Silvanus Phillips Thompson

“ SHALL we have a school in the workshop, or a workshop in the school? Or what other combination can we devise that will permit mental and scientific training to proceed after the age has been attained at which serious manual labor must begin? Hitherto we have been contented at most to organize night schools, evening classes, and so-called Mechanics' Institutes for our apprentices, leaving it to their own caprice whether they chose to employ their leisure hours in self-improvement or squander them in self-indulgence. ”

“ ON TRUE COMPOUND INTEREST AND THE LAW OF ORGANIC GROWTH. Let there be a quantity growing in such a way that the increment of its growth, during a given time, shall always be proportional to its own magnitude. This resembles the process of reckoning interest on money at some fixed rate; for the bigger the capital, the bigger the amount of interest on it in a given time. ”

“ He must measure, he must weigh, in order that he might go on to calculate. ’The first step,' he wrote, 'toward numerical reckoning of properties of matter ... is the discovery of a continuously varying action of some kind, and the means of observing it definitely, and measuring it in terms of some arbitrary unit or scale division. But more is necessary to complete the science of measurement in any department, and that is the fixing on something absolutely definite as the unit of reckoning.' It was in this spirit that Thomson approached the subject of the transformation of heat. ”

“ And ought we, then, to be surprised if, in pursuance of the system we have deliberately marked out for the rising generation, we keep our future artisans, till they are fifteen or sixteen, employed in no other work than sitting at a desk to follow, pen in hand, the literary course of studies of our educational code, we discover that on arriving at that age they have lost the taste for manual work, and prefer to starve on a threadbare pittance as clerks or book-keepers rather than by the less exacting and more remunerative labor of their hands? ”

“ Now in what sense is it true that a speed of yards per second is the same as yards per minute? Ten yards is not the same as yards, nor is one second the same thing as one minute. What we mean by saying that the rate is the same, is this: that the proportion borne between distance passed over and time taken to pass over it, is the same in both cases. ”

“ The life and soul of science is its practical application ; and just as the great advances in mathematics have been made through the desire of discovering the solution of problems which were of a highly practical kind in mathematical science, so in physical science many of the greatest advances that have been made from the beginning of the world to the present time have been made in the earnest desire to turn the knowledge of the properties of matter to some purpose useful to mankind' (see Popular Lectures and Addresses, i. 79) . ”

“ What, then, must be done? "Apprenticeship is absolutely necessary for the purpose of acquiring a practical knowledge of a trade; without this there can be no guarantee for good and efficient workmanship." Such is the dictum of one who speaks with authority from the point of view of labor, and the sentiment is the expression of that which all admit. Better education of the children—such, in fact, as is contemplated by the provisions of the Elementary Education Act of 1870—may, it is hoped, quicken the intelligence ere the are is reached at which apprenticeship begins: but will it do more? ”

“ When a motor-car whizzes by us, we say: What a terrific rate! When a spendthrift is flinging about his money, we remark that that young man is living at a prodigious rate. What do we mean by rate? In both these cases we are making a mental comparison of something that is happening, and the length of time that it takes to happen. If the motor-car flies past us going yards per second, a simple bit of mental arithmetic will show us that this is equivalent–while it lasts–to a rate of yards per minute, or over miles per hour. ”

“ If the availability of the energy in a hot body be proportional to its absolute temperature, it follows that as the earth and the sun — indeed, the whole solar system itself — cool down towards one uniform level of temperature, all life must perish and all energy become unavailable. This far-reaching conclusion once more suggested the question of a beginning of the Cosmos, a question which had arisen in the consideration of the Fourier doctrine of the flow of heat. ”

“ Time was when, for the most part, the skilled artisan, who was master of his trade, worked at home in his own house, assisted, it might be, by a few younger workmen or journeymen. Into his house and family he would receive one or two young lads to learn, during a seven years' engagement, the art and mystery of his craft; the master himself working and teaching them his work, feeding and clothing them, and receiving from them in return the value of the services which, as they became more apt in their work, they were able to render. ”

