In physics it is usual to employ the letters of the alphabet as a sort of shorthand to represent words. So that the letter m stands for the mass of a body. So again g stands for the attractive pull of the earth at a given place. w stands for the weight of the body. Hence then, since the weight of a body depends on its mass and also on the attractive pull of the earth, we express this in short language by saying, w = m × g; or w is equal to m multiplied by g; the symbol = being used for equality, and × the sign of multiplication. In common use × is usually omitted, and when letters are put together they are intended to be understood as multiplied. So that this is written
w = mg.
Of course by this equation we do not mean that weight is mass multiplied into the force of gravity, we only mean that the number of units of weight is to be found by multiplying the number of units of mass into the number of units of the earth’s force of gravity.
In the same way, if when estimating the number of waggons, w, that would be wanted for an army of men, n, which consumed a number of pounds, p, of provisions a day, we might put
w = np.
But this would not mean that we were multiplying soldiers into food to produce waggons, but only that we were performing a numerical calculation.
Time is one of the most mysterious of our elementary ideas. It seems to exist or not to exist, according as we are thinking or not thinking. It seems to run or stand still and to go fast or slowly. How it drags through a wearisome lesson; how it flies during a game of cricket; how it seems to stop in sleep. If we measured time by our own thoughts it would be a very uncertain quantity. But other considerations seem to show us that Nature knows no such uncertainty as regards time, that she produces her phenomena in a uniform manner in uniform times, and that time has an existence independent of our thoughts and wills.
The idea of a state of things in which time existed no more was quite familiar to mediæval thinkers, and was regarded by many of them as the condition that would exist after the Day of Judgment. In recent times Kant propounded the theory that time was only a necessary condition of our thoughts, and had no existence apart from thinking beings—in fact, that it was our way of looking at things.
Scientifically, however, we are warranted in treating time as perfectly real and capable of the most exact measurement. For example, if we arrange a stream of sand to run out of an orifice, and observe how much will run out while an egg is being boiled hard, we find as a fact that if the same quantity of sand runs out, the state of the egg is uniform. If we walk for an hour by a watch, we find that we can go half the distance that we should if we walked two hours. It is the correspondence of these various experiments that gives us faith in the treatment of time as a thing existing independently of ourselves, or, at all events, independent of our transient moods.
The ideas of time acquired by the races of men that first evolved from a state of barbarism were no doubt derived from the observation of day and night, the month and the year.