Fullers Calculating Slide-Bule. 59 



The rules just referred to, however, will only give results 

 correct to two figures, and on this account they have been 

 available only for rough approximate calculations, or merely 

 looked upon as mathematical curiosities. To give results 

 with even three figures one would require (reckoning twenty 

 divisions to the inch) a straight rule S ft. -i in. long, or a 

 circular rule 1 ft, -± in.: and to give results with four figures, 

 one 83 ft. 4 in. or 13 ft. 3 in. respectively; and hence their 

 inapplicability for other than approximate calculations. 



This great difficulty in regard to length of scale has, 

 however, at length been overcome by arranging the scale on a 

 spiral. The instrument I exhibit to-night — the Calculating 

 Slide-Rule of Professor George Fuller, C.E., of Queen's 

 College, Belfast, Ireland — has a single logarithmic scale, 

 500 inches in length, wound in a spiral form round a 

 cylinder barely six inches long by three inches in diameter. 

 The old plan of placing scale against scale has been aban- 

 doned, and two indices — one fixed and the other movable — 

 are substituted instead. This rule will give correct results 

 to four and sometimes to five figures, and is therefore much 

 more reliable than a table of four-figure logarithms. There 

 is, moreover, an additional scale for finding the logarithms 

 themselves if required, and on the inner cylinder of the slide 

 are arranged, for ready reference, many useful mathematical 

 tables and formulas, including a table of natural sines. 



In regard to matters of calculation generally, I may state 

 that I have received the greatest assistance in statistical 

 calculations from the Arithmometer, Logarithms, and Recip- 

 rocals. In the calculation of percentages, or in calculations 

 involving a constant divisor, I consider Reciprocals* by 

 far the most convenient and readiest of the three methods 

 just named. The Arithmometer, I am of opinion, is still 

 unsurpassed when exact results in over six figures are 



opposite side. The movable face has three scales— viz. , a scale of numbers, 

 a scale of squares, and a scale of sines ; whilst the fixed face contains a 

 scale of cubes, and a scale for finding, in conjunction with the scale of num- 

 bers, the logarithm of a number, or vice versa, By means of these scales, 

 ordinary results in multiplication and division may be obtained ; the squares, 

 cubes, square and cube roots may be found simply by inspection, and rough 

 arithmetical and trigonometrical calculations involving such powers and 

 roots may be readily made, — correct to the second, and often with an approxi- 

 mation to the third, figure. In many respects the " Cercle" is much more 

 useful and convenient than the Carpenter's Slide-Bule ; its price in France is 

 30 francs (about 25s.). A less portable but more useful instrument, having 

 a greater length of scale, is also obtainable. 



* A valuable work on Beciprocals is bv Lieut. -Col. Oakes, A.I. A. London : 

 C. & E. Layton. 1865. 



