The second method uses a sliding linear L scale available on some models. Addition and subtraction are performed by sliding the cursor left for subtraction or right for addition then returning the slide to 0 to read the result. Standard linear rules[ change change source ] The length of the slide rule is quoted in terms of the nominal length of the scales. Models a couple of meters long were sold to be hung in classrooms for teaching purposes.
Tulliver found himself confronted by any little difficulty he write as sum difference or multiple of logarithms inventor accustomed to make the trite remark, "It's a puzzling world. Solomon himself, who may be supposed to have been as sharp as most men at solving a puzzle, had to admit "there be three things which are too wonderful for me; yea, four which I know not: Men have spent long lives in such attempts as to turn the baser metals into gold, to discover perpetual motion, to find a cure for certain malignant diseases, and to navigate the air.
From morning to night we are being perpetually brought face to face with puzzles. But there are puzzles and puzzles. Those that are usually devised for recreation and pastime may be roughly divided into two classes: Puzzles that are built up on some interesting or informing little principle; and puzzles that conceal no principle whatever—such as a picture cut at random into little bits to be put together again, or the juvenile imbecility known as the "rebus," or "picture puzzle.
It is simply innate in every intelligent man, woman, and child that has ever lived, though it is always showing itself in different forms; whether the individual be a Sphinx of Egypt, a Samson of Hebrew lore, an Indian fakir, a Chinese philosopher, a mahatma of Tibet, or a European mathematician makes little difference.
Theologian, scientist, and artisan are perpetually engaged in attempting to solve puzzles, while every game, sport, and pastime is built up of problems of greater or less difficulty.
The spontaneous question asked by the child of his parent, by one cyclist of another while taking a brief rest on a stile, by a cricketer during the luncheon hour, or by a yachtsman lazily scanning the horizon, is frequently a problem of considerable difficulty. In short, we are all propounding puzzles to one another every day of our lives—without always knowing it.
A good puzzle should demand the exercise of our best wit and ingenuity, and although a knowledge of mathematics and a certain familiarity with the methods of logic are often of great service in the solution of these things, yet it sometimes happens that a kind of natural cunning and sagacity is of considerable value.
For many of the best problems cannot be solved by any familiar scholastic methods, but must be attacked on entirely original lines.
This is why, after a long and wide experience, one finds that particular puzzles will sometimes be solved more readily by persons possessing only naturally alert faculties than by the better educated. The best players of such puzzle games as chess and draughts are not mathematicians, though it is just possible that often they may have undeveloped mathematical minds.
It is extraordinary what fascination a good puzzle has for a great many people. We know the thing to be of trivial importance, yet we are impelled to master it; and when we have succeeded there is a pleasure and a sense of satisfaction that are a quite sufficient reward for our trouble, even when there is no prize to be won.
What is this mysterious charm that many find irresistible? The curious thing is that directly the enigma is solved the interest generally vanishes. We have done it, and that is enough.
But why did we ever attempt to do it? The answer is simply that it gave us pleasure to seek the solution—that the pleasure was all in the seeking and finding for their own sakes. A good puzzle, like virtue, is its own reward. Man loves to be confronted by a mystery, and he is not entirely happy until he has solved it.
We never like to feel our mental inferiority to those around us. The spirit of rivalry is innate in man; it stimulates the smallest child, in play or education, to keep level with his fellows, and in later life it turns men into great discoverers, inventors, orators, heroes, artists, and if they have more material aims perhaps millionaires.
In starting on a tour through the wide realm of Puzzledom we do well to remember that we shall meet with points of interest of a very varied character. I shall take advantage of this variety.
People often make the mistake of confining themselves to one little corner of the realm, and thereby miss opportunities of new pleasures that lie within their reach around them. One person will keep to acrostics and other word puzzles, another to mathematical brain-rackers, another to chess problems which are merely puzzles on the chess-board, and have little practical relation to the game of chessand so on.
This is a mistake, because it restricts one's pleasures, and neglects that variety which is so good for the brain. And there is really a practical utility in puzzle-solving. Regular exercise is supposed to be as necessary for the brain as for the body, and in both cases it is not so much what we do as the doing of it from which we derive benefit.
The daily walk recommended by the doctor for the good of the body, or the daily exercise for the brain, may in itself appear to be so much waste of time; but it is the truest economy in the end. Albert Smith, in one of his amusing novels, describes a woman who was convinced that she suffered from "cobwigs on the brain.
They keep the brain alert, stimulate the imagination, and develop the reasoning faculties. And not only are they useful in this indirect way, but they often directly help us by teaching us some little tricks and "wrinkles" that can be applied in the affairs of life at the most unexpected times and in the most unexpected ways.
There is an interesting passage in praise of puzzles in the quaint letters of Fitzosborne. Here is an extract: It is an art, indeed, that I would recommend to the encouragement of both the Universities, as it affords the easiest and shortest method of conveying some of the most useful principles of logic.
It was the maxim of a very wise prince that 'he who knows not how to dissemble knows not how to reign'; and I desire you to receive it as mine, that 'he who knows not how to riddle knows not how to live. I am not referring to acrostics, anagrams, charades, and that sort of thing, but to puzzles that contain an original idea.Here is a history of questions and answers processed by "Ask the Physicist!".
If you like my answer, please consider making a donation to help support this service.. If there is a link to a previously answered question, be patient. History of Science. A few cultural facts about the evolution of scientific nomenclature and scientific notations.
Mathematics, chemistry, etc. May 07, · Expressing A Single Logarithm As A Sum Or Difference. History of Science.
A few cultural facts about the evolution of scientific nomenclature and scientific notations. Mathematics, chemistry, etc. Computer - History of computing: A computer might be described with deceptive simplicity as “an apparatus that performs routine calculations automatically.” Such a definition would owe its deceptiveness to a naive and narrow view of calculation as a strictly mathematical process.
In fact, calculation underlies many activities that are not normally thought of as mathematical. Several important formulas, sometimes called logarithmic identities or logarithmic laws, relate logarithms to one another..
Product, quotient, power, and root. The logarithm of a product is the sum of the logarithms of the numbers being multiplied; the logarithm of the ratio of two numbers is the difference of the logarithms.