This is one of the simplest forms of a calculating machine known. Within its limits it gives correct and instant answers to many different calculations, and is moreover, quite simple to use. It has limits so far as accuracy of the answer is concerned, as this depends upon the size instrument that is used, and how finely it is engraved. Considering, however, that in the ordinary calculations of engineers, builders, architects, etc., there are factors the true value of which is unknown, an instrument that will quickly give the result of a long calculation within an accuracy of, say 1 A per cent., is very valuable. It should be made clear that this so-called want of accuracy is not the fault of the instrument, but due to the fact that the answer cannot sometimes be read by the eye to within, say 11/2 per cent., owing to the fineness of the scale, and that this is itself again dependent upon the type of the calculation. It is made in several forms and sizes, the most popular size being about 10in. long, about 11/4in. wide, and about gin. thick. The body has a groove formed in it of about one third of the width, in this groove a movable slide is placed. Four scales are engraved on the slide rule, the first is on the body near the top edge of the groove, the second is on the top edge of the slide, the third is on the lower edge of the slide, and the fourth is on the lower edge of the groove. These for convenience may be called the A, B, C and D scales respectively. Scales A and B are exactly alike, and scales C and D are alike, but scales A and B differ from scales C and D. On most slide rules provision is made for holding a piece of glass with a fine hair-line thereon in such a way that this hair-line can be brought over any required line on the rule, merely to mark the place as it were. It is not necessary here to draw special attention to the manner in which the slide rule is marked or divided up, the reader can easily see this by inspecting one, neither is it necessary to explain very fully just why it gives the results it does. The position is assumed to be such that the reader wishes to know how to use the slide rule, with only enough explanation as to enable him to remember the procedure. Let it be supposed that it is desired to multiply 2 by 3 and that we have 3 strips of paper, a book of logarithms and a pencil. Take one piece ot paper, mark it off to a length equal to the logarithm of 2 = -301, cut it off at that length. Mark and cut off the second piece of paper to a length equa1 to the log. of 3 - -477. Mark and cut off the third piece of paper equal to the log. of 6 - '778. Place the first and second pieces of paper exactly end to end, the third piece of paper will be found to be exactly the same length. In other words we have cut 2 pieces of paper in such a way that the result of placing them end to end is not to add their values together but to multiply them together. Also it will be clear that if we take the longer piece of paper and take away from it the length of one of the short pieces of paper then it is obvious that a length equal to the other short paper will be left, which, means that subtracting a short length from the longest length gives the result of division and not subtraction as in ordinary arithmetic.

The above explanation must be grasped and clearly realised, after which the use of the slide ride, and the reason for the movements are perfectly obvious, and will never be forgotten. Now take the rule, move the slide out to the right until the first line on the left marked 1 and termed the index of scale B, comes under 2 on scale A ; now move the hair line until it comes over 3 on scale B. That is, we have added a length of scale A marked 2 to a length of scale B marked 3 and the answer is under the hair-line on scale A, i.e., 6. If the reader will get the clear reason for the above fixed in his mind, all multiplications become perfectly easy and obvious. To divide 6 by 2, place the 2 on scale B under 6 on scale A, the answer is above the index point on scale B, i.e., 3 on scale A. Here we took 6 on scale A and took away from it the length marked 2 on scale B, leaving the length marked 3 on scale A. For rapid multiplication and division it is merely necessary to work on the above principles, and get constant practice; it is just a mechanical operation.

As to scales C and D, these are merely larger editions of half of scales A and B, as will be seen by inspection, and can be used in the same way and for the same purpose, with the necessary modifications that the position of the scales are reversed, and that more frequent movement of the slide may be required. Combined multiplication and division can be carried out, doing first one operation and then the other, and so on, taking no notice of any results given until the final operation is completed. In such a case a beginner is often puzzled to determine where the decimal point should be placed, or how many digits there should be in the answer. By far the simplest way to determine this is bv a rough cancellation which can frequently be done mentally, also a check should be taken on this by applying common sense as to whether the result appears correct so far as regards the decimal place or the number of digits.

From the simple operation of multiplication and division it is easy to pass on to those of finding square and cube roots, also other roots, squares and cubes of any number, sizes, tangents, and logarithms, but for such details the reader is referred to text books on the slide rule. Those who use slide rules much, finally become so expert and at home with them that they can scarcely bring themselves to ever use ordinary pencil and paper methods.