420) of a change of form in the Greenwich mural quadrant led to the introduction of astronomical circles at the Royal Observatory, and to his own appointment as its head.
1) is a wooden quadrant in.
Turning, therefore, to a globe, Asia, viewed as a whole, will be seen to have the form of a great isosceles spherical triangle, having its north-eastern apex at East Cape (Vostochnyi), in Bering Strait; its two equal sides, in length about a quadrant of the sphere, or 6500 m., extending on the west to the southern point of Arabia, and on the east to the extremity of the Malay peninsula; and the base between these points occupying about 60° of a great circle, or 4 500 m., and being deeply indented by the Arabian Sea and the Bay of Bengal on either side of the Indian peninsula.
Xnyviaicos, ribbon), a quartic curve invented by Jacques Bernoulli (Acta Eruditorum, 1694) and afterwards investigated by Giulio Carlo Fagnano, who gave its principal properties and applied it to effect the division of a quadrant into 2 2 m, 3.2 m and 5.2 m equal parts.
The astrolabe quadrant or cross-staff enabled the mariner to determine"his latitude with a certain amount of accuracy, but for his longitude 1 See fig.
In the first quadrant there is no root after zero, since tan u> u, and in the second quadrant there is none because the signs of u and tan u are opposite.
The first root after zero is thus in the third quadrant, corresponding to m =1.
ABC is a quadrant in which the line AB and the arc AC are divided into the same number of equal parts.
The quadratrix of Tschirnhausen is constructed by dividing the arc and radius of a quadrant in the same number of equal parts as before.
The hake moves laterally on a quadrant and it is thus possible to give the plough a tendency to left or right by moving the hake in the reverse direction.
For this purpose the following apparatus should be provided: - (i) two small metal tea-trays and some clean dry tumblers, the latter preferably varnished with shellac varnish made with alcohol free from water; (2) two sheets of ebonite rather larger than the tea-trays; (3) a rod of sealing-wax or ebonite and a glass tube, also some pieces of silk and flannel; (4) a few small gilt pith balls suspended by dry silk threads; (5) a gold-leaf electroscope, and, if possible, a simple form of quadrant electrometer (see Electroscope and Electrometer); (6) some brass balls mounted on the ends of ebonite penholders, and a few tin canisters.
In speaking of quadrant elevation a brief reference was made to the necessity for making an allowance for difference of level of gun and target.
The pattern is that of a true sight, that is to say, the base plate is capable of movement about two axes, one parallel to and the other at right angles to the axis of the gun, and has cross spirit-levels and a graduated elevating drum and independent deflection scale, so that compensation for level of wheels can be given and quadrant elevation.
In smooth-bore days the term mortar meant a piece of ordnance of a peculiar shape resting on a bed at a fixed angle of quadrant elevation of 45°.
In coast defence artillery, owing to the fact that the guns are on fixed mountings at a constant height (except for rise and fall of tide) above the horizontal plane on which their targets move, and that consequently the angle of sight and quadrant elevation for every range can be calculated, developments in sights, in a measure, gave way to improved means of giving quadrant elevation.
The arrangements for giving quadrant elevation consisted of an arc, called index plate (see fig.
A yard scale of varnished paper, made out locally for quadrant elevation with regard to height of site, was usually pasted over this.
This form of laying is of two kinds: (I) that in which the gun can be layed for direction over the sight on the target itself, or on some aiming point close by, but from Indirect indistinctness or other causes quadrant elevation is preferred; and (2) that used when the target is completely laying.
The old method of giving quadrant elevation by clinometer was obviously too slow.
The gonio plate below is divided into 4 quadrants, and each quadrant into 10 spaces of 9° each 11 11 numbered in hundreds from o 'o 900.
An automatic sight is a sight connected in such a manner with the elevating gear of the gun, that when the sight is directed on the water-line of a target at any range the gun will ---- have the proper quadrant g B elevation for that range.
The automatic sight has, however, distinct limitations; it depends for its accuracy on height of site, and at long ranges even from a high site it cannot compare for accuracy with independent range-finding and careful laying or accurately applied quadrant elevation; it is also useless when the water line of the target is obscured, as may often be the case from the splashes caused by bursting shell.
Raining dials placed on the mountings where they can be read by the layers, and more accurate elevation indicators have made laying by quadrant elevation, and in certain cases giving direction by means of graduated arc and pointer, both accurate and rapid, so that once more this system of laying is coming into favour for long ranges.
In the navy the conditions of an unstable platform rendered quadrant elevation of little use, and necessitated a special pattern of tangent sight to facilitate firing the moment the roll of the ship brought the sights on the target.
