Besides scales of the kind just described, which are termed plain divided scales, there are in common use what are known as diagonal scales, an illustration of one of which is shown in Fig. 118. The scale represented is that of 1 1/2 inches to the foot. The left-hand unit of division has been divided by means of the vertical lines into 12 equal parts, representing inches. In width the scale is divided into 8 equal parts by means of the parallel lines running its entire length. Next the diagonal lines are drawn, as shown.

Fig. 117. - Plain Scale (1 inch to the Foot)

By a moment's inspection it. will be seen that, by means of these diagonal lines, one-eighth of an inch and multiples thereof are shown on the several horizontal lines. A distance equal to the space from A to B, as marked on the scale, is read (first at the right for feet) 2 feet (then to the left for inches by means of the vertical lines figured both at top and bottom) 6 inches (and last, by means of the diagonal line, figured at the end of the scale, for fractions) and three-eighths. The top and bottom lines of the scale measure feet and inches only. The other horizontal lines measure feet, inches and fractions of an inch, each horizontal line having its own particular fraction, as shown. Such scales are frequently quite useful, as greater accuracy is obtained and, as the reader will sec, may be constructed by any one to any unit of measurement, and divided by the number of horizontal lines into any desired fractions.

Fig. 118. - Diagonal Scale (1 1/2 inches to the foot).

A scale in common use, and known as the triangular scale, is shown in Fig. 110. The shape of this scale, which is indicated by the name, and which is also shown in the cut, presents three sides for division. 13y dividing each of these through the center lengthways by a groove, as shown, six spaces for divisions are obtained, and by running the scales in pairs - that is, taking two scales, one of which is twice the size of the other, and commencing with the unit at opposite ends - the number of scales which may be put upon one of these instruments is increased to twelve. This article, which may be had in either boxwood, ivory or plated metal, and of 6, 12, 18 or 24 inches in length, is probably the most desirable for general use of any sold.

Fig. 119 - Triangular Boxwood Scale.

A flat scale is also manufactured in both boxwood and ivory. Fewer scales or divisions can be put upon it than upon the triangular scale, yet for certain purposes it is to be preferred to the latter. There are less divisions to perplex the eye in hunting out just what is required, and accordingly, there is less liability to error in its use. However, the limited number of scales which it contains greatly restricts its usefulness.

Fig. 120 shows another form of the flat scale, in quite common use in the past, but now virtually discarded in favor of more convenient dimensions and shapes. This scale combines with the various divisions of an inch the divisions of the protractor, as shown around the margin. The fact that the divisions of an inch for purposes of a scale are located in the middle of the instrument, away from the edge, which makes it necessary to take off all measurement with the dividers, renders the article awkward for use, and the arrangement of the divisions of the circle, on the margins, is less satisfactory for use than the circular protractor.

Fig. 120. - Flat Scale with Divisions of the Protractor on the Margins.