the piston moves up and down in the cylinder it rotates the crankshaft and converts the straight line motion into rotary motion.

00For straight line depreciation, we would normally expect your items to be depreciated over a minimum period of three years.

00I mean who gives a toss about the transfer between funds to reflect the straight line devaluation of the fixed asset.

00On their backs they have a fin called a dorsal fin which helps them to swim in a straight line.

00Writing down the equation of a straight line given a diagram with a parallel line and the y intercept.

00However, it is rare that relationships in biology, including enzyme kinetics, follow a straight line.

00To produce a finite straight line continuously in a straight line.

00plunger rods attached to the outer free ends travel in substantially straight-line motion.

00regression coefficient for a straight line through origin is.

00Outline shapes Outline shapes, such as triangles, rectangles and parallelograms, consist of a series of straight-line segments between the vertices.

00The normal toe-in setting is up to 20 minutes, which provides good straight-line stability.

00straight-line depreciation method.

00straight-line segments used to produce the field.

00straight-line graph, pick two points on the graph.

00straight-line stability.

00straight-line basis over the lease term.

00straight-line distance from rim to shoulder being 48cm.

00Finally, we get down to our first proposition: Proposition 1. On a given straight line to construct an equilateral triangle.

00It was nervous at the rear and very twitchy even in a straight line.

00A straight line extension of the curve can lead to a gross underestimate.

00veer away from the straight line of God's revealed will.

00His mind has a lightning-like zig zag which is its straight line of smiting.

00in a straight line broken only by the mouths of the Don-Nai and Mekong.

00In discussing the effect of wear upon a screw, it will be convenient to imagine the thread unrolled and forming a wedge, of which we can represent the unworn bearing-side by a straight line AB (fig.

00io) to be the surface of the sea, b c the bottom, and c c the straight line made by the cable; then, if a hill H, which is at any part steeper than the inclination of the cable, is passed over, the cable touches it at some point t before it touches the part immediately below t, and if the friction between the cable and the ground is sufficient the cable will either break or be left in a long span ready to break at some future time.

00Its greatest length in a straight line along the mainland is from N.W.

00This is most clearly marked on the side of the Apennines, where the great Aemilian Way, which has been the high road from the time of the Romans to our own, preserves an unbroken straight line from Rimini to Piacenza, a distance of more than 150 m., during which the underfalls of the mountains continually approach it on the left, without once crossing the line of road.

00The Via Flaminia was the earliest and most important road to the north; and it was soon extended (in 187 B.C.) by the Via Aemilia running through Bononia as far as Placentia, in an almost absolutely straight line between the plain of the P0 and the foot of the Apennines.

00In all, there is a wonderful amount of specialization, though perhaps in a very straight line from generalized forms; but the affinity to Australian or Polynesian types is in many cases clearly traceable, and it cannot be supposed but that these last are of cognate origin with those of New Zealand.

00Reverse curves are compound curves in which the components are of contrary flexure, like the letter S; strictly the term is only applicable when the two portions follow directly one on the other, but it is sometimes used of cases in which they are separated by a " tangent " or portion of straight line.

00Napoleon, in making the road over the Simplon, deviated from the straight line in order to leave it standing.

00In the Orthorrhapha, in the pupae of which the appendages of the perfect insect are usually visible, the pupa-case generally splits in a straight line down the back near the cephalic end; in front of this longitudinal cleft there may be a small transverse one, the two together forming a T-shaped fissure.

00Indeed, he never shook off the erroneous ideas of his time regarding the paths of projectiles, further than to see that no part of them could be a straight line.

00GAYAL, a domesticated ox allied to the Gaur, but distinguished, among other features, by the more conical and straighter horns, and the straight line between them.

00The straightness of a straight line and the planeness of a plane require consideration.

00representing only 47 in a straight line.

00Stations which are placed in a straight line across a sea are then connected and " sections " are made.

00This correction may be indicated in the diagram by a straight line drawn from o through the point at which the line of I = moo intersects that of H = o 28 (Rayleigh, Phil.

00The curve thus constructed should be a straight line inclined to the horizontal axis at an angle 0, the tangent of which is 1.6.

00Rowland, believing that the curve would continue to fall in a straight line meeting the horizontal axis, inferred that the induction corresponding to the point B-about 17,500-was the highest I Phil.

00The latter gives values of the constants a and b for different samples of iron and steel, some of which are shown in the following table :- K=a+bH For most samples of steel the straight-line law was found to hold approximately up to H=3; in the case of iron and of soft steel the approximation was less close.

0024 was converted into an almost perfectly straight line passing through the origin, and lying below the horizontal axis; while the permeability of the metal was greatly diminished by the operation.

00in a straight line from source to mouth.

00in a straight line S.S.E.

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.

00the contraction along a given straight line will in general have different values in any two neighbouring crystals, and the crystals consequently become slightly detached from one another.

