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Voyager Rare Books Maps & Prints

Article written by: John Lawrence on the Fuller’s Spiral Slide Rule

 A conventional professional slide rule has a number of scales; for example my own has 10 on the fixed sides and 8 on the slide. They include linear, logarithmic, inverse, squares, cubes and trigonometric scales which can be used for a variety of calculations. In general use it is a safe bet that the logarithmic scales were used (past tense as electronic calculators have surely rendered slide rules obsolete) for multiplication and division more than any other. Multiplication is achieved by adding two or more lengths of logarithmic scale,

since (log a – log1) + (log b – log1) = log ab and similarly for division.

The accuracy of the calculation is limited by the length of the rule, and convenient rules are about 13 inches long. This limitation presumably led George Fuller to develop the spiral slide rule, with a scale 41ft 8in in length, equivalent to a straight rule 83ft 4in long. The outer cylinder d, of Fuller’s Spiral Slide Rule carries a single spiral logarithmic scale and can be moved up and down and rotated about the axial cylinder f, which is held by the handle e. Fixed to the handle is a brass pointer, or index, b. An inner cylinder g can also move up and down and rotate within f, like a telescope tube. Cylinder g carries another brass limb N with two indexes a and c, whose distance apart is equal to the axial length of the spiral.

The spiral logarithmic scale (Fig. 2) runs from 100 at the top of cylinder d, through 50 cycles to 1000 at the bottom. To make a simple multiplication the index b is set to the multiplicand on the scale; index a is set to 100; d is then rotated so that the multiplier is brought to either a or c and the product is read off at c. In this way the log of the multiplier is effectively added to the log of the multiplicand. The extension of this method to division and multiple combinations of multiplication and division ‘is left to the student!’

In principle, values can be set and read off to five significant figures, but this does depend on the precision to which the three indexes can be set, and of course on the accuracy of the scale itself.

I discovered the instrument illustrated more than 30 years ago when I was browsing amongst the scientific books in the basement ofDawson’s bookshop, that was then inPall Mall. Behind a row of books was a mahogany box containing the instrument.  After a little bargaining I bought it. Interestingly it had a tie-on label with the words ‘Mrs Paget Thomson’ and an address inLondon. The bookseller confirmed that his company had acquired the rule from the estate of Sir George Paget Thomson, suggesting that it had probably belonged to him or to his father J.J. Thomson, both physics Nobel Laureates. This may explain why it is in such pristine condition; the hand book suggests that its accuracy ‘is sufficient for almost all the calculations required by the Engineer, Architect, or Actuary’ but perhaps not for a theoretical physicist!

The instrument is a thing of beauty itself; the two end pieces and the handle are of polished mahogany; the handle unscrews and is stored in the inner brass cylinder. The inner cylinder is of brass, polished and lacquered. The axial cylinder and the cylinder carrying the scale appear to have been made by winding and gluing a long strip of paper round a former. Considerable skill must have been used to ensure that where the printed scale joined together the transition from one loop of the spiral to the next was accurate; indeed it is almost invisible and the 50 joins in the scale appear to be perfect.

The axial cylinder the surface of which is not used in calculation, carries a vast amount of useful data: inches and fractions as decimals of a foot, quarters and pounds as decimals of a hundredweight, ounces as decimals of a pound, pence as decimals as decimals of a shilling, shillings and pence as decimals of a pound, and more as well as physical constants and a table of sines.

This particular model is dated 1902 and numbered 1580 and was made by W.F. Stanley of Great Turnstile. A sales leaflet gives the price as £3. The instruction book is ated 1907. An apparently identical model in theScienceMuseumcollection is dated 1880 and numbered 849, suggesting that about 30 were made annually at the turn of the century. Little seems to be known about George Fuller other than that he was at one time Professor of Engineering at Queen’s College,Belfastand a Member of the Institution of Civil Engineers.

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