Square roots, using the same scale:—Bring the number under either of the indices, and the square root will be found upon one of the two inner circles of the same dial.
Cube root:—In this case it is necessary to first bring the 1 on the front dial under the fixed index, then set the movable index to the number, and the cube root will be found on one of the inner circles of the back or fixed dial.
To use the trigonometrical dial:—Bring the needle of this dial over the angle of which the sine or tangent is required, and read upon the other dial (indicated by the needle) the natural trigonometrical line upon the inner circle, or its logarithm upon the outer circle.
The book of instructions supplied with the instruments, written by Professor George Fuller, C.E., for the author, gives all directions for working and also gauge points from which calculations are made as with the slide rule.
875.—In reduction of factors of a calculation collectively Boucher's calculator may take more than one turn or less than unity. The author has added a central index to record the number of turns. This is said to be of great value for the perfection of the instrument, Fig. 426.
876.—Slide Rules, of which there are great varieties, are of too complex a nature to discuss, except very briefly, in our limited space, particularly as general descriptions have been often given. The ordinary logarithmical scales of Gunter (1619), known as Gunter's lines, are placed upon most slide rules. The arithmetical lines are lettered A, B, C, D, and E. A and B are alike: these are technically termed double radius log. lines. They are used for all processes of multiplication and division. C and D are also alike and are termed single radius log. lines. They are used together for ordinary multiplication and division, and in conjunction with A and B scales for squares and square roots. The E line, not originally a Gunter's line, but found early in the century on several rules, is termed a triple radius log. line. The numbers of the divisions on this line are the cubes of the numbers of the corresponding divisions of the D line, with which it generally works. All these lines work reciprocally together, performing the most complex calculations by simply setting them to numbers or gauge points of which given solutions are required, as for instance, the first four lines in combination give answers to such questions as:—To divide by a number two numbers multiplied together, one of which is squared; to divide the product of two numbers by the square of a third number, etc., each of which calculations is performed at a single setting. By inversion of the slide A to C the reciprocal of a given number is found, also the mean proportional between two numbers, the fourth term is inverse proportion, etc. Trigonometrical calculations are performed by the lines of sines, tangents, etc. Instructions are to be found in the books supplied with the rules, and as a part of many works. Among the most complete books may be mentioned "The Slide Rule," by R. G. Blaine, M.E., and "The Slide Rule," by Chas. N. Pickworth. These both contain very full information on the subject.
877.—The Slide Rules in most general use are A. Nestler's and A. W. Faber's. Both these well-known firms make a very complete series, applicable to a great variety of technical calculations.
878.—The reviser has recently completed from the designs of the author an entirely automatic dividing engine for these rules, which is the only one in existence.
A great number of slide rules are made for special purposes only: some of these are very useful to the civil engineer.