单词 | planimeter |
例句 | In this project you investigate how a planimeter works, and you use Green’s theorem to show the device calculates area correctly. Calculus, Volume 3 2016-03-30T00:00:00Z The planimeter affords a much quicker and more accurate method of obtaining the average steam pressure from a diagram. Modern Machine-Shop Practice, Volumes I and II 2012-03-23T02:00:33.140Z At least two such readings were taken for each home range; then these planimeter values were converted into square feet. Comparative Ecology of Pinyon Mice and Deer Mice in Mesa Verde National Park, Colorado 2012-02-24T03:00:32.243Z We saw also a planimeter, which not only calculated mechanically the area of a figure, but gave also its center of gravity, moment of inertia, etc. Scientific American, Vol. XLIII.?No. 1. [New Series.], July 3, 1880 A Weekly Journal Of Practical Information, Art, Science, Mechanics, Chemistry, And Manufactures 2012-01-05T03:00:30.823Z Areas were measured with a planimeter; distances traveled by individuals were measured with a cartometer. Natural History of the Ornate Box Turtle, Terrapene ornata ornata Agassiz 2011-10-01T02:00:30.200Z The planimeter measures the number of turns through which the wheel rotates as we trace the boundary; the area of the shape is proportional to this number of wheel turns. Calculus, Volume 3 2016-03-30T00:00:00Z There are two methods of doing this, one by means of a planimeter or averaging instrument, and the other by means of lines called ordinates. Modern Machine-Shop Practice, Volumes I and II 2012-03-23T02:00:33.140Z The apparatus used in engine testing, in addition to that used in boiler testing, consists of a steam engine indicator and reducing device for taking diagrams, and a planimeter for measuring them afterwards. Steam Engines Machinery's Reference Series, Number 70 2010-12-20T17:12:10.227Z They ranged from astrolabes to slide rules to planimeters to mechanical and electrical calculators to modern computers. 2010-02-04T11:00:00Z He called attention to what he termed "compound compasses," a class of linkages that included Watt's parallel motion, the pantograph, and the polar planimeter. Kinematics of Mechanisms from the Time of Watt As the planimeter traces C, the pivot moves along the y-axis while the tracer arm rotates on the pivot. Calculus, Volume 3 2016-03-30T00:00:00Z Coffin’s averaging instrument or planimeter is shown in Fig. Modern Machine-Shop Practice, Volumes I and II 2012-03-23T02:00:33.140Z General Construction of Planimeter The planimeter is an instrument for measuring areas in general, and especially for measuring the areas of indicator cards. Steam Engines Machinery's Reference Series, Number 70 2010-12-20T17:12:10.227Z The area of the wound is traced carefully on transparent paper, and then computed by using a mathematical machine, called a planimeter, which measures areas. Manhood of Humanity. The instrument we are about to describe is an improvement on the hatchet planimeter and is due to Prof. Goodman, of Leeds. Scientific American Supplement, No. 1082, September 26, 1896 Assume the orientation of the planimeter is as shown in Figure 6.49. Calculus, Volume 3 2016-03-30T00:00:00Z In all applications of the planimeter the rod is brought back to its original position. Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary" A planimeter of this type is shown in Fig. Steam Engines Machinery's Reference Series, Number 70 2010-12-20T17:12:10.227Z He showed a polar planimeter in which the integrating surface is a sphere. Scientific American Supplement, No. 315, January 14, 1882 From the point, A, a line, AB, is drawn in any direction to the boundary; the tracing point of the planimeter is now placed at A, with the hatchet at X, Fig. Scientific American Supplement, No. 1082, September 26, 1896 Instead of trying to measure the area of the region directly, we can use a device called a rolling planimeter to calculate the area of the region exactly, simply by measuring its boundary. Calculus, Volume 3 2016-03-30T00:00:00Z But all were driven out of the field by Amsler's simpler planimeter. Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary" Measuring the card with a planimeter shows the mean effective pressure to be 48.2 pounds. Steam Engines Machinery's Reference Series, Number 70 2010-12-20T17:12:10.227Z The simple finding of areas we may omit, as the planimeter will do that equally well. Scientific American Supplement, No. 794, March 21, 1891 Amsler's planimeter was taken as the standard, the area measured by it being independently checked by an assistant. Scientific American Supplement, No. 1082, September 26, 1896 To measure the area of a region, we simply run the tracer of the planimeter around the boundary of the region. Calculus, Volume 3 2016-03-30T00:00:00Z Altogether different from the planimeters described is the hatchet planimeter, invented by Captain Prytz, a Dane, and made by Herr Hatchet planimeters. Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary" It thus answers the same purpose as Ainslee's polar planimeter, and though not so handy, is free from the defect due to the sliding of the integrating wheel on the paper. Scientific American Supplement, No. 288, July 9, 1881 Excluding such cases, we see that the accuracy of the integraph scarcely falls behind that of the planimeter and is quite efficient for practical purposes. Scientific American Supplement, No. 794, March 21, 1891 Hence if the curve is drawn, any planimeter may be used for finding the value of the integral. Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary" Notice that the wheel cannot turn if the planimeter is moving back and forth with the tracer arm perpendicular to the roller. Calculus, Volume 3 2016-03-30T00:00:00Z To use this simple instrument as a planimeter requires the possibility of selecting the point R. The geometrical theory here given has so far failed to give any rule. Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary" In fact, a planimeter may often be used with advantage to solve problems more complicated than the determination of a mere area, by converting the one problem graphically into the other. Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary" If the error of its reading be not sensibly greater than that of a planimeter, it is certainly worth double the money. Scientific American Supplement, No. 794, March 21, 1891 Amsler has modified his planimeter in such a manner that instead of the area it gives the first or second moment of a figure about an axis in its plane. Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary" This part is therefore a simple planimeter, in which the one end of the arm moves in a straight line instead of in a circular arc. Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary" To use Amsler's planimeter, place the pole O on the paper outside the figure to be measured. Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary" Then these arms with their wheels will again be planimeters. Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary" Such instruments do not, as a rule, represent their results graphically, and we may take, as characteristic examples of them, Amsler's planimeter and some of the sphere integrating machines. Scientific American Supplement, No. 794, March 21, 1891 The absolute term A0 equals the mean ordinate of the curve, and can therefore be determined by any planimeter. Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary" The theory of other planimeters can then be easily understood. Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary" In the planimeters described the recording or integrating apparatus is a smooth wheel rolling on the paper or on some other surface. Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary" In most cases the curve has to be followed by hand, and the error will be greater—greater probably for the integraph than for the planimeter, as the former is distinctly hard to guide well. Scientific American Supplement, No. 794, March 21, 1891 |
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