There are several well-known methods of constructing a sole-shape, and they are based upon the theories that have been advocated from time to time as to the best form of shoe. Some of these ideas, advanced chiefly by medical men, have been tested, and in practice do not give the results that should be expected. This failure is often due to the fact that the ideal shape has been designed without taking into account the full action of the foot.

Sole-Shapes to follow Camper's Theory may be produced by equally dividing the bottom-width, or tread, on either side of a central line that passes through the seat-line, so that one-half of the seat-width is on each side. The toe is thus the same for both halves of the shape. It is the principle adopted for constructing sole-shapes for "straights." Fig. 64 is an illustration of a "rights and lefts " shape upon this plan.

Sole-Shapes upon Meyer's Principle are constructed with the inside line from joint to toe, coinciding with the line that comes from the inside point of the heel or seat (Fig. 65, AB). It makes a peculiar twisted form, that is usually very uncomfortable to wear if the boot or shoe has a heel.

It also tends to the production of corns on the small toe, and the- wrinkles that are formed in the upper leather, caused by the shape not conforming to the foot, abraise the upper surface of the toes. The illustration, Fig. 66, gives an idea of a sole-shape designed upon the Meyer theory applied to a foot.

Hannibal's System of constructing a sole-shape is a more practicable one than either Camper's or Meyer's. A central line is drawn, equal in length to the size to be designed (cd, Fig. 67). The width of the seat is equally divided, and a portion placed on each side of the length-line cd. Two lines are drawn, parallel to the length-line, through q and r (the seat-width), and the parallelogram opqr completed (Fig. 67). The centre of the line cd is obtained, and the line ah drawn. The line ss is situated one-sixth of the entire length from the heel end d. The positions of the outside and inside joint-line are obtained by measuring 1 in. and If in. respectively above cd. This is only for size sevens adults', and the other sizes are obtained from this data by the proportion (longitudinally) that these points are in relation to the length (see Fig. 69).

To ascertain the tread-width of the shape and its relation on either side of the line cd, the seat width is taken away from the tread, and the remainder divided into four equal parts, one-fourth being placed on the inside joint, and the remaining three-fourths on the outside joint. Through these points the shape has to pass, and the shape of the toe may be varied to suit the requirements of the case.

The Pass-May Method of designing a sole-shape is an extension of Hannibal's system, and the method furnishes particulars and proportions that enable a certain shape or shapes to be reproduced with a certain amount of exactness.

In Fig. 68 an illustration of a two-fitting insole-shape is given, constructed on this method. A line, AB, is drawn, equal in length to the size required, say women's fours, i.e. 92/3 in. long. Divide the seat-width into two equal parts, and mark a moiety each side, a, b. Through ab draw lines parallel to the central line AB. The line AB is next to be divided into six equal parts, and through the divisions thus made (1, 2, 3, 4, and 5) lines are drawn at right angles to the central line, and parallel to the lines ab and cd. The width of the seat is subtracted from the full width of the tread, and the difference divided into four equal parts (see Fig. 68, Nop). One of the divisions is now measured from the point indicated by the line that passes through 2, towards the left-hand, and marks the position on the inside joint (see W, Fig. 68).

Fig. 66.

Below point r on the line db mark (for size 4)

A in. Join Ww. On this slanting line, from W, mark off the full width of tread NP, and thus obtain K. Through R draw a line parallel to db. At a distance of 3/8 in. (for size 4) from R mark M. Divide equally 3 and 4, and draw waist-line, which is to be made three-fourths of the width of seat. One eighteenth of the length (or one-third of Al) is to he marked from A, and a line drawn across, also onetwenty-fourth of the length (or one-fourth of 5B) to be marked from B, and a line drawn. Join c and 1d, and where it crosses the one-eighteenth line mark ee. Join 5a and 5b, and mark ff. Divide Tt into two equal parts in point X, and S to be one-fourth of Tt. With dotted lines join KB, and where it passes the line through waist, mark Y; join WB, and where it crosses the line through 4, mark Z; and join AV, and where it cuts the line through 3, mark 0. To complete, join with a suitable curve the points A, e, S, R, M, X, H, 1/16 in. inside C, v, 1/16 in. insidef f, B, f1/16. inside V, Z, Y, 0, W, K, e, A.

Fig. 67.

