To maintain simplicity of measurement notation, and to obviate the making of two girths of the same dimensions, several methods are adopted that may be termed irregular. One of these systems has a difference of 1/8 in. between the joint-girths of the 6, 7, 8, and 9; in. between the 10, 11, 12, and 13 ; and 1/4 in. between the 1, 2, 3, 4, 5, 6, 7, and 8. The instep-girths in this scale increase 3/16 in. between the 6's and l's, and 1/4 in. between the l's and 8's. The best method upon this principle is to make a difference in joint-girth of 3/16 in. from size 1 (4 1/3 in.) to size 10 (7 1/3 in.) and 1/4 in. for the rest of the scale for males, and 3/16 in. from size 1 (4 1/3 in.) to size 1 (8| in.) for females. The scale is given below with tread and seat measurements :Male Scale (3 fitt.).

 Sizes. Joint. Instep. Tread. Seat. 1 ............... 4 9/16........ 4 21/22 1 3/4 1 3/16 2 ............... 4 3/4 4 27/32 ......... 1 13/16 ......... 1 1/4 3 ............... 4 15/16 5 1/32. 1 7/8 1 5/16 4 ............... 5 1/8 5 7/32 ......... 1 15/16 1 3/8 5 ............... 5 5/16 5 13/32 ......... 2 ......... 1 7/16 6 ............... 5 1/2 5 19/32 2 1/12 ......... 1 1/2 7 ............... 5 11/16 ......... 5 7/8 ......... 2 1/6 ......... 1 9/16 8 ............... 5 7/8 ......... 6 1/16 ......... 2 1/4 ......... 1 5/8 9 ............... 6 1/16 ......... 6 1/4 ......... 2 1/3 1 11/16 10 ............... 6 1/4 ......... 6 7/16 ......... 2 5/12......... 1 3/4 11 ............... 6 1/2 ......... 6 25/32 ......... 2 1/2 ......... 1 13/16 12 ............... 6 3/4 ......... 7 1/32 2 7/12 1 7/8 13 ............... 7 ......... 7 9/32 2 2/3 ......... 1 15/16 1 ............... 7 1/4 ......... 7 17/32 ......... 2 3/4 2 2 ............... 7 1/2 7 25/32 ......... 2 5/6 2 1/16 3 ............... 7 3/4 ......... 8 1/32 ......... 2 1l/16 2 1/8 4 ............... 8 ......... 8 9/32 3 ......... 2 3/16 5 ............... 8 1/4 ......... 8 17/32 ......... 3 1/12 ......... 2 1/4 6 ............... 8 1/2 ......... 8 7/8 ......... 3 1/6 ......... 2 5/16 7 ............... 8 3/4 ......... 91/6 ......... 3 1/4 ......... 2 3/8 8 ............... 9 ......... 9 3/8 ......... 3 1/3 ......... 2 7/16 9 ............... 9 1/4 ......... 9 5/8 ......... 3 5/12 ......... 2 1/2 10 ............... 9 1/2 ......... 9 7/8 ......... 3 1/2 ......... 2 9/16

Female Scale (3 fitt).

 Sizes. Joint. Instep. Tread. Seat. 1 ............... 4 9/16 ......... 4 11/16 ......... 1 3/4 ......... 1 5/16 2 ............... 4 3/4 ......... 4 7/8 ......... 1 13/16 ......... 1 23/54 3 .............. 4 15/16 ......... 5 1/16 1 7/8 ......... 1 13/32 4 ............... 5 1/8 ......... 5 1/4 ......... 1 15/16 ......... 1 29/64 5 .............. 5 5/16 ......... 5 7/16 2 ......... 1 1/2 6 ............... 5 1/2 5 5/8 ......... 2 1/16 ......... 1 35/64 7 .............. 5 11/16 5 15/16 ......... 2 1/8 ......... 1 19/32 8 ............... 5 7/8 ......... 6 1/8 ......... 2 3/16 ......... 1 41/64 9 ................. 6 1/16 ......... 6 5/16 ......... 2 1/4 ......... 1 11/16 10 ............... 6 1/4 ......... 6 1/2 ......... 2 5/16 ......... 1 47/64 11 ............... 6 7/16 ......... 6 13/16 ......... 2 3/8 ......... 1 25/32 12 ............... 6 5/8 ......... 7 ......... 2 7/16 ......... 1 53/64

Female Scale (3 fitt.)-(continued).

