This is about how to calculate the recipes for each of the glazes in a line blend. See here for the practicalities of making a line blend.

Suppose we have two glazes, *A* and *B*, and we want to make a line blend between them consisting of a certain number of glazes, which we’ll call *n*. How do we calculate the percentage of a material in a given glaze in the line blend?

To keep things simple, we’ll first assume that the batches of *A* and *B* have the same weight. We’ll label the glazes in the line blend using the index *i*, where *i* = 0 corresponds to *A*, and *i* = *n* - 1 corresponds to *B*. The table below shows the relative proportions into which *A* and *B* are divided.

So the *i*-th glaze consists of *n* - 1 - *i* parts *A* and *i* parts *B*. To convert this to a percentage, we need to divide by *n* - 1 - *i* + *i* = *n* - 1 and multiply by 100%. Therefore the *i*-th glaze consists of (*n* - 1 - *i*) / (*n* - 1) 100% *A* and *i* / (*n* - 1) 100% *B*, so if *P*_{A} is the percent of a material in recipe *A*, and *P*_{B} is the percent of the same material in recipe *B*, the percent of that material in the *i*-th glaze is

(*n* - 1 - *i*) / (*n* - 1) *P*_{A} + *i* / (*n* - 1) *P*_{B} = [(*n* - 1 - *i*) *P*_{A} + *i* *P*_{B}] / (*n* - 1)

Now suppose that the weights of two batches are not necessarily equal, and have relative weights *W*_{A} and *W*_{B}. The table of relative proportions now looks as follows:

Therefore the *i*-th glaze consists of (*n* - 1 - *i*)*W*_{A} parts *A* and *i* *W*_{B} parts *B*, and to convert this to a percentage, we need to divide by (*n* - 1 - *i*)*W*_{A} + *i* *W*_{B} and multiply by 100%