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SPX ‘O otboTo~®°®o®oaoef ) .. n Z,S ~ O O O O O (I G O O O O iDO~' 7 + .2 3 !. 3 • ! a 10 .11 12 13 14 13 1e i O 3 3_ 2. 1 I1 WY Steiger$ Han1W.Egli 10eo See also:Zurich As See also:log 1=o, the beginning A has the number r and B the number ro, hence the unit of length is AB, as log ro= r. The same See also:division is repeated from B to C. The distance 1,2 thus represents log 2, 1,3 gives log 3, the distance between 4 and 5 gives log 5–log 4=log , and so for others. In See also:order to multiply two See also:numbers, say 2 and 3, we have log 2 X3 =log 2 +log 3. Hence, setting off the distance 1,2 from 3 forward by the aid of a pair A Bbe performed. It is then convenient to make the scales circular. A number of rings or disks are mounted See also:side by side on a See also:cylinder, each having on its rim a log-See also:scale. The " Callendar See also:Cable Calculator," invented by Harold See also:Hastings and manufactured by See also:Robert W. See also:Paul, is of this See also:kind. In it a number of disks are mounted on a See also:common See also:shaft, on which each turns freely unless a See also:button is pressed down whereby
C
of compasses will give the distance log 2+log 3, and will bring us to 6 as the required product. Again, if it is required to find
of 7, set off the distance between 4 and 5 from q backwards, and the required number will be obtained. In the actual scales the spaces between the numbers are subdivided into ro or even more parts, so that from two to three figures may be read. The numbers 2, 3. . . in the See also:interval BC give the logarithms of ro times the same numbers in the interval AB; hence, if the 2 in the latter means 2 or • 2, then the 2 in the former means 20 or 2.
Soon after See also:Gunter's publication (1620) of these " logarithmic lines," See also:Edmund See also:Wingate (1672) constructed the slide See also:rule by repeating the logarithmic scale on a See also:tongue or " slide," which could be moved along the first scale, thus avoiding the use of a pair of compasses. A clear See also:idea of this See also:device can be formed if the scale in fig. 4 be copied on the edge of a See also:strip of See also:paper placed against the See also:line A C. If this is now moved to the right till its r comes opposite the 2 on the first scale, then the 3 of the second will be opposite 6 on the See also:top scale, this being the product of 2 and 3; and in this position every number on the top scale will be twice that on the See also:lower. For every position of the lower scale the ratio of the numbers on the two scales which coincide will be the same. Therefore multiplications, divisions, and See also:simple proportions can be solved at once.
Dr See also: These rules are manufactured by A. G. See also:Thornton of See also:Manchester.
Many different forms of slide rules are now on the See also:market. The handiest for See also:general use is the Gravet rule made by See also:Tavernier-Gravet in See also:Paris, according to instructions of the mathematician V. M. A. See also:Mannheim of the Ecole Polytechnique in Paris. It contains at the back of the slide scales for the logarithms of sines and tangents so arranged that they can be worked with the scale on the front. An improved See also:form is now made by See also:Davis and Son of See also:Derby, who engrave the scales on See also: Tavernier-Gravet makes them of that See also:size and longer, even a See also:metre See also:long. But they then become somewhat unwieldy, though they allow of See also:reading to more figures. To get a handy long scale See also:Professor G. See also:Fuller has constructed a See also:spiral slide rule See also:drawn on a cylinder, which admits of reading to three and four figures. The handiest of all is perhaps the " Calculating Circle " by See also:Boucher, made in the form of a See also:watch. For various purposes See also:special adaptations of the slide rules are met with—for instance, in various exposure meters for photo-graphic purposes. General See also:Strachey introduced slide rules into the Meteorological See also:Office for performing special calculations. At some blast furnaces a slide rule has been used for determining the amount of See also:coke and See also:flux required for any See also:weight of ore. Near the See also:balance a large logarithmic scale is fixed with a slide which has three indices only. A load of ore is put on the scales, and the first See also:index of the slide is put to the number giving the weight, when the second and third point to the weights of coke and flux required. By placing a number of slides side