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SPIRAL SLIDE RULE.
A STRAIGHT SLIDE RULE 83 FEET 4 INCHES LONG, OR, A CIRCULAR RULE 13 FEET 3 INCHES
GEORGE FULLER, M. INST. C.E.,
PROFESSOR OF ENGINEERING IN THE QUEEN'S UNIVERSITY, IRELAND.
E. & F. N. SPON, 46, CHARING CROSS.
New YORK: 446, BROOME STREET.
SPIRAL SLIDE RULE.
The method of performing by mechanical means the work of addition and subtraction required when multiplying and dividing numbers by means of logarithms, originated with Gunter about the year 1606. He constructed a linear scale which was composed of two equal parts, and each half divided into parts proportional to the logarithms of numbers from 10 to 100. With this scale he used a pair of compasses for making the additions and subtractions.
About the year 1630, Oughtred invented the two similar logarithmic scales sliding in contact, which are at present in use; and he is stated to have used both straight and concentric circular scales. The advantage of this arrangement is, that the resul is obtained by one motion of the sliding scale ; and not only are multiplication and division thus worked, but questions in proportion, or the combination of the two, are solved by a single movement of the slide.
The simplicity of this method of calculating with figures is so great, that it seems strange it has not been more used; but the following considerations will, it is believed, account for this :
In testing the relative advantages of different methods of making arithmetical calculations, the mental effort required, the time occupied, and the truth of the result have all to be taken into account. Now, in judging the ordinary slide rule by these points, it will be found that the facilities it offers are more apparent than real.
It is easy, with a little practice, to place one of the lines of the slide either opposite to a division of the rule or in a required position between two divisions, if these are not very close together. When the space, however, between two consecutive marks is very small, then great difficulty arises, from the strain upon the eyesight and the minute motion of the slide.
For example, in the ordinary slide rule with the scale 5 inches long, the breadth of the division from 99 to 100 is about to of an inch. Therefore to mark such a number as 996, this space must be mentally divided into ten equal parts, each part consequently being too of an inch, a magnitude quite inappreciable without a magnifying glass. The effort and time for the above is, however, slight, compared to that required when a point on one scale between two divisions has to be placed or read as agreeing with a point on the other, also between two divisions. For in this case (which is the most common, owing to the number of divisions on
the ordinary slide rule necessarily being few) the division on one scale has to be mentally divided, and the particular point required fixed in the mind by its distance from the nearest division. Then the division on the other scale has to be mentally divided, and that part of it read which agrees with the point on the first scale previously fixed in the mind. Thus, for example, suppose it is required to place 554 on one scale to agree with 643 on the other. There are marks at 55 and 56 on one scale, and at 64 and 65 on the other; but the 4 part of the distance between 55 and 56 has to be made to coincide with the part of that between 64 and 65: the difficulty not being to divide either of these distances into ten parts, if they are not very small, but to combine the two operations together.
If at the same time the spaces between the marks are very small, the difficulty is greatly increased by the strain upon the eyesight.
With regard to the truth of the result, Mr. Heather, in his · Treatise on Mathematical Instruments,' writes in relation to the foot slide rule : “ The solution in fact may be considered as obtained to within a two-hundredth part of the whole.” Now this approximation, though close considering the length of scale of the instrument, and sufficient for some, is not near enough for very many of the calculations required by engineers and architects.
From the above it appears that a slide rule to