00For the desulphurization of zinc blende where it is not intended to collect and save the sulphur there are many mechanical kilns, generally classified as straight-line, horse-shoe, turret and shaft kilns; all of these may be made to do good work on moderately clean ores which do not melt at the temperature of desulphurization.

00Beyond the fort are various public buildings leading to Otoo Street, the main thoroughfare, which runs two miles in a straight line to Christiansborg.

00This line has been twice modified by treaties between Bolivia and Brazil, but without the consent of Peru, which claimed all the territory eastward to the Madeira between the above-mentioned line and the Beni-Madidi rivers, the line of demarcation following the Pablo-bamba, a small tributary of the Madidi, to its source, and thence in a straight line to the village of Conima, on Lake Titicaca.

00The line adopted starts from Lake Suches, the source of a small river of that name flowing into the north of Lake Titicaca, crosses the Cordillera by the Palomani to the Tambopata river, follows that stream to the mouth of the Lanza, thence crosses to the source of the Heath river, which forms the dividing line down to its junction with the Madre de Dios, descends that river to the mouth of the Torosmonas, thence in a straight line north-westerly to the intersection of the Tahu.amanu river by the 69th meridian, and thence north on that meridian to the Brazilian frontier.

00The vapour tension may approximate to a linear function of the composition, and the curve will then be practically a straight line.

00Also the notion that snakes when attacking are able to jump off the ground is quite erroneous; when they strike an object, they dart the fore part of their body, which was retracted in several bends, forwards in a straight line.

00Since the potential rises proportionately to the quantity in the conductor, the ends of these ordinates will lie on a straight line and define a triangle whose base line is a length equal to the total quantity Q and V height a length equal to the final potential V.

00Newton defined the diameter of a curve of any order as the locus of the centres of the mean distances of the points of intersection of a system of parallel chords with the curve; this locus may be shown to be a straight line.

00Thence it crosses that lake in a straight line and afterwards the Ruwenzori to its highest point, Margherita peak, whence it follows the Lamia River to its junction with the Semliki.

00The Avenue Jules Ferry is intersected by a north-to south street running in a straight line over two miles.

00It is also convenient to regard as coming under mensuration the consideration of certain derived magnitudes, such as the moment of a plane figure with regard to a straight line in its plane, the calculation of w]iich involves formulae which are closely related to formulae for determining areas and volumes.

00The rectangle, for instance, has so far been regarded as a plane figure bounded by one pair of parallel straight lines and another pair at right angles to them, so that the conception of " rectangularity " has had reference to boundary rather than to content; analytically, the rectangle must be regarded as the figure generated by an ordinate of constant length moving parallel to itself with one extremity on a straight line perpendicular to it.

00Draw any straight line at right angles to CA and DB (produced if necessary), meeting them in M and N.

00If we take a series of right trapezia, such that one side (§ 23) of the first is equal to one side of the second, the other side of the second is equal to one side of the third, and so on, and place them with their bases in a straight line and their equal M sides adjoining each other, we get a figure such as c i ll Mabcdefs (fig.

00(iii) Take any straight line intersecting or not intersecting the figure, and draw perpendiculars Aa, Bb, Cc, Dd,.

00In the case of a plane area or a plane continuous line the moment with regard to a straight line in the plane is the same as the moment with regard to a perpendicular plane through this line; it is the sum of the products of each element of area or length by its distance from the straight line.

00- The solid or surface generated by the revolution of a plane closed figure or a plane continuous line about a straight line in its plane, not intersecting it, is a solid of revolution or surface of revolution, the straight line being its axis.

00On a straight line OX in any plane take a point N at distance x from 0, and draw an ordinate NP at right angles to OX and equal to S/1, where 1 is some fixed length (e.g.

00When the value of dyldx is not very small E is no longer constant, but is rather greater in compression and rather less in extension than -yP. This can be seen by considering that the relation between p and is given by a curve and not by a straight line.

00The cylinder is mounted on an axis and turned round, while the style attached to the vibrating body is in light contact with it, and traces therefore a wavy circle, which, on taking off the paper and flattening it, becomes a wavy straight line.

0072 with arcs of the length 1,, l2, l3, &c., and with the radii r1, r 2, &c. (note, for a length 2l 1 at each end the radius will be infinite, and the curve must end with a straight line tangent to the last arc), then let v be the measured deflection of this curve from the straight line, and V the actual deflection of the bridge; we have V = av/b, approximately.

00It imitates the motions made in polishing a speculum by hand by giving both a rectilinear and a lateral motion to the polisher, while the speculum revolves slowly; by shifting two eccentric pins the course of the polisher can be varied at will from a straight line to an ellipse of very small eccentricity, and a true parabolic figure can thus be obtained.

