The Fundamentals of Engineering Science

This is one of my favourite books on the physical sciences. It is easy to learn from, a joy to teach from, and one of the most used books on my shelf at work. It is imported from England by Dover and covers what is called in this country “elementary physics” — at a level somewhere between high school and college. The mathematics required for reading it is rudimentary algebra and geometry. The last 10% of the book assumes you have the amount of trigonometry typically included in a high-school algebra or geometry course. What is truly amazing is how much physics you can learn from this book without knowing much more than arithmetic to start with. It is the best pre-calculus physics book I have seen. It does not make the common mistake of trying to cover material that can be treated adequately only with calculus. Even so, the coverage is very broad. The basic subject-matter is mechanics (eight chapters) and electricity (six chapters), with single chapters devoted to fundamental quantities and units, vectors, mechanics of solids, atomic structure, heat, fluid statics, energy conversion, and properties of materials.

But enough of what the book covers — the beauty is in how it covers it. At the outset he gives an explicit and rational method for dealing with units and their conversion, thus removing one of the biggest stumbling blocks for students and engineers alike. His method makes it almost impossible to make a mistake. As a virtuoso illustration, he applies it to the conversion of 2kgf/sq.m. into 0.41lbf/sq.ft. through eight intermediary conversion factors, and comes through the whole mess unscathed! Throughout the text, there are numerous worked examples. These are done in great detail with full explanations and great care to keep track of units. Further, the way in which he organizes and lays out computations is a model of logic and clarity. Real-life engineering problems are usually much more complex than textbook examples and very often orderly work habits make the difference between getting the right answer and getting the wrong one — or none at all.

The writing in this text is simple, straightforward, and down to earth.

When the engineer James Watt was developing the early steam engines, he needed some comparison between his engines and the type of “drive” in common use at the time. He wanted to measure the working capacity of his engines in terms that his prospective customers would readily understand. Horses were frequently used to perform mechanical tasks at that time, and so Watt decided to measure the rate at which a horse could work. He would then be able to claim with some justification that one of his engines could replace a certain number of horses.

He chose a good, strong dray horse, and set it to work pulling various weights up a mineshaft. From his observations, he calculated that the horse could perform 22,000 ft.lbf. of work in a minute, on the average. However, to be on the safe side, in case one of his customers might have a particularly strong horse working for him he added 50% and said that a horse could work at the rate of 33,000 ft.lbf/min.

This value has since become an accepted unit of power known as the HORSE POWER.

Yet simple as it is, there is an implicit understanding of Rand's theory of measurement in this statement, in particular, her dictum that a unit of measurement must have a size consistent with everyday experience. And, an understanding of what happens when this dictum is not followed is implicit in the following:

It has been stated that an atom is extremely small. Any attempt to give an impression of its size ends up in unimaginably large numbers or equally unimaginable small ones. For example, it can be said that there are about a million million million atoms in a grain of fine table salt — which has roughly the same significance as saying that an atom is extremely small!

He goes on to say that “on the atomic scale, ‘size’ in the normally understood sense has no real meaning”, a truth that many philosophers of science have yet to realize. Further philosophic wisdom is shown by:

Until the late nineteenth century, atoms were considered to be complete units which could not be divided; that is, they were considered to be the fundamental particles of which the various elements are built. Atoms are now known to be themselves composed of a number of particles, which IN THE PRESENT STATE OF KNOWLEDGE, are taken to be fundamental particles.

I have emphasized the point at which Titcomb recognizes that knowledge is contextual. It is an error to assume that the simplest particles discovered so far, at any point in history, are the fundamental particles. This error was made by the nineteenth-century atomists, and is still being made by physicists today with regard to current elementary particles. They could stand to read Titcomb — or Jonathan Swift:

So, naturalists observe, a flea,
Hath smaller fleas that on him prey;
And these have smaller still to bite 'em;
And so proceed AD INFINITUM.

On that ironic note I rest my case. There is little more I can say — go read the book yourself.

Robert Hayden is a math major at MIT and is currently working as an engineer.