A circular piece of this paper is folded twice upon itself so as to form a quadrant, one of the folds is pulled out, and the cone thus obtained is supported in a glass or porcelain funnel having an apical angle of 60°.
The instrument consists of a high-voltage continuous-current dynamo which creates a potential difference between the needle and the two quadrants of a quadrant electrometer (see Electrometer).
Prony (1755-1839) in the formation of the great French tables of logarithms of numbers, sines, and tangents, and natural sines, called the Tables du Cadastre, in which the quadrant was divided centesimally; these tables have never been published (see Logarithms).
He introduced several practical improvements, such as the measurement of time to tenths of a second; and he prevailed upon the government to replace Bird's mural quadrant by a repeating circle 6 ft.
It is found that the alteration of the tangent elevation is almost insensible, but the quadrant elevation requires the addition or subtraction of the angle of sight.
There are methods of measuring electrical power by means of electrostatic voltmeters, or of quadrant electrometers adapted for the purpose, which when so employed may be called electrostatic wattmeters.
The title of Gunter's book, which is very scarce, is Canon triangulorum, and it contains logarithmic sines and tangents for every minute of the quadrant to 7 places of decimals.
The next publication was due to Vlacq, who appended to his logarithms of numbers in the Arithmetica logarithmica of 1628 a table giving log sines, tangents and secants for every minute of the quadrant to ro places; there were obtained by calculating the logarithms of the natural sines, &c. given in the Thesaurus mathematicus of Pitiscus (1613).
In the same year Vlacq published at Gouda his Trigonometria artificialis, giving log sines and tangents to every ro seconds of the quadrant to ro places.
Briggs appreciated clearly the advantages of a centesimal division of the quadrant, and by dividing the degree into hundredth parts instead of into minutes, made a step towards a reformation in this respect, and but for the appearance of Vlacq's work the decimal division of the degree might have become recognized.
The first logarithms to the base e were published by John Speidell in his New Logarithmes (London, 1619), which contains hYPerbolic log sines, tangents and secants for every minute of the quadrant to 5 places of decimals.
The next great advance on the Trigonometria artificialis took place more than a century and a half afterwards, when Michael Taylor published in 1792 his seven-decimal table of log sines and tangents to every second of the quadrant; it was calculated by interpolation from the Trigonometria to 10 places and then contracted to 7.
I „ Logarithms of the ratios of arcs to sines from 04 00000 to 0 4.05000, and log sines throughout the quadrant 4 „ Logarithms of the ratios of arcs to tangents from 0 4 00000 to 0 4.05000, and log tangents throughout the quadrant 4 The trigonometrical results are given for every hundred-thousandth of the quadrant (to" centesimal or 3" 24 sexagesimal).
There are three fronts; the principal, towards College Green, is a colonnade of the Ionic order, with façade and two projecting wings; it connects with the western portico by a colonnade of the same order, forming the quadrant of a circle.
Flamsteed, from measurements made in 1689 and succeeding years with his mural quadrant, similarly concluded that the declination of the Pole Star was 40" less in July than in September.
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.
The pilots were all Indians, and they used the forestaff and quadrant for their observations.
In the second part Peregrinus describes first an improved floating compass with fiducial line, a circle graduated with 90 degrees to each quadrant, and provided with movable sights for taking bearings.
He ascertained the distribution of electricity among several spheres (whether equal or unequal) placed in contact in a straight line; and he measured the distribution of 2 In 1878 Clerk Maxwell repeated Cavendish's experiments with improved apparatus and the employment of a Kelvin quadrant electrometer as a means of detecting the absence of charge on the inner conductor after it had been connected to the outer case, and was thus able to show that if the law of electric attraction varies inversely as the nth power of the distance, then the exponent n must have a value of 2 t Isua.
A vast improvement in this instrument was made by the invention of the quadrant electrometer by Lord Kelvin, which is the most sensitive form of electrometer yet devised.
- Kelvin's Quadrant Electrometer.
If the two quadrants are at different potentials, the needle moves from one quadrant towards the other, and the image of a spot of light on the scale is therefore displaced.
They found from observations that the particular quadrant electrometer they used might be made to follow one or other of three distinct laws.
Guided by these experiments, Ayrton, Perry and Sumpner constructed an improved unifilar quadrant electrometer which was not only more sensitive than the White pattern, but fulfilled the theoretical law of working.
Let v l, v 2, v 3 be the instantaneous potentials of the two ends and middle of the circuit; let a quadrant electrometer be connected first with the quadrants to the two ends of the inductive circuit and the needle to the far end of the non-inductive circuit, and then secondly with the needle connected to one of the quadrants (see fig.
Quadrant electrometers have also been designed especially for measuring extremely small potential differences.