00On the assumption of uniform pressure up the bore, practically realizable in a Zalinski pneumatic dynamite gun, the pressure-curve would be the straight line HK of fig.

003 parallel to AM; the energycurve AQE would be another straight line through A; the velocitycurve AvV, of which the ordinate v is as the square root of the energy, would be a parabola; and the acceleration of the shot being constant, the time-curve AtT will also be a similar parabola.

00If the pressure falls off uniformly, so that the pressure-curve is a straight line PDF sloping downwards and cutting AM in F, then the energy-curve will be a parabola curving downwards, and the velocity-curve can be represented by an ellipse, or circle with centre F and radius FA; while the time-curve will be a sinusoid.

00But if the pressure-curve is a straight line F'CP sloping upwards, cutting AM behind A in F', the energy-curve will be a parabola curving upwards, and the velocity-curve a hyperbola with center at F'.

00in a straight line S.

00to the IIIth meridian, thence in a straight line (nearly W.N.W.) to a point on the Colorado river 20 m.

00A system of circles is coaxal when the locus of points from which tangents to the circles are equal is a straight line.

00Since the area of a circle equals that of the rectilineal triangle whose base has the same length as the circumference and whose altitude equals the radius (Archimedes, KIKXou A ir, prop.i), it follows that, if a straight line could be drawn equal in length to the circumference, the required square could be found by an ordinary Euclidean construction; also, it is evident that, conversely, if a square equal in area to the circle could be obtained it would be possible to draw a straight line equal to the circumference.

00A given straight line being viewed as equal in length to the circumference of a circle, he sought to find the diameter of the circle.

00The diameter sought is the straight line from A to the limiting position of the series of B's, say the straight line AB co.

00The proof of the correctness of the construction is seen to be involved in the following theorem, which serves likewise to throw new light on the subject: - AB being any straight line whatever, and the above construction being made, then AB is the diameter of the circle circumscribed by the square AB CD (self-evident), AB, is the diameter of the circle circumscribed by the regular 8-gon having the same perimeter as the square, AB, is the diameter of the circle circumscribed by the regular 16-gon having the same perimeter as the square, and so on.

00For in such a construction every point of the figure is obtained by the intersection of two straight lines, a straight line and a circle, or two circles; and as this implies that, when a unit of length is introduced, numbers employed, and the problem transformed into one of algebraic geometry, the equations to be solved can only be of the first or second degree, it follows that the equation to which we must be finally led is a rational equation of even degree.

00De Rationis Sectione had for its subject the resolution of the following problem: Given two straight lines and a point in each, to draw through a third given point a straight line cutting the two fixed lines, so that the parts intercepted between the given points in them and the points of intersection with this third line may have a given ratio.

00De Inclinationibus had for its object to insert a straight line of a given length, tending towards a given point, between two given (straight or circular) lines.

00As the star decreases in latitude, this circle will be viewed more and more obliquely, becoming a flatter and flatter ellipse until, with A is zero latitude, it degenerates into a straight line (fig.

00contains also (I), under the head of the de determinate sectione of Apollonius, lemmas which, closely examined, are seen to be cases of the involution of six points; (2) important lemmas on the Porisms of Euclid (see PoRIsM); (3) a lemma upon the Surface Loci of Euclid which states that the locus of a point such that its distance from a given point bears a constant ratio to its distance from a given straight line is a conic, and is followed by proofs that the conic is a parabola, ellipse, or hyperbola according as the constant ratio is equal to, less than or greater than i (the first recorded proofs of the properties, which do not appear in Apollonius).

00Following Euclid, a right angle is formed by a straight line standing upon another straight line so as to make the adjacent angles equal; any angle less than a right angle is termed an acute angle, and any angle greater than a right angle an obtuse angle.

00Galileo proceeded to measure the motion of a body on a smooth, fixed, inclined plane, and found that the law of constant acceleration along the line of slope of the plane still held, the acceleration decreasing in magnitude as the angle of inclination was reduced; and he inferred that a body, moving on a smooth horizontal plane, would move with uniform velocity in a straight line if the resistance of the air, and friction due to contact with the plane, could be eliminated.

00Newton assumed the possibility of choosing a base such that, relatively to it, the motion of any particle would have only such divergence from uniform velocity in a straight line as could be expressed by laws of acceleration dependent on its relation to other bodies.

00The south side, running nearly due east and west, is about equally long, if measured from the end of the west wall to the point which the east wall would touch when produced due south in a straight line from the place at which it was demolished to make way for " Nero's house."

00from Ochamps to Anseremme in a straight line.

0069-180), in 1678, was a new set of dialogues on physical questions, most of which he had treated in a similar fashion before; but now, in dealing with gravitation, he was able to fire a parting shot at Wallis; and one more demonstration of the equality of a straight line to the arc of a circle, thrown in at the end, appropriately closed the strangest warfare in which perverse thinker ever engaged.4 We must now turn back to trace the fortunes of Hobbes and his other doings in the last twenty years of his life.

