The rule consists of an outer cylinder that can be moved up or down, and turned round upon the cylindrical axis which is held by the handle. Upon the outer cylinder a single spiral, logarithmical scale is continued from end to end, the total length of which makes the scale 500 inches long. This is graduated into 7250 divisions. One index is fixed to the handle. A second index is attached to the inner tube blocked out by a flange to read upon any part of the scale; so that altogether there are three tubes which work together telescopically, by means of which the indices may be set to any position on the graduated cylinder. Stops are placed so that the indices may be brought to zero. By these means, the indices being set to any of the gauge points, the logarithmical scale, moving by itself, will maintain the same proportion for any numbers. In this rule a single log. radius is repeated by coincidence of indices, so that its scale of divisions, 41 feet 8 inches long, if compared with an ordinary double radius slide rule, becomes equal to a slide rule of 83 feet 4 inches long. The ordinary 12-inch slide rule has about 80 divisions to each radius, so that it is easily seen how much more exact quantities may be brought out with a rule of 7250 divisions. It is a most valuable rule for calculations for the tacheometer. Copious tables of gauge points for civil engineers are printed upon the central tube, which is supplemented by a book of instructions. The value of this rule has been much extended by scales to facilitate subtense calculations, by Mr. W. N. Bakewell, C.E., in the "Fuller-Bakewell" slide rule.
Fig. 428.—Improved Fuller's slide rule.
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An additional improvement, as shown at Fig. 428, has now been effected in these instruments by adapting the case to support the rule when in use, thus overcoming the objection of being always obliged to hold it in the hand.
The use of Professor Fuller's rule is, however, confined to arithmetical computations. The numerical solution of formulæ comprising trigonometrical functions can only be performed by extracting, with considerable loss of time, the values of these functions from a book of tables. To do so requires a certain effort of mind with its consequent risk of mistakes. This limitation has restricted its use in a considerable body of calculations, such, for example, as in the computation of the co-ordinates of surveys from the lengths and bearings of their lines, a method of plotting which is very largely used by land surveyors at present; in astronomical computations; in civil and mechanical engineering, etc.; the use of logarithms being preferred on the score of speed, although the degree of accuracy attained with Professor Fuller's rule is amply sufficient in the large majority of cases.
Fig. 429.—Barnard's co-ordinate spiral slide rule.
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886.—The Co-ordinate Spiral Slide Rule has been designed to meet these requirements by Mr. H. O. Barnard, A.C.H., F.R.A.S., etc., Superintendent of Trigonometrical Surveys, Ceylon, Fig. 429. Like Professor Fuller's rule, upon which it is an improvement, it enables the user to perform with speed and accuracy arithmetical computations involving multiplication, division, proportion, continuous fractions, powers, roots, and logarithms; but in addition, the natural and logarithmic values of trigonometrical functions of any angle can be determined by inspection with the same accuracy as in numerical computation, while the products, quotients, etc., of these functions, by lengths or numbers, integral or fractional, are obtained with equal ease, rapidity and precision. The scope of its operations will be gathered from the examples which are given to illustrate its use in the instructions supplied with the rule.