1085543r
[Commentary:
This folio shows a shorter calculation (or rough work) for the sequences shown in Add MS
f.
of males in the fourth and fifth generations.
The left hand column begins with a population of 220, from which the sequence 1, 3, 6, ..., 63, 69, 73 is successively subtracted, while the sequence 63, 69, 73, 75, 75, 73, .... 15, 10, 6 is successively added, giving rise to the sequence 220, 282, 348, ..., 660, 670, 660, ....
The right hand column begins with a population of 715, from which the sequence 1, 4, 10, ..., 348, 415, 450 is successively subtracted, while the sequence 282, 348, 415, ..., 663, 660, ... is successively added, giving rise to the sequence 715, 996, 1340, ....
Harriot makes an error in this column, adding 633 instead of 670 after subtracting 165, but this is rectified in the rightmost column.]
The left hand column begins with a population of 220, from which the sequence 1, 3, 6, ..., 63, 69, 73 is successively subtracted, while the sequence 63, 69, 73, 75, 75, 73, .... 15, 10, 6 is successively added, giving rise to the sequence 220, 282, 348, ..., 660, 670, 660, ....
The right hand column begins with a population of 715, from