The Design of Non-Linear Scales for Slide Rules

Abstract

Many school children experience considerable difficulty in reading the 0 scale on conventional slide rules. This investigation sets out to provide design recommendations for a scale of acceptable accuracy which can be understood by children with a wide range of abilities. Eight different scale designs, including the conventional design, were compared at a scale-reading task using secondary modern schoolboys as subjects. The scales were presented in booklet form. Errors in the results are classified as either gross errors, i.e. those caused by misunderstanding, or interpolation errors. Analysis shows that the simplest designs, i.e. those with the fewest gradations and numerals, lead to fewer gross errors, and can be read faster than the conventional design. The simpler designs, however, led to more interpolation errors than the conventional design mainly because interpolation errors were not possible (for three significant figure accuracy) at the lower end of the conventional scales. Inconsistency in the meaning of gradations and numerals in different parts of the scale seems to be the main source of misunderstanding on the conventional design. The recommended scale has gradations at the 0.1 positions and numbering only at the 1,2…10 positions. It is suggested, however, that the introduction of such a simplified scale for school slide rides might meet with some resistance, and a scale with consistent numbering and with gradations at the 0.05 position is recommended as a more acceptable alternative.