Assuming that the reader appreciates the advantages of shortened calculation, due to the slide rule, or the use of logarithms, the first instrument that may be noticed is one embodying an application of the principle of the slide rule in a remarkably handy and compact form. This is the calculating slide rule invented by Professor Fuller, of Queen’s College, Belfast, equivalent to a straight slide rule 83 feet 4 inches long, or a circular rule 13 feet 3 inches in diameter. From the illustration given it may be seen that the rule consists of a cylinder which can be moved up and down upon, and turned round, an axis, which is held by a handle. Upon this cylinder is wound spirally a single logarithmic scale. Fixed to the handle of the instrument is an index. Two other indices, whose distance apart is the axial length of the complete spiral, are fixed to an inner cylinder, which slides in like a telescope tube, and thus enables the operator to place these indices in any required position relative to the outer cylinder containing the logarithmic scale. Two stops—one on the fixed and the other on the outer or movable cylinder—are so placed that when they are brought in contact the index points to the commencement of the scale. [Illustration: FIG. 24. FULLER’S RULE.] Regarding the manner of using the instrument a few general notes may be given. As in the ordinary slide rule the operations of multiplication and division are performed by the addition or subtraction of the parts of the scale that represent in length the logarithm of the numbers involved in the operations. For example, suppose the following calculation is to be worked out (6248 × 5936 × 4217)/(7963 × 4851) = 4049 To do this in the ordinary way would keep the smartest arithmetician busy for a considerable time, whereas by means of the instrument under notice the result is attained in little over one minute’s time. The motions in the operation are as follows:—Hold the rule by the handle in one hand and move the scale cylinder by the other until the number 6248 is opposite the index attached to the handle portion. Now, move the inner cylinder (by the top) until one or other of the indices (according to the distance of the number from the bottom of the instrument) on the index arm is opposite the number 7963. The scale cylinder is again moved till the number 5936 is opposite one of the indices just referred to, and the inner cylinder carrying the index arm is then moved till one or other of the indices is opposite 4851. Finally, the scale cylinder is moved till the number 4217 is opposite one of the indices on the arm; and the result of the whole operation—4049—is found opposite the index first-mentioned, _i.e._, that attached to the handle portion of the instrument.