00A straight line of latitude runs through all of these.

00The Suez Canal runs in a straight line for 20 m.

00The error of flatness of the joints from a straight line and a true square is but thth in.

00Turkey claimed that the peninsula of Sinai consisted only of the territory south of a straight line from Akaba to Suez, and that Egyptian territory north of that line was traced from Rafa to Suez.

00an approximately straight line as far as a point on the gulf of Akaba at least 3 m.

00Peaucellier's discovery of the straight line link motion associated with his name, and he also invented the skew pentagraph.

00A joint commission was appointed, which marked out the boundary from Rafah, about midway between Gaza and El-Arish, in an almost straight line S.S.W.

00Between the debouchment of the Upper Murghab from the Firozkhoi uplands into the comparatively low level of the valley above Bala Murghab, extending eastwards in a nearly straight line to the upper sources of the Shibarghan stream, the Band-i-Turkestan range forms the northern ridge between the plateau and the sand formations of the Chul.

00Deduction is analysis when it is regressive from consequence to real ground, as when we start from the proposition that the angles of a triangle are equal to two right angles and deduce analytically that therefore (i) they are equal to equal angles made by a straight line standing on another straight line, and (2) such equal angles are two right angles.

00in a straight line and attains a maximum width N.

00The light reflected from the fixed mirror traces a straight line on the paper, serving as a base line from which the variations in declination are measured.

00It is therefore adequately represented, for mathematical purposes, by a straight line AB drawn in the direction in question, of length proportional (on any convenient scale) to the magnitude of the force.

00If funiculars be drawn for two positions 0,0 of the pole in the force-diagram, their corresponding sides will intersect on a straight line parallel to 00.

00When the given forces are all parallel, the force-polygon consists of a series of segments of a straight line.

00For diagrammatic purposes each member is sufficiently represented by a straight line terminating at the two joints; these lines will be referred to as the bars of the frame.

00The co-ordinates of any point on (13) may be written x=rcosO, y=rsrnO, z=csin2O; (14) hence if we imagine a curve of sines to be traced on a circular cylinder so that the circumference just includes two complete undulations, a straight line cutting the axis of the cylinder at right angles and From Sir Robert S.

00Again, any plane w is the locus of a system of null-lines meeting in a point, called the null-point of c. If a plane revolve about a fixed straight line p in it, its ntill-point describes another straight line p, which is called the conjugate line of p. We have seen that the wrench may be replaced by two forces, one of which may act in any arbitrary line p. It is now evident that the second force must act in the conjugate line p, since every line meeting p, p is a null-line.

00P,, we draw any system of parallel planes meeting a straight line OX in the points Mi, M2,

00The curve of positions corresponding to (4) is a parabola, and that of velocities is a straight line.

00If two masses m1, nil moving in the same straight line impinge, with the result that the velocities are changed from u1, u2, to ui, ui, then, since the impulses on the two bodies must be equal and opposite, the total momentum is unchanged, i.e.

00(I) A parallel projection of a straight line is a straight line.

00(3) A parallel projection of a straight line or a plane surface divided in a given ratio is a straight line or a plane surface divided in the same ratio.

00For the condition of equilibrium of forces not parallel is that they shall be represented in direction and magnitude by the sides and diagonals of certain parallelograms, and of parallel forces that they shall divide certain straight lines in certain ratios; and the parallel projection of a parallelogram is a parallelogram, and that of a straight line divided in a given ratio is a straight line divided in the same ratio.

00The most common forms for the paths of the points of a piece of mechanism, whose motion is simple shifting, are the straight line and the circle.

00Shifting in a straight line is regulated either by straight fixed guides, in contact with which the moving piece slides, or by combinations of link-work, called parallel motions, which will be described in the sequel.

00Shifting in a straight line is usually reciprocating; that is to say, the piece, after shifting through a certain distance, returns to its original position by reversing its motion.

00That for a pair of turning pieces with parallel axes, and for a turning piece and a shifting piece, the line of contact is straight, and parallel to the axes or axis; and hence that the rolling surfaces are either plane or cylindrical (the term cylindrical including all surfaces generated by the motion of a straight line parallel tO itself).

00That for a pair of turning pieces with intersecting axes the line of contact is also straight, and traverses the~ point of intersection of the axes; and hence that the rolling surfaces are conical, with a common apex (the term conical including all surfaces generated by the motion of a straight line which traverses a fixed point).

00In a pair of pieces in rolling contact every straight line traversing the line of contact is a line of connection.

00To work with a wheel of any other figure, its section must be a rolling curve, subject to the condition that the perpendicular distance from the pole or centre of the wheel to a straight line parallel to the direction of the motion of the rack shall be constant.

