SLIDING RULE, an instrument invented by the rev. William Oughtred, an English divine and mathematician, for the purpose of solving arithmetical problems mechani cally, consists of three pieces of wood, of which two are fastened together by-slips of brass at a sufficient distance from each other to permit of a third sliding between them. The size of instrument which best combines convenience with accuracy is one about 2 ft. long, 2 in. broad, and + in. thick. One side of the rule has the following scales marked on it in order: a line of tenths of in., of equal parts divided into tenths and hundredths of ft.; three lines of numbers, each line consisting of the numbers from 1 to 10 twice repeated; a line of sine thumbs (logarithmic sines of each quarter-point of the compass); a line of meridioual parts; and a line of equal parts. Of these, two of the linas of numbers are on the middle piece or slider. On the other side are—two lines of natural scales, including sines, secants, tangents, equal parts, etc.; two lines of logarith mic sines, two lines of logarithmic tangents, a third line of logarithmic sines, and a line of versed sines. Of these, one line of logarithmic eines and one of tangents are upon the slider. The scale in most common use is that of numbers, and it description of the way in which it is used will give a key to the whole working of the instrument. It is
necessary, however, to notice as a preliminary, that the scale of numbers is not evenly divi led, as in this case only addition and subtraction could be performed, but is divided in proportion, not to the numbers. but to their logarithms, so that 3, whose logarithm is very nearly the half of that of 10, stands almost half-way between 1 and 10; and similarly of the other numbers. All questions of numerical proportion can thus be easily worked by means of the line of numbers on the slider, and the adjacent and corresponding one on the fixed part of the rule. To find a fourth proportional to three given numbers, we place the first term (on the slider) opposite to the second term (on the fixed sealel, and opposite the third term (on the slider) is the fourth or number required (on the scale). Multiplication is performed by making 1 the first term of a proportion, and division by making it the second or third. The other scales marked on the rule are useful in the solution of trigonometrical, geographical, and nautical problems. and the results obtained are much more accurate than one at first sight would believe. Sliding rules of circular form have been made by the French, but they are not in any way preferable to the ordinary straight form.