It may surprise the casual reader to be told that an absolutely exact measurement is an impossibility. It is safe to say that out of a million similar articles--articles made with the intention that they shall be exactly alike--there are no two which are, in fact, absolutely similar. They may be made with the same machines and the same tools, handled by the same man, but machines and tools wear or get out of adjustment, while man's liability to err is proverbial. Astronomers are the greatest experts in the art of measurement, and they recognise the possibility, nay, the probability, of error so frankly as to make every measurement several times over; if it be an important one they make it, if possible, a great many times over, and then take the average of the results. By this means they eliminate, to a certain extent at any rate, the error which cannot be avoided. That process is to allow for errors on the part of their instruments, for the most part. To deal with personal errors another method is used as well, for it is known that some observers have a natural tendency to err on one side more or less, while others tend to make mistakes in some degree on the other side. This tendency to err is known as the "personal equation" of the observer, and there are machines and tests by which the personal equation of each man can be determined, or perhaps it would be more correct to say estimated, so that in all observations made by him the proper allowance can be added or deducted. But of course it would be extremely difficult to apply such methods in a workshop. It would never do to have to measure everything several times over, hoping that the average would come out in such manner as to indicate that the thing being measured was the size required. Instead, therefore, of wasting time seeking an accuracy which is known to be unattainable, the manufacturing engineer adopts a scientific system of measurement wherein a certain amount of inaccuracy is determined upon as permissible, and then simple appliances are used to see that it does, in fact, fall within those limits. For instance, a round bar is to be made, say, an inch in diameter. Now we know from what has just been said that, when made, we have no means of telling whether the bar is really and truly an inch in diameter or not. We consider, then, what it is for, and decide, say, that it will be near enough so long as we are sure that it is not larger than one inch plus one thousandth, nor less than one inch minus one thousandth. So long as it does not exceed or fall short of its reputed size by more than one thousandth of an inch, then we know that it will answer its purpose. Now, having come to that decision, we can build up a system upon which any intelligent workman can proceed, with the result that all the inch bars which he makes will be the same size within the limits of 1/1000 over or under, so that the greatest possible difference between any two will be 1/500.