00Let r1 be the radiusvector of a point of contact on the wheel, Xi the ordinate from the straight line before mentioned to the corresponding point of contact on the rack.

00It also determines the forms of the teeth of straight racks, if one of the centres be removed, and a straight line EIE, parallel to the direction of motion of the rack, and perpendicular to CilCi, be substituted for a pitch-circle.

00Let C1, C1 be the centres of two wheels, B~IB1, B2IB1 their pitch-circles, I the pitch-point; let the obliquity of action of the teeth be constant, so that the same straight line P1 I?z shall represent at once the constant line of connection of teeth and the path of contact.

00Teeth for a given Path of Contact: Sangs Method.In the preceding section the form of the teeth is found by assuming a figure for the path of contact, viz, the straight line.

00where perpendicular to the straight line TI; so FIG.

00The figure of the path of con tact is that traced on a fixed plane by the tracing-point, when the rolling curve is rotated in such a manner as always to touch a fixed straight line EIE (or EIE, as the case may be) at a fixed point I (or I).

00The teeth of a rack, of the same, set, are traced by rolling the rolling curve on both sides of a straight line.

00Teeth of Skew-Bevel Wheels.The crests of the teeth of a skew-bevel wheel are parallel to the generating straight line of the hyperboloidal pitch-surface; and the transverse sections of the teeth at a given pitch-circle are similar to those of the teeth of a bevelwheel whose pitch surface is a cone touching the hyperboloidal surface at the given circle.

00If the axes of the ~ shafts are in the same straight line, the coupling consists in so connecting their the same straight line combinations of contiguous ends that they shall rotate as one piece; but if the axes are not in C

00Oldhams coupling may be used with advantage where the axes of the shafts are intended to be as nearly in the same straight line as is possible, but where there is some doubt as to the practibility I or nermanency of their exact continuity.

00Then, if the two ends of the stroke be in one straight line with the axis of the crank, S=2R; (37)

00and if these ends be not in one straight line with that axis, then S, L R, and L+R, are the three sides of a triangle, having the angle opposite S at that axis; so that, if 0 be the supplement of the arc between the dead-points, Si=2(L2+Ri)_2(Li_R~ cos0,)

00Draw BE perpendicular to CB, cutting CD produced in E, then E is the instantaneous axis of the bar ADB; and the direction of motion of A is at every instant perpendicular to EAthat is, along the straight line ACa.

0078.* An example of an approximate straight-line motion composed of three bars fixed to a frame is shown in fig.

00If the respective lengths are made in the proportions AC: CD: DB = I: 1.3: o4 the middle point P of DB will describe an approximately straight line parallel to AC within limits of length about equal to AC. C. N.

00Peaucellier, a French engineer officer, was the first, in 1864, to invent a linkwoik with which an exact straight line could be drawn.

00It can be proved that the point C always moves in a straight line at right angles to the line EF.

00There are other arrangements of bars giving straight-line motions, and these arrangements together with ths general properties of mechanisms of this kind are discussed in How to Draw a Straight Line by A.

00116), he fixed at any one point a in any one of the links produced in either direction, and if any straight line be drawn from this point to cut the links in the points b and a, then the points a, b, c a b 0

00will be in a straight line for - - - - .

00The combination of the parallelogram with a straight-line motion, for guiding one of the points in a straight line, is illustrated in Watts parallel motion for steam-engines.

00Adding the centres corresponding to these several axes to the figure, it will be seen that there are six centres in connection with the four-bar chain of which four are permanent and two are instantaneous or virtual centres; and, further, that whatever be the configuration of the chain these centres group themselves into three sets of three, each set lying on a straight line.

00Kennedy independently, which may be thus stated: If any three bodies, a, b, c, have plane motion their three virtual centres, ~ Ob~, 0,,, are three points on one straight line.

00Now let PT be a tangent to the curve at P, cutting OX in T; PT=PYXsecant obliquity, and this is to be a constant quantity; hence the curve is that known as the tractory of the straight line OX, in which PT = OR = constant, This curve is described by having a fixed straight edge parallel to OX, along which slides a slider carrying a pin whose centre is T.

00Originally nomads (hunters and fishers), all the Finnic people except the Lapps and Ostyaks have long yielded to the influence of civilization, and now everywhere lead settled lives as herdsmen, agriculturists, traders, &c. Physically the Finns (here to be distinguished from the Swedish-speaking population, who retain their Scandinavian qualities) are a strong, hardy race, of low stature, with almost round head, low forehead, flat features, prominent cheek bones, eyes mostly grey and oblique (inclining inwards), short and flat nose, protruding mouth, thick lips, neck very full and strong, so that the occiput seems flat and almost in a straight line with the nape; beard weak and sparse, hair no doubt originally black, but, owing to mixture with other races, now brown, red and even fair; complexion also somewhat brown.