“ Moreover, we are usually dealing with more than one variable at once, and thinking of the way in which one variable depends on the other: for instance, we think of the way in which the height reached by a projectile depends on the time of attaining that height. Or we are asked to consider a rectangle of given area, and to enquire how any increase in the length of it will compel a corresponding decrease in the breadth of it. Or we think of the way in which any variation in the slope of a ladder will cause the height that it reaches, to vary. ”

“ Here one realizes one advantage possessed by this municipal school over those in which the atelier is simply the workshop of a great business. In the early stages, when workmanship is very imperfect, it is not always well to strive to produce a salable article. Better waste wood, says the superintendent of the shops, than spoil the making of a good apprentice. Better to let the young workman see something of all the different corners of his trade, than by too fine a division of labor to keep him all his years learning only to shape chair-legs. ”

“ In 1884 Thomson delivered at Baltimore twenty lectures 'On Molecular Dynamics and the Wave Theory of Light.' His hearers, mostly accomplished teachers and professors, numbered twenty-six. The lectures, reported verbatim at the time, were issued with many revisions and additions in 1904. They show Thomson's speculative genius in full energy and brilliance. Ranging from the most recondite problems of optics to speculations on crystal rigidity, the tactics of molecules and the size of atoms, they almost embody a new conception of the ultimate dynamics of physical nature. ”

“ If we want to go so far that not even a Whitworth’s measuring machine would detect it, we should merely have to go to about terms. A microscope would not show even the term! So the infinite number of operations is no such dreadful thing after all. The integral is simply the whole lot. But, as we shall see, there are cases in which the integral calculus enables us to get at the exact total that there would be as the result of an infinite number of operations. ”

“ Without the shadow of a doubt the truth that there is—and alas, that there is—much truth in the outcry concerning the inferiority of training and capacity of the British artisan, may be very largely imputed to the relaxation and degeneration of the old system of apprenticeship; for, with all its faults, it did at least provide that a skilled master should become personally responsible for the training of the apprentice in his craft. ”

“ Further, by a most ingenious use of the integrating factor to solve the differential equation for the quantity of heat needed to alter the volume and temperature of unit mass of the working substance, he gave precise mathematical proof of the theorem that the efficiency of the perfect engine working between given temperatures is inversely proportional to the absolute temperature. ”

“ Why does anybody want to differentiate twice over? We know that when the variable quantities are space and time, by differentiating twice over we get the acceleration of a moving body, and that in the geometrical interpretation,
as applied to curves, means the slope of the curve. But what can mean in this case? Clearly it means the rate (per unit of length ) at which the slope is changing—in brief, it is a measure of the curvature of the slope. ”

“ Hence we know that in all cases we are justified in neglecting the small quantities of the second—or third (or higher) —orders, if only we take the small quantity of the first order small enough in itself.
But, it must be remembered, that small quantities if they occur in our expressions as factors multiplied by some other factor, may become important if the other factor is itself large. Even a farthing becomes important if only it is multiplied by a few hundred. ”

“ It is an education which, so far as it goes beyond the three elements of reading, writing, and arithmetic, is framed in all its essential features upon an exclusively collegiate type of studies; grammar, history, geography, foreign languages, and the like, being introduced, to the utter exclusion in all the most important of the successive "Standards" of any teaching of drawing, of mechanics, of the simplest facts of science or of natural history—of all, in fact, that most nearly concerns the workman throughout his entire career. ”

“ By showing you that what one fool can do, other fools can do also, it lets you see that these mathematical swells, who pride themselves on having mastered such an awfully difficult subject as the calculus, have no such great reason to be puffed up. ”

“ In all the constructive trades the greater part of a workman's instructions are given to him in the form of working drawings. Yet we suffer the budding artisan to pass through the schools ignorant of the first rudiments of a science that is as essential to his work as are the four rules of arithmetic. ”

“ You don’t forbid the use of a watch to every person who does not know how to make one? You don’t object to the musician playing on a violin that he has not himself constructed. You don’t teach the rules of syntax to children until they have already become fluent in the use of speech. It would be equally absurd to require general rigid demonstrations to be expounded to beginners in the calculus. ”