Fig. 68. Ladies Fours Two Fitting Shape

How to obtain Proportions for other Sizes of such measurements as the 1 in. and 13/4 in. in Hannibal's method (Fig. 67), or -3/16 in. and § in. in the Pass-May method (Fig. 68), and any other arbitrary measure that is measured longitudinally. Draw a line AB (Fig. 69) equal in length to the size that the arbitrary measure is decided upon, and from A mark off the proportions - such as 1 in., 13/4 in. (Fig. 67), 3/16 in., and 3/8 in. (Fig. 68) - that it is required to ascertain in some other size. Let AC denote this. Now draw a line, AD (Fig. 69), equal in length to the size whose proportion is being sought. Join DB with a dotted line, and through C, parallel to DB, draw the line CE. The AE measured from A is the required proportion.

Fig. 69.

A System of Sole-Shape Construction, based upon the Principles illustrated in Fig. 60, will conclude the description of this section. It will also show how the various shaped toes that are usually called for may be produced upon a system.

Fig. 70 illustrates the construction of a shape for a women's size 4, fitting 2 (from the scale facing the title-page), and is given in Nos. 1, 2, and 3 toe for 11/2 in. heel. Data used. - (a) The line of contact moves forward - in. for each 1/2 in. elevation of the heel of the foot; (b) the line from the inside joint to the toe travels inwards towards the "line of muscular action" 1/9 in. for each 1/2 in. elevation of the heel of the foot;

(c) the seat is situated equally distant on either side of the central line XY;

(d) the waist is three-fourths of the seat,* and is proportioned either side of the line XY, one-third to inside, and two-thirds to outside of the waist; (e) the joint-width or tread is situated on either side of the line XY in the proportion of four-ninths of the entire width to the inside, and the remainder to the outside.

## To Construct

Make a line, XY, equal in length to the size required (say 9f in.). From X mark off the length allowance added over the foot (21/2 sizes), B, Fig. 70. From B measure two-sevenths of BY, and mark C. Divide BY into six equal portions, and from Y mark S.

The shape is for, say, 11/2 in. heel, therefore mark above 0 towards B the point T, allowing 1/18 in. for each 1/2 in. heel elevation, i.e. 3/18 To obtain W, the distance between TS is equally divided.

Fig. 70.

* This proportion varies in sewrounds, shooting-boots, etc., and must be modified to suit the kinds of work.

Through Y, S, W, T, and X draw lines at right angles to XY, and the position-lines will be obtained for seat, waist, and tread. The toe-line is found by taking a point midway between XT. The seat-width is equally divided, and one-half placed each side the line XY. Through ss' lines are drawn as far as the waist-line and parallel to XY. Four-ninths of the tread is measured from T to form the inside joint, and the remaining five-ninths from T to form the outside joint. Parallel to XY draw lines from the waist-line through t and t', as shown in the diagram, Fig. 70. One-third of the waist-measure is marked from W towards w, and the remaining two-thirds put from W towards id. One-third of the distance t'r is marked from t', and point 0 found. A dotted line, M, is drawn from 8 through t. From M is measured towards X 1/9- in. for each 1/2 in. of heel elevation (here 3/9 in.), and R marked. Join Rt.

To obtain the toes Nos. 1, 2, or 3, divide line XP in point *. Join t', and where it crosses the toe-line mark K. Divide line X* into three equal parts (1, 2, Fig. 70), and also XH into six equal parts, and number 1', 2', 3'. Join from 1 to K and from 2 to K, and through 1', 2', 3' draw lines parallel to XP, and where 1' crosses the line that is drawn from 1 to K it gives the point through which No. 1 toe will pass. Similarly, where the line 2' passes the line 2K is the point through which No. 2 toe will pass, and where 3' passes the line, *K will be the point for No. 3 toe to pass. To complete the shape, draw from X through either 1, 2, or 3 toe, towards t', and thence through 0 towards w'. Bending the curve inwards, it comes to point a', and then passes through Y. The other side of the shape is determined by continuing through s, w, t, and according to the shape toe finish at X.

Pointed or Square Toes are not always to be put on shapes because the foot is tapering or square respectively; but if the shape and last be suitably constructed in other respects the toe may be designed to suit the "fashion" without injury to the foot. In a pointed toe, for instance, if the toe is placed, not in the centre of the tread, but opposite the second toe, and the curves from this point on either side be gradual, a comfortable boot may be produced. Fig. 71 will give an illustration of this principle, and Fig. 72 show how the foot may remain uninjured by a pointed toe.