00on that parallel to its intersection with the 111th meridian of longitude west of Greenwich, from that point of intersection in a straight line to the Colorado river, 20 m.

00Single and two-reel machines are generally constructed on the " straight line " principle, i.e.

00The distance from Mt Ararat to Serrakhs in a straight line is about 930 m.

00in a straight line.

00The treaty gave to Portugal all lands which might be discovered east of a straight line drawn from the Arctic Pole to the Antarctic, at a distance of 370 leagues west of Cape Verde.

0010 20' S., and designated a straight line to the source of the Javary as the frontier, which gave to Brazil a large area of territory; but when the valuable rubber forests of the upper Purus became known the Brazilians invaded them and demanded another modification of the boundary line.

00north of Fort Olimpo and run south-west in a straight line to an intersection with the Pilcomayo in long.

00The new boundary line starts from the summit of the Sapaleri (or Zapalegui), where the Argentine, Bolivian and Chilean boundaries converge, and runs west to Licancaur, thence north to the most southern source of Lake Ascotan which it follows to and across this lake in the direction of the Oyahua volcano, and thence in a straight line to the Tua volcano, on the frontier of the province of Tarapaca.

00When the ellipse becomes a circle, the meridian line becomes a straight line parallel to the axis, and the film passes into the form of a cylinder of revolution.

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.

00At first the tension will diminish, but if the process be continued the tension will reach a minimum value and will afterwards increase to infinity as the chain between A and B approaches to the form of a straight line.

00in a straight line N.E.

00In a straight line the two towns are only 80 m..

00' The total length of the Passaic is about 100 m., but its course is so irregular that the distance in a straight line from its source to its mouth is only about 15 m.

00Schizodentalium: ventral border of posterior aperture with a series of small holes in a straight line.

00Seen from the valley, this straight line of lofty heights, culminating in Crossfell, presents the nearest approach in England to the appearance of a mountain range.

00The low island of Anglesey, which is built tip of the fundamental Archaean rocks, is important as a link in the main line of communication with Ireland, because it is separated from the mainland by a channel narrow enough to be bridged, and lies not far out of the straight line joining London and Dublin.

00KuKAos, circle, and Ethos, form), in geometry, the curve traced out by a point carried on a circle which rolls along a straight line.

00The simplest instance of a caustic by refraction (or diacaustic) is when luminous rays issuing from a point are refracted at a straight line.

00In November 1768, at a general council of the Six Nations with Sir William Johnson and representatives of Pennsylvania and Virginia, held at Fort Stanwix, on the site of the present Rome, New York (q.v.), at which was signed a treaty establishing the boundary line between the English possessions and the territory claimed by the Six Nations, the Indians sold for $io,000 to Thomas Penn (1702-1775) and Richard Penn (1706-1771), respectively, the second and third sons of William Penn - the founder of Pennsylvania - by his second wife, the remaining land in the province of Pennsylvania to which they claimed title, namely the tract lying south of the west branch of the Susquehanna river and of a straight line from the north-west corner of what is now Cambria county to the present Kittanning (in Armstrong county), and all of the territory east of the Allegheny river below Kittanning and south of the Ohio river.

00The new building, the shell of which was completed in 1906, faces the Rettifilo, a new wide street which leads from the Borsa in a straight line to the railway station; at the back it joins the former building, which is at a higher level.

00There are over 120 separate chambers, the caverns extending nearly a mile in a straight line.

00Correspondingly, the straight line a a represents uniformly distributed supply, also cumulatively recorded, of the same quantity of water over the same period.

00Now, in order that a reservoir may enable the varying flow, represented cumulatively by the irregular line, to be discharged in a continuous and uniform flow to satisfy a demand represented cumulatively by the straight line a a, its capacity must be such that it will hold not only the II% surplus of the same year, but that, on June loth, when this surplus has been used to satisfy the demand, it will still contain the water c d-19%stored from a previous year; otherwise between June 10th and August 31st the reservoir will be empty and only the dry weather flow of the stream will be available for supply.

00The reservoir begins to fall at the end of February, and continues to do so with few and short exceptions until the end of August, and it so happens that about the end of August this dotted line, b b representing actual cumulative demand, crosses the straight line a a of uniform demand, so that the excess of demand, represented by the slope from June to September, is balanced by the deficiency of demand, represented by the flatter slope in the first five months, except as regards the small quantity b e near the end of February, which, not having been drawn off during January and February, must overflow before the end of February.

00In the same way we may group in a single diagram any number of consecutive driest years, and either ascertain the reservoir capacity necessary for a given uniform yield (represented cumulatively by a straight line corresponding with a'a', but drawn over all the years instead of one), or conversely, having set up a vertical from the most trying point in the line of cumulative flow (c or c in fig.