“ Apprenticeship, with its wholesome rules, having decayed in everything but form, the lads who enter the shops are never properly instructed, but are made the drudges of the older workmen. What wonder that they acquire habits of idleness and carelessness that not only pursue them through the whole of their work, but, worse than this, corrupt and undermine their morals? ”

“ When an integral is to be thus defined between two limits, we call the lower of the two values the inferior limit, and the upper value the superior limit. Any integral so limited we designate as a definite integral, by way of distinguishing it from a general integral to which no limits are assigned. ”

“ Then, and not till then, will the apprenticeship of the future constitute a powerful instrument, not merely for the intellectual, moral, and social improvement of the working-classes, but for the promotion of the wealth and prosperity of the whole nation. ”

“ You will surely realize from this chapter and the preceding, that in many respects the calculus is an art rather than a science: an art only to be acquired, as all other arts are, by practice. Hence you should work many examples, and set yourself other examples, to see if you can work them out, until the various artifices become familiar by use. ”

“ Nothing is made in the shops that will not sell; the apprentices learn the value not only of materials but of time; and, though the works that successfully pass under their hands are graduated to their capacity and experience, they are precisely of the same character as those which apprentices in any ordinary workshop would have to undertake. The masters and foremen of the various ateliers appear to take great interest in their pupils, and pride themselves on the success of their instruction. ”

“ To accelerate a mass requires the continuous application of force. The force necessary to accelerate a mass is proportional to the mass, and it is also proportional to the acceleration which is being imparted. ”

“ With the extension of trade and the wider use of machinery the number and power of the adult employed workmen increased, and with their increase of power came a jealousy, on the one hand, toward the masters; on the other, toward the apprentices, who were regarded as cheapening labor when employed in too great numbers. The conflict which arose between employer and employed gradually merged into one between capital and labor. ”

“ On one side is imaginary; that is, there is no value of that can be represented by a graph; the latter is therefore entirely on the right side of the axis of (see Fig. 30) .
On plotting the graph it will be found that the curve goes to the origin, as if there were a minimum there; but instead of continuing beyond, as it should do for a minimum, it retraces its steps (forming what is called a “cusp”) . There is no minimum, therefore, although the condition for a minimum is satisfied, namely . It is necessary therefore always to check by taking one value on either side. ”

“ Obviously, with such facts as these staring us in the face, we must admit a flaw in the training given in our primary schools if its result is in so large a number of cases to destroy the natural capacity for manual labor. The fault is not so much in the amount of education as in the nature of the studies. For many trades the training of the hand to work may, and in some must, begin at an earlier age than that at which many children leave the elementary school. In some trades, indeed, the masters definitely refuse to take apprentices above a certain age ”

“ If we think of the curve which will represent as a function of , it will be such that its slope at any point will be proportional to the ordinate at that point, and will be a negative slope if is positive. So obviously the curve will be a die-away curve (p. 156) , and the solution will contain as a factor. But, without presuming on this bit of sagacity, let us go to work. As both and occur in the equation and on opposite sides, we can do nothing until we get both and to one side, and to the other. To do this, we must split our usually inseparable companions and from one another. ”

“ Cæteris paribus, the better educated our artisans are, the better workmen will they make; but we must take care that the education is of the right sort. Now, what will be the verdict of future generations on learning that the education which this great and powerful nation offers to the children of its artisans, to the class that will form the artisans of the next generation, was of a character purely literary, in no sense technical or even scientific? ”

“ Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present to my fellow fools the parts that are not hard. Master these thoroughly, and the rest will follow. What one fool can do, another can. ”

“ The pupils of this school are not apprenticed at all in the ordinary sense; there is no contract, and they earn nothing. Most of them are very young—even as young as eight or nine years—nor have they yet completed their elementary education. If they stay out the prescribed three years' course, they not only get as good a schooling as in any of the ordinary elementary schools, but they will also have seen something of constructive industry. During the first two years they are sent to work for a day at a time, in rotation, in one or other of the occupations of the workshop. ”