GB2148564A

GB2148564A - Logarithmic calculating appliance

Info

Publication number: GB2148564A
Application number: GB08328320A
Authority: GB
Inventors: Herbert John Duce
Original assignee: Individual
Current assignee: Individual
Priority date: 1983-10-24
Filing date: 1983-10-24
Publication date: 1985-05-30
Also published as: GB8328320D0

Abstract

A calculating appliance based on the same mathematical principle as is the common slide-rule, but in which the scales are inscribed in sections, suitably spaced, on sheets of material designed to be used in pairs, one sheet being placed over the other and manipulated by the operator; the upper sheet is either transparent, or the material between adjacent sections of scale is cut away, in such manner that the sections of scale on both sheets are in view to the operator.

Description

SPECIFICATION Logarithmic calculating appliance The technical field to which the invention relates is that of mathematics. The background art is that of the common slide-rule.

The invention is that of an appliance for carrying out mathematical operations such as are adapted to being carried out with the common slide-rule. It embodies the principle of the slide-rule, namely, that of manipulating suitably graduated scales placed side-by-side.

Whereas, however, the scales of the slide-rule are continuous, each scale of the appliance now being described is arranged in sections placed one following the other, suitably spaced, thus giving an appliance of far greater compactness than that of a slide-rule having an equivalent degree of accuracy.

2. The appliance described in paras. 2 and 3 to illustrate the invention is for multiplication and division of numbers and for finding logarithms of numbers. It consists of two flat sheets of material, on each of which a scale is inscribed, the material of one sheet being transparent; in use this is the upper sheet, and is set in appropriate position over the other, or lower, sheet by the operator. The layout of the basic scale on each sheet is generally similar to that which is usual in the case of the common slide-rule apart from the separation of the scale into sections in the case of the appliance now being described.

Thus each scale, if continuous, would occupy an equal rectangular space of relatively short vertical dimension and longer horizontal dimension, the graduations being marked along a horizontal edge. The manner of construction of the basic scale, as in the case of the sliderule, is that the distance of any number along the scale, measured from the extreme lefthand point of the scale, and expressed as a decimal of the length of the scale, is equal to the mantissa of the logarithm of that number; the graduations marked along the scale are numbered 100, 101, 102 and soon to 998, 999 and 100.Thus graduation 100 is the beginning, or extreme left-hand point, of the scale, graduation 101 is placed along the scale at a distance of .0043 of the length of the scale (0043 being the mantissa of the logarithm of 101), and so on; the end, or extreme right-hand point, of the scale becomes graduation 100 again. This basic scale is inscribed on each sheet in ten separate sections of equal length, hence the first section extends from graduation 100 to a point between graduations 1 25 and 126, the second section from this latter point to a point between graduations 1 58 and 159, and so on to the tenth section which extends from a point between graduations 794 and 795 to graduation 100, the end point of the scale.

These ten sections of scale are inscribed in order one below the other and in addition a 10th section is inscribed above the 1 sot section, and a 1 sot section is inscribed below the 1 0th section. (It is not neccessary, for the functioning of the appliance, to have the complete length of the two additional sections of scale, but it is necessary to have the righthand end point of the upper (ooth) section and the left-hand end point of the lower (1st) section; these points are both positions of graduation 100, making four such positions in all, which are lettered A, B, C and D.) All these sections of scale have their horizontal edges parallel, their left-hand end points lying in one vertical straight line, and their righthand end points lying in another vertical straight line; the separation between adjacent sections is equal to the vertical dimension of the rectangular space occupied by a section.

Thus the arrangement is such that the upper sheet may be set in position over the lower sheet by the operator whereby sections of scale of the lower sheet, or parts thereof, are in view between sections of scale of the upper sheet. Multiplication and division are carried out in the same manner, in principle, as in the case of the slide-rule, except that, in the case of multiplication, one only of the four positions of graduation 100 will in general be appropriate for use in any specific calculations.

3. To enable the appliance to be used for finding the mantissa of the logarithm of any number, the numbers 0, 1, 2 and so on to 9 are inscribed in a column to the left in line with the 1 sot, 2nd, 3rd and so on 10th sections of scale respectively on one sheet, and a further scale equal in length to a section of scale and graduated in 1 Oths and 1 O0ths of its length is inscribed along an edge of the other sheet.To find the mantissa of the logarithm of a given number the scale graduated in tenths and hundredths is set against the section of scale of the other sheet on which the given number lies; then the number to the left in line with this section of scale on which the given number lies is the first digit of the required mantissa, and the distance along this section of scale at which it lies, measured in hundredths of the length of the section of scale, gives the second and third digits of that mantissa.

4. A variation of the arrangement of the scales of the appliance described in para. 2 will now be described. The lower sheet has inscribed on it continuous double-sections of the scale as described in para. 2, arranged as follows: 1 st + 2nd sections 2nd + 3rd sections and so on to 9th + 10th sections 10th + 1 sot sections 1 sot + 2nd sections and so on to 10th and 1st sections; the upper sheet has inscribed on it ten single sections of scale in order from the 1 sot to the 10th.

5. A further variation of the appliance will be briefly described. The sheets of material are in the form of hollow cylinders fitting closely one around the other, the one being able to rotate around and slide along the other. The scales are inscribed along the cylinders parallel to the axis of rotation, there being on each cylinder ten sections of scale in order from the 1 sot to the 10th, the spacing between the 1 sot and the 10th sections being equal to that between the other pairs of adjacent sections. In this variation also, ten double-sections of scale from a 1 sot + 2nd double-section in order to a 1 ooth + 1 sot double-section may replace the single sections.

6. In all appliances described above the upper sheet could be of opaque material, the material between adjacent sections of scale being cut away.

7. In the appliances as described in para.

2 the number of sections into which the scale is divided need not necessarily have been ten.

The arrangements described in para. 3, and which enable the appliance to be used for finding logarithms of numbers, are only applicable where the basic scale is separated into ten sections, although in certain other cases, as for instance when the basic scale is separated into five sections or into twenty sections, these arrangements are still applicable in principal, but would require some modification in their detailed application.

8. Further sheets of material, on which are inscribed scales suitable for calculations involving other mathematical functions, may be incorporated in the appliances described above. Any scales which, if inscribed in continuous form on a slide-rule, would be suitable for use together, would be suitable for use in the appliances described above.

Claims

1. A calculating appliance, based on the principle of the common slide-rule, in which scales, such as would be suitable for use one in conjunction with the other if inscribed on a slide-rule, are inscribed in sections on sheets of material. The sheets are designed to be placed one above the other and manipulated by the operator, the upper sheet being either of transparent material, or the material between adjacent scales is cut away, in such manner that scales of the lower sheet are in view to the operator between scales of the upper sheet.

2. The arrangement of the material of the appliance as claimed in Claim 1 in a cylindrical form, the outer cylinder being able to rotate around and slide along the inner one.

3. The provision of guides to facilitate the manipulation of the sheets of appliances as claimed in Claims 1 and 2.

4. In an appliance as claimed in Claims 1 and 2, the separation of the complete scales into ten sections, the inscription of the digits O to 9 against the sections of scale, and the provision of a further scale equal in length to the other sections of scale and graduated in tenths and hundredths, whereby the appliance may be used as a table of logarithms.

5. A calculating appliance substantially as described herein.