003 - representing, in percentage of the total annual flow of the driest year, the capacity of reservoir which it may be convenient to provide) we may draw a straight line a"' a" of uniform yield from the head of that vertical to the previous point of maximum excess of cumulative flow.

0019, the maximum movement from the original straight line being about I ft.

00Aschan (Ber., 1902, 35, p. 33 8 9) depicts these cases by representing the plane of the carbon atoms of the ring as a straight line and denoting the substituted hydrogen atoms by the letters X, Y, Z.

00In June 1696 Bernoulli addressed a letter to the mathematicians of Europe challenging them to solve two problems - (1) to determine the brachistochrone between two given points not in the same vertical line, (2) to determine a curve such that, if a straight line drawn through a fixed point A meet it in two points P 1, P 2, then AP 1 m +AP 2 m will be constant.

00in a straight line from those of the Ucayali.

00It is one of the most crooked streams in the world, and its length in a straight line is less than half that by its curves.

00(The straight line and the point are not for the moment regarded as curves.) Next to the circle we have the conic sections, the invention of them attributed to Plato (who lived 430-347 B.C.); the original definition of them as the sections of a cone was by the Greek geometers who studied them soon replaced by a proper definition in piano like that for the circle, viz.

00and flows almost in a straight line through the heart of the kingdom to the Danube.

00which act upon each other, their motions are so related that the centre of gravity of the entire system moves in a straight line with a constant velocity.

00Rounding the southern end of the island, there is no other inlet save the small bay north of Fort Dauphin, at the southern end of the straight line of coast already mentioned.

00To investigate the form of the curve use may be made of the definition: the ellipse is the locus of a point which moves so that the ratio of its distance from a fixed point (the focus) to its distance from a straight line (the directrix) is constant and is less than unity.

00The straight line and the line through the centre parallel to the chords are named conjugate diameters; each bisects the chords parallel to the other.

00The tail I should be high set on, the croup being continued in a straight line to the tail, and not falling away and drooping The Baron: (1842) Stockwell$ (1849) Pocahontas (1837) Echidna (1838) Glencoe (1831) Marpessa (1830) Whalebone* (1807) Peri (1822) { Bob Booty (1804) Flight (1809) Whisker* (1812) Economist (1825) Floranthe (18,8) Blacklock (1814) Miss Pratt (1825) tGadabout (1812) 'Selim (1802) Bacchante (1809) Tramp (1810 Trampoline (1825) Web (1808)) { Orville: (1799) Eleanor*t (1798) Marmion (,806) Harpalice (1814) Sir Hercules (1826) Birdcatcher: (1833) Don Quixote (1784) Evelina (1791) (Golumpus (1802) Daughter of (18,o) Walton (1799) Parasol (1800) Moses* (1819) Quadrille (1815) ?

00I12), Cistaceae, and most gymnosperms. In such an ovule a straight line drawn from the hilum to the micropyle passes along the axis of the ovule.

00A third way to predict the future that I believe is reliable rejects both the slavish following of the straight line and the purely speculative approach.

00They tell me that if the fox would remain in the bosom of the frozen earth he would be safe, or if he would run in a straight line away no foxhound could overtake him; but, having left his pursuers far behind, he stops to rest and listen till they come up, and when he runs he circles round to his old haunts, where the hunters await him.

00Outline shapes Outline shapes, such as triangles, rectangles and parallelograms, consist of a series of straight-line segments between the vertices.

00The best test for moderate AMS is to have the person walk a straight line heel to toe just like a sobriety test.

00The normal toe-in setting is up to 20 minutes, which provides good straight-line stability.

00Normal press ups, aim to keep a straight line through your back.

00Depreciation for tax purposes is calculated by systematically applying the straight-line depreciation method.

00Current path files The current path files list the straight-line segments used to produce the field.

00For a straight-line graph, pick two points on the graph.

00Rentals under operating leases are charged on a straight-line basis over the lease term.

00The highest mark was 20cm up the bell, the total straight-line distance from rim to shoulder being 48cm.

00Finally, we get down to our first proposition: Proposition 1. On a given straight line to construct an equilateral triangle.

00It was nervous at the rear and very twitchy even in a straight line.

00A straight line extension of the curve can lead to a gross underestimate.

00By nature, we 're like shopping trolleys - inclined to veer away from the straight line of God 's revealed will.

00His mind has a lightning-like zig zag which is its straight line of smiting.

00The straight line from start-up to sustainable success is largely a myth (though of course there are exceptions to this rule).

00These are easy to turn but hard to coax into just traveling in a straight line.

00Since they're designed for negotiating rapids, they are not meant for steering in a straight line and will not do so very well even in calm waters.

00The key to any kind of stenciling is to make sure you're stenciling along a straight line the same way you would with a wallpaper border.

00Women with allergies, constant smudgy liner or who simply can't apply a smooth, straight line will benefit from permanent eyeliner.

