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THE present era is sometimes termed the mechanical age because so many operations which, in earlier days, were carried out slowly and often painfully by hand, are now performed by machines with an enormous saving in time and effort.
The slide rule cannot be regarded as a modern invention since the first design dates from the early part of the seventeenth century, but every year sees additions and variations made and the up-to-date instrument has, as might be expected, advanced greatly beyond the earlier types. Every year a considerable number of Patent Specifications are lodged in the British Patents Office to give protection to the latest inventions in slide rule technique, and we may say fairly that the slide rule in its own field is keeping pace with modern mechanical advance.
This Teach Yourself Book is published to increase the popularity of the slide rule. It is hoped that it may help to remove the fallacy that there is something difficult or even mysterious connected with a simple instrument with which everybody who has calculations to make should be acquainted.
Among the technicians and artisans upon whom we so much depend for the maintenance and improvement of national prosperity, are many who have frequently to make calculations. They would be hampered in their activities if the improvements we have referred to had not extended to expediting their work. The slide rule and other instruments which give the same facilities for rapid calculations, are covered by the term "Mechanical Calculation".
It is unfortunate that, for some reasons not easy to see, the slide rule is sometimes regarded as a difficult instrument with which to become proficient. There is a tendency for some people to become facetious in their references to this simple instrument. Journalists and broadcasters are great offenders in this respect and some of their references are unbelievably absurd and show a lack of elementary knowledge.
The clumsy and unscientific system of monetary units and measures in weights, lengths, areas, etc., which have grown up and are still used in this country, give some slight difficulty in applying the slide rule to calculations in which they are involved and since the scales of slide rules are, in most cases, subdivided in the decimal system, any notations of weights and measures which are similarly designed, such as the metric system, lend themselves readily to calculation by slide rule.
We shall find, however, that when working in our monetary system of pounds, shillings and pence, or in lengths in miles, yards and feet, or in any of our awkward units, the slide rule can be employed to simplify our work and give results quickly, and with a degree of accuracy sufficient for practical requirements.
We have said that, in general, slide rule scales are subdivided in decimal fractions, and since there are still some people who cannot easily calculate in the decimal system, we give at an early stage a simple explanation of the principles of this system. Perhaps we need hardly add that any sections of this book which deal with matters with which the reader is quite familiar may be glanced at and passed over.
We shall find that the underlying principle of the slide rule is calculation by logarithms. Just as a man may be an expert motor-car driver without understanding the principles of the internal-combustion engine and the mechanism of his car, so can a slide rule be used without the slightest knowledge of logarithms. In fact, we hesitated at including the section on logarithms, in case the mention of the term might cause discouragement and increase the sense of awe with which some people regard the slide rule. The section on logarithms may be disregarded entirely, and indeed we ask that it should be, on the first reading of this book, but when the rudiments of the slide rule have been mastered - and again we stress the simplicity of these - it may be that some readers will find interest and advantage in learning something of the first principles of "logs" - one of the most fascinating parts of elementary mathematics.
Another factor which has contributed to the reluctance of people to purchase a slide rule lies in the erroneous impression that it is a costly instrument. Naturally enough, people are averse to paying two or three pounds for an instrument which they fear may be of little use to them. Inexpensive slide rules have been available in this country for over thirty years, and their makers claim that for accuracy and utility they are equal to the more expensive varieties which have been manufactured for a much longer period. The first "Unique" slide rule, the 10" log-log model, was produced at a popular price for students. Its introduction was welcomed, and it met with success. There are now about a score of different slide rules in the "Unique" range, and sales have progressively increased, and it may fairly be said that this make of rule is now the "best seller" in this country. "Unique" slide rules carry all the useful scales, including the log-log scale, in most models. In the expensive type of rule the inclusion of the log-log scale means a much higher-priced instrument than the "standard" or ordinary models. The log-log scale in the "Unique" range is included at no increase in the cost of the rule. The makers of "Unique" slide rules introduced a new technique in manufacture by printing the scales and coating them with transparent plastic material. This important change allowed of a great reduction in the manufacturing cost as compared with the older method of separately dividing the scales.
