Grading other Sizes and Fittings of sole-shapes may be done in one or two systems, and by machine. The shifting systems for a short range of sizes or fittings are very simple, but in the hands of an inexperienced person, the waists of the fittings are out of true proportion. The radial system produces grades, in the ratio that the several widths are to the length, and this is not what is required to suit the grade of the widths.

Fig. 71. Fig. 72.

The Pass-May System of grading Fittings is illustrated in Fig. 73, where AB is the length-line, and CD the tread, and EF the seat-line. The amount of grade is decided upon for the tread (see table, p. 78), say it is in. for each fitting. Following, strictly, this system, it is said one-eighteenth is required for the seat, the location from the point B being one-sixth of the entire length, and one-half of the tread location; therefore one-half the grade of the tread is advocated.*

The tread location is one-third of AB; therefore, if the grade used for fittings at the tread is 1/9 in., three times this amount, viz. 1/3 in., will be required to be used at the end B, so that, when shifting out to get the line from the toe A to D, or A to C, the required grade, 1/9 in., may be obtained at CD. Adhering to the system, it is advocated that one-half of this, viz. 1/6 in., is to be placed on both sides of AB, at point B. This will give ab.

This amount is repeated at point A, and cd is indicated - this will give the seat-grade as 1/18 in.

* This, however, is not correct. The ratio of EF to CD in width is what governs the grade; and suppose EF were made three-fourths of CD, then three-fourths of the grade added to CD would be required for EF.

It should be noted this would only be correct when the shape graded has one-half of the tread-line equidistant of the central line AB; otherwise the amount (in this case 1/3 in.) should be divided in the same proportion as the tread, and placed with the larger portion of the grade towards b, and the lesser towards a, so that the tread may be increased in correct proportion.

Fig. 73.

(If the correct proportion of the seat-grade is required, the grade should be multiplied by the ratio of the location of the seat to the whole length, and this product equally divided one moiety, being placed on each side of A.)

To obtain the curve at seat FB, for the fitting larger, place directly over the marked-out shape (Fig. 73) the cut-out shape, so that the lines of tread, seat, and length of both the pattern and tracing coincide. When in this position, move the central line on the pattern towards d, keeping B of pattern and tracing level. Mark from F to B. Next return the central line of pattern to the line AB of traciug, and move the pattern towards c, so that the central line of pattern and c coincides, while the point B on the pattern and tracing remain together. Trace EB, and the seat of a fitting larger than the pattern will be outlined. To obtain the curves AD and AC, place the pattern over the tracing so that length, tread, and seat-lines of the pattern and tracing are identical in position. Move B on the pattern (while keeping A in place) towards b, and mark the curve from A to D. Return the pattern at B, from b to a - keeping A of pattern directly over A of tracing - and mark the curve from A to C. To construct the waist-curve on this system, place the pattern and tracing level at tread and seat-lines, and then move the waist-curve, for the outside waist, towards DF, and trace the outline. This repeated for the other side gives the inside waist-curve CE.

A System of Grading, to be accurate, should not only give the total grade at a width, but should divide it in the same proportion as the ratio of the inside and outside of the pattern, so that the original proportion and shape may be preserved throughout the series. A system that answers to these requirements (based upon the principle shown in Fig. 70) is illustrated in Fig. 74. The principle of scaling fittings and sizes consists of adding the required grade in the same proportions and locations as existing in the original; and the test of the accuracy of this principle lies in the fact that independently constructed fittings and sizes will be the same as those scaled.

## Application

The main lines - length, tread, seat, waist, and toe - are extended on the tracing of the original shape to be graded. Then - preferably by means of a proportional compass - the increases or grades are divided and placed on the extended line. To do this, take the compasses, and span with the long leg the whole width of, say, the tread; and then adjust the nut by trial, until the small legs exactly span, say, the inside half of the tread. This will give the ratio of tT (Fig. 74) to the whole tread-width iK. The screw of the proportional compass will now be tightly fixed, and if the original shape be constructed upon the system illustrated in Fig. 70, the ratio will be tT equals four-ninths of tX. (Fig. 74). Without readjusting the compass, span with the long legs the whole distance of the tread-width about to be graded, and with the small legs from T (Fig. 74) mark the inside-joint position t' of a fitting larger. Keeping the same distance in the compass, with the long legs place one point on the newly marked point t', and in the direction of the outside joint mark the full width of the fitting greater, and thus indicate the outside joint X'. If not working to a scale of measurements for seat-width, the grade of this line may be obtained by again setting the proportional compasses so that in the long legs the whole width of the original tread is spanned, while the smaller legs span the original seat (or more easily applied, half the seat). Then, while the compasses are at this ratio, span with the long legs the whole tread of the new fitting to be constructed, and the small legs will give the whole seat of the new fitting (or if the half-seat was spanned in the original, the half-seat of the new fitting will be obtained, and can be marked both sides of S, thus saving the division). If working to a scale of seat-widths, the measure may be transferred direct.

Fig. 74. Shewing Fittings O T0 6 Graded With The 0.3, And 6 Outlined N0. 1t Oe.

To obtain the waist, or any other part, proceed in the same way. For instance, span in the long legs half the seat sS (Fig. 74), and with the short legs the distance of the width Ww. Then fix the nut of the compass. With the compass in this ratio, span with the long legs the new half-seat measure, and the short legs will indicate, measured from W, the inside half of the new waist measure. In the Fig. 74 the shapes of No. 1 toe have been outlined for 0, 3, and 6 fittings, showing the method of obtaining the same shape by grade and construction.