00With your non-dominant hand, tug lightly on the outer edge of your lid, making it taut and allowing yourself to draw a straight line right where your lashes meet your lid.

00Gradually work this line outward towards the outer corner of your eye in a straight line that continues to follow your lash line.

00Again, this measurement is a straight line.

00When choosing family portrait poses, don't simply arrange the subjects in a straight line.

00If using fruit, spread the fruit in a straight line about 1/3 of the way up from the bottom of the tortilla.

00Or you can put them in a straight line along the top, bottom or center of the page.

00The bra strap should make a straight line across your back.

00Walking in a straight line may become difficult and speech may be slurred.

00Cut a straight line off the top of the round face cake.

00Give the command to heel, and walk in a straight line.

00No longer do you have to use the straight line shape.

00Marking the outside perimeter layout first will ensure that your footing holes are in a straight line.

00However, it tends to look its best when laid out in a straight line and square to the walls.

00Then use chalk or a pencil to draw a straight line connecting the two centers.

00Bateau is a neckline that rests in a straight line that meets at the shoulders, measuring equally on the front and the back.

00For women with large hips, select a short that fits close at the hip and then drops in a straight line to just above the knee.

00To examine the lenses for imperfections, hold the glasses at an arm's length, then look through them at a straight line in the distance, such as the edge of a window.

00Slowly move the lens across the straight line.

00Have your dog sit, then get him down onto his belly (DOWN), then touch your dog and draw a straight line horizontally.

00Long blunt cut: Hair is cut in a straight line.

00A simple straight line that flips at the end will add movement and swing to tresses kept above shoulder length.

00You can create your own straight line amortization chart with an Excel spreadsheet.

00For example, Mortgage-x.com has several different pre-formatted spreadsheets including a straight line amortization chart which can be quickly created using an Excel spreadsheet.

00To do it best, you want to keep your body in a straight line with your feet pointed.

00This gives you more power and will keep you on a straight line.

00Pawns - These pieces, which number eight of each color, form a straight line across the board in front of the other pieces.

00The rooks are allowed to move in a straight line either across the board or in a line toward the opposing player's side of the game board.

00There's a math truism that says, the shortest distance between two points is a straight line.

00The stones are set in a straight line without additional accent stones.

00Ladder designs with two bars holding one or more diamonds in a straight line.

00Lay the stacks in a straight line on a table, and cut a piece of string or yarn slightly longer than the length of the hearts.

00Keep toenails short and clean, by cutting in a straight line across the top of the nail.

00With the right end of the lace insert it in the opposite side hole creating a straight line.

00Some of these knots are formed in a straight line that creates a band, while others express mystical shapes like the triangle and circle.

00Use your sewing machine to stitch a straight line about a quarter of an inch from the edge of the fabric.

00Lift your butt and hips off of the floor until your body forms a straight line from your shoulders to your knees.

00When you get into a pushup position, make sure your body forms a straight line from your heels to your head.

00Keep your body in a straight line from your head to your toes and hold for 30 seconds to one minute.

00Your front shin should remain in a straight line with your ankle.

00Your right shin should remain in a straight line with your ankle.

00What the plank should look like from the side is a straight line from your heels, up your legs over your back to the crown of your head.

00Side plank: Form a straight line again from feet to head, but with only one hand supporting you and your body, which is facing the side instead of the ground.

00Keeping a straight line from the crown of your head down to your toes, push yourself up off the ground with your hands shoulder width apart, flat on the ground.

00In the up position, your arms are completely straight, your legs are completely straight and your body from your head to your heels forms a straight line down the general line of your spine.

00As you lower yourself toward the ground, your body should move in one motion and should always form a straight-line all the way down.

00Make sure your body forms a straight line from heel to head.

00Make sure that you flatten your back, creating a straight line with your body from your head to your heels.

00If you find yourself popping your booty up into the air or if you feel your back begin to sway, move into the half-plank by dropping your knees to the ground, maintaining the straight line of your body.

00Step your feet behind you and place your toes on the ground - your body should form a straight line from head to heels.

00Hold the kettlebell in one hand with your arm extended in a straight line from your shoulder.

00Engage your abs and lift your hips off the floor so that your body forms a straight line from your feet to your head.

00Follow the typical relay race format of having a challenge for each team, such as carrying an egg on a spoon or running in a straight line blindfolded.

00Though her story of Harry Potter is continuously rising in intensity, Rowling's style of telling her tales stays on the same, straight line.

00The rules of life guide us in a straight line, though our journey is never a straight line and it takes a wise person to know when those rules must be bent or broken.

00A classic French manicure features the white tips in a straight line across the end of the nail.

00

The word usage examples above have been gathered from various sources to reflect current and historial usage. They do not represent the opinions of YourDictionary.com.