This book, however, is not published primarily to boost any particular make of slide rule. All slide rules are difficult to manufacture, and in most cases are honestly worth the prices charged for them. Some shopkeepers charge more than the recognised retail prices fixed by the manufacturers, and purchasers should be vigilant and resist any attempt at this sort of imposition.
We would, with all respect, urge members of the teaching profession to make more effective efforts to introduce the slide rule into schools. The proper place to become acquainted with this invaluable time-saver is in the classrooms of the primary schools; normal boys and girls of the age of 13 or 14 years are able to attain proficiency in its use. More often than not the student does not become acquainted with the slide rule until he or she reaches a technical school or college, and even in such institutions the slide rule is by no means the universal and everyday instrument it deserves to be.
The writer has had long experience of teaching in a technical college, and has never had the least difficulty in arousing interest in the application of the slide rule to practical problems. There was never any necessity to urge students to adopt the rule; directly a slide rule appeared in a classroom and was demonstrated, students expressed the desire to acquire one, and within a week or two the majority had done so. A few minutes devoted to instruction were sufficient to teach the fundamentals. We know that the slide rule is used in a number of primary and central schools by teachers who think as we do. Unfortunately, we also know that even in some grammar and secondary schools a slide rule is almost unknown.
We would particularly direct attention to Section 8, which deals with slide rules designed for commercial calculations. We say, without fear of being proved wrong, that every individual who has to make calculations can, at times, use a slide rule to great advantage, and this statement applies to the commercial man. The slide rule costs but a few shillings, and takes little time to master. To refuse to investigate the potentialities of the instrument is to adopt a non-possumus attitude.
The commercial rule can be recommended also for technical work since it incorporates the ordinary C and D scales, which deal with the bulk of the work, and four other scales, which automatically multiply or divide by 12 or 20, without using the slide, and a reciprocal scale. For many purposes this rule is more adaptable than the usual type with A, B, C and D scales.
The monetary slide rule is scaled directly in £, s. d., and for some purposes, for example in checking invoices, is more convenient to use than the commercial rule. It carries also the
C and D scales and so provides facilities for straightforward multiplication and allied operations.
We hope we shall not be accused of unduly stressing the advantage of slide rules which depart from the standard type. We can only attribute to the conservatism with which most of us are endowed the fact that the large majority of slide rules in use are of the standard type whose salient features are the A, B, C and D scales. Men who have used a slide rule for years have never handled any other than the standard type; to them we would suggest a change to a more efficient instrument, several of which we mention later. The standard type slide rule, except for the beginner, is moribund.
For the tyro we advise first the reading of Sections 1 and 3, making sure he can read the scales. He should read also Section 2 if he is likely to have any difficulty with decimals.
He should then study Section 4 thoroughly, since this is the most important part of the early instruction. This section deals with C and D scales, which are by far the most used scales of the standard slide rule.
He should use his slide rule for the examples and problems given in the text and work through additional simple examples he can make up for himself, using numbers which can be easily reduced mentally. Such examples (6 x 9 x 16) / (2 x 4) as which gives 108 as the result. He may say that it is not worth while using a slide rule to calculate a result he can obtain mentally, and he would be quite right, but we are here advising how to approach the slide rule and to gain experience and confidence in using it.
The student may then use these figures (6.42 x 9.35 x 16.7) / (2.04 x 4.41) which he cannot cope with mentally. He should obtain as a result 111·5 and he will see how the position of decimal point has been fixed.
For the experienced reader we recommend the dualistic slide rule as being the best available for general purposes. This rule is discussed in Section 11. It is quicker in action, more accurate in its results and the irritating necessity of traversing the slide when using the more usual type of slide rule is eliminated.
We include in the explanatory sections of the book examples in respect of which the movements of slide and cursor are indicated. Often there are alternative ways of selecting various factors, giving rise to alternative ways of moving the slide and cursor. For practice some of these should be worked out by the reader.
Problems are inserted for the student to solve, and a check can be made by comparing results with those given at the end of the book. To reduce typography in the worked examples, abbreviations are used; these are mentioned in Section 4.
© Hodder Stoughton, reproduced with permission.