 Sizes. Joint. Instep. Tread. Seat. 13 ............... 6 13/16 ......... 73 2 1/2 ......... 1 7/8 1 ............... 7 ......... 73 2 9/16 ......... 1 59/64 2 ............... 7 1/4 ......... 7 3/4 ......... 95 1 31/32 3 ............... 7| ......... 8 ......... 2 11/16 ......... 2 1/64 4 ............... 7 3/4 ......... 8 1/4 ......... 2 3/4 ......... 2 1/16' 5 ............... 8 ......... 8 1/2 ......... 2 13/16 ......... 97 6G ............... 8 1/4 ......... 8 3/4 ......... 2 7/8 ......... 95 7 ............... 8 1/2 ......... 9 ......... 2 15/16 ......... 913

The American Standard Measurements are recognized throughout the American last industry. The fittings are lettered instead of numbered. Below is the standard size 7's and 10's men's in three widths, C, D, and E.

 Size. Ball. Instep. Long-heel. Bottom. Width C ......... 7 ...... 8 4/8 ...... 9 ..... 12 2/8 ...... 3 ,, 10 ...... 9 2/8 ...... 9 6/8 ..... . 13 ...... 3 6/64 Width D ......... 7 ...... 8 6/8 ...... 9 2/8 ..... 12 4/8 ...... 3 2/24 ,, 10 ...... 9 4/8 10 ..... 13 2/8 ...... 3 8/24 Width E ......... 7 ...... 9 ...... 9 4/8 ..... 12 6/8 ...... 3 4/24 ,, 10 ...... 9 6/8 ...... 10 2/8 ..... . 13 4/8 ...... 3 10/24

The Ninth System of arranging the measurements is a good one, as there are no "breaks" in the gradation, and the girths are suitable for the foot's development. The standard from which the measures are taken is ladies' size 4, and for the joints and insteps would be as follows: -

 1 fitt. 2 fitt. 3 fitt. 4 fitt. 5 fitt. 6 fitt Joints 7 1/9 ...... 7 2/3 ...... 7 8/9 ...... 8 1/9 ...... 8 1/3 ...... 8 5/9 Instep 8 1/9 ...... 8 2/9 ...... 8 3/9 ...... 8 4/9 ...... 8 5/9 ...... 8 2/3

A difference of 2/9 in. is made between size and size and fitting and fitting for the joint and instep measurement. This arrangement would give the rises for the different fittings suitable to the requirements of the foot, being 6/9 in. in the one fitting and 1/9 in. in the six fitting. Its objection is that it gives the same rise for adults and infants.

Alden's Method of arranging the measurements is a practicable one, and consists in establishing a standard measure of girths that has been found by experience to be suitable and correct This is taken as size 8's in men's and 4's in women's, and would be 91/8 joints and 91/2 instep for the men's, and 77/8 joints and 81/4 instep for the women's. At the other end of the scale about to be made, another measurement, that experience has found to be correct, is selected, and the intermediate difference between the respective girths is subdivided into as many equal parts as there are sizes intervening. This latter part of the system is highly approved, as it obviates the expression of fractions, that would be difficult to practicably utilize, while at the same time the accuracy of the sub-division is maintained. The system will be illustrated by reference to the production of a women's and girls' scale.

The women's standard is size 4, the length of which is 9| in. One-half this length is size 21/2 (415/18 in.), and this is the other smaller standard selected Joints. Instep. Tread.

Women's, size 4 ......... 77/8 ......... 81/4 ......... 23/4

Children's, size 21/2 ......... 413/16 ......... 5 ......... 125/32

To obtain the intermediate sizes the differences between these two extremes is divided into 141/2, the number of sizes between 21/2 and 4. To complete the scale of fittings, 9/32 is added to the adult joints for the larger fittings, and one-half this, i.e. 9/64 for the child's. To obtain the insteps, 7/32 is added to the adult, and one-half this, i.e. to infants'. The adult tread is increased by 2/16 in. for each fitting larger, and one-half 2/32, for infants' bottom-widths.

Alden's Scale.

