last grading system introduced by USMC based on proportional differences between successive sizes, rather than fixed absolute increments as in arithmetic grading
US Patent 1,948,547
Applied March 15, 1930, Granted February 27, 1934
Heretofore it has been the custom to grade lasts and shoes arithmetically, that is, by equal increments per unit of increase in nominal length and width. These increments are, in size grading, ⅓ inch in length, as measured on the size-stick, and ¼ inch in perimeter at the ball, as measured by a tape around that part of the forepart known as the ball, per unit increase in length; and in width grading, ¼ in perimeter at the ball per unit increase in width.
the magnification factors necessary to produce [all lasts of a series] from one another in turn are not equal
shoes of the same nominal size but of different styles will fit differently
machine should be set differently for a long style than for a short when treating shoes other than the model size
By geometric grading is meant that successive members of a series of graded objects vary by a uniform percentage of a given characteristic, from one to another, instead of by a uniform absolute amount, from one to another.
the grading factors are constant for all styles
the large objects differ more from one another in absolute dimensions than do the small ones
Any one of the lasts shown can be regarded as a model…