by side, drawn if need be to different scales of length, more complicated calculations maythe disk is clamped to the shaft. Another disk is fixed to the shaft. In front of the disks lies a. fixed zero line. Let all disks be set to zero and the shaft be turned, with the first disk clamped, till a desired number appears on the zero line; let then the first disk be released and the second clamped and so on; then the fixed disk will add up all the turnings and thus give the product of the numbers shown on the several disks. If the division on the disks is drawn to different scales, more or less complicated calculations may be rapidly performed. Thus if for some purpose the value of say ab3 (cc is required for many different values of a, b, c, three movable disks would be needed with divisions drawn to scales of lengths in the proportion r: 3: The See also:instrument 11 now on See also:sale contains six movable disks. Continuous Calculating See also:Machines or Integrators.—In order to measure the length of a See also:curve, such as the road on a See also:map, a See also:wheel is rolled along it. For one 'revolution of the wheel the path described by its point of contact is tJurvo• meters equal to the circumference of the wheel. Thus, if a cyclist See also:counts the number of revolutions of his front wheel he can calculate the distance ridden by multiplying that number by the circumference of the wheel. An ordinary See also:cyclometer is nothing but an arrangement for counting these revolutions, but it is graduated in such a manner that it gives at once the distance in See also:miles. On the same principle depend a number of See also:instruments which, under various See also:fancy names, serve to measure the length of any curve; they are in the shape of a small See also:meter chiefly for the use of cyclists. They all have a small wheel which is rolled along the curve to be measured, and this sets a See also:hand in See also:motion which gives the reading on a See also:dial. Their accuracy is not very See also:great, because it is difficult to See also:place the wheel so on the paper that the point of contact lies exactly over a given point; the beginning and end of the readings are therefore badly defined. Besides, it is not easy to See also:guide the wheel along the curve to which it should always See also:lie tangentially. To obviate this defect more complicated curvometers or kartometers have been devised. The handiest seems to be that of G. Coradi. He uses two wheels; the tracing-point, halfway between them, is guided along the curve, the line joining the wheels being kept normal to the curve. This is See also:pretty easily done by See also:eye; a See also:constant deviation of 8° from this direction produces an See also:error of only 1%. The sum of the two readings gives the length. E. Fleischhauer uses three, five or more wheels arranged symmetrically See also:round a tracer whose point is guided along the curve; the planes of the wheels all pass through the tracer, and the wheels can only turn in one direction. The sum of the readings of all the wheels gives approximately the length of the curve, the approximation increasing with the number of the wheels used. It is stated that with three wheels practically useful results can be obtained, although in this See also:case the error, if the instrument is consistently handled so as always to produce the greatest inaccuracy, may be as much as 5%. Planimeters are instruments for the determination by See also:mechanical means of the See also:area of any figure. A pointer, generally called the "tracer," is guided round the boundary of the figure, and then the area is read off on the recording apparatus Pte°t' meters. of the instrument. The simplest and most useful is See also:Amsler's (fig. 5). It consists of two bars of See also:metal OQ and QT, which are hinged together at Q. At 0 is a See also:needle-point which is driven into the See also:drawing-See also:board, and at T is the tracer. As this is guided round the boundary of the' figure a wheel W mounted on QT rolls on the paper, and the turning of this wheel See also:measures, to some known scale, the area. We shall give the theory of this instrument fully in an elementary manner by aid of See also:geometry. The theory of other See also:plan- meters can then be easily FIG. 5. understood. Consider the See also:rod QT with the wheel W, without the See also:arm OQ. Let it be placed with the wheel on the paper, and now moved perpendicular to itself from AC to BD (fig. 6). Additional information and CommentsThere are no comments yet for this article.
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