 Fitt. 1. Fitt. 2. Fitt. 3. Fitt. 4. Fitt. 5. Difference. Children's 21/2, joint-girth .. 4 34/64 4 43/64 4 52/64 4 61/64 5 6/64 9/64 „ 21/2, instep-girth. 4 50/84 4 57/64 5 5 7/64 5 14/64 7/64 „ 21/2 rise 16/64 14/64 12/14 10/64 8/64 2/64 „ 2.1, tread-width. 1 21/32 1 23/32 1 25/32 1 27/32 1 29/32 2/32 Women's 4, joint-girth 7 10/32 7 /19/32 7 28/32 8 5/32 8 14/32 9/32 „ 4, instep-girth . 7 26/32 8 1/32 8 8/32 8 15/32 8 22/32 7/32 „ 4, rise 16/32 14/32 12/32 10/32 8/32 2/32 „ 4, tread-width . 2 1/2 2 5/8 2 3/4 2 7/8 3 1/8

To construct the completion of the scales it is necessary to subdivide the various measurements, which may be done as follows: - Draw a line AB (Fig. 58), and upon it mark as many sizes (1/3 in.) as there are intervening between the extremes. In this case there are 14 1/2, numbered 21/2 to 4. Through each of these divisions erect perpendicular lines, and make the two extremes, 21/2 and 4, measure respectively 125/32| and 23/4, if the tread-widths were being obtained. Connect these two points (125/32 and 2|, Fig. 58) by a straight line, and where it crosses the several perpendicular lines it will give the widths for all the sizes, measured from the line AB.

The joint, instep, and widths are marked on a slip of paper, a separate strip being used for each fitting.

An Improved Scale of Measurements is drawn on the front piece, side by side with English and French length-measures. They are arranged for lasts to make medium-substance goods upon, and should be increased or decreased by 1/9 in. for stouter and lighter work respectively for girth-measurements, and 1/18 in. for bottom-widths. The scale contains all the vital principles of a correct scale, and has an advantage of expressed dimensions. It is given in six fittings, and the outside measurements are for size 1 (41/3 in. length) and size 4 (9f in. length), thus giving sixteen sizes between.

Scale of Measurements for Lasts (Medium Work).

Joints.

 Fittings. Size 1. Size 4. Total difference. Difference per size. 0 4 7 1/18 3 1/18 55/288 1 4 3/18 7 1/3 3 3/18 57/288 2 4 3/9 7 11/18 3 5/18 59/288 3 4 1/2 7 8/9 3 7/18 61/288 4 4 2/3 8 1/6 3 1/2 63/388 5 4 5/6 8 1/9 3 11/18 65/388 6 5 8 13/18 3 13/18 67/388 Increase 3/18 5/18 1/18 1/144

Bottom- Widths.

 Fittings. Size 1. Size 4. Total difference. Difference per size 0 1 19/36 2 17/36 17/18 17/288 1 1 12/36 2 21/36 1 18/288 2 1 23/36 2 25/36 1 1/18 19/283 3 1 25/36 2 29/36 1 1/9 20/288 4 1 27/36 2 33/36 1 3/18 21/288 5 1 29/36 3 1/36 1 2/9 22/288 6 1 31/36 3 5/36 1 5/18 23/288 Increase 1/18 1/9 1/18 1/288

Insteps.

 Fittings. Size 1. Rise over joint. Size 4. Rise over joint. Difference between the girths. Difference per size. Rise increase per size. 0 4 7/18 7/18 7 15/18 7/9 3 4/9 31/146 7/288 1 4 1/2 3/9 8 6/9 3 1/2 63/288 3/144 2 4 11/18 5/18 8 3/18 5/9 3 5/9 32/144 5/288 3 4 13/18 2/9 8 3/9 4/9 3 11/18 65/288 2/144 4 4 15/18 3/18 8 1/2 3/9 3 6/9 33/144 3/288 5 4 17/18 1/9 8 6/9 2/91/9 3 13/18 67/288 1/144 6 5 1/18 1/18 8 15/18 3 7/9 34/144 1/288 Increase 1/9 1/18 1/6 1/9 1/18 1/288 1/288

Seats.

 Fittings. Size 1. Size 4. Difference between seats. Difference per size. 0 1 13/72 1 3/36 49/72 12 1/4/288 1 1 2/9 1 17/18 13/18l 13/288 2 1 19/72 2 1/36 55/72 13 3/4/288 3 1 11/36 2 1/9 29/36 14 1/2/288 4 1 25/72 2 7/36 61/72 15 1/4/288 5 1 7/16 2 5/18 8/9 16/288 6 1 31/72 2 13/36 67/72 16 3/4/288 Increase 3/72 3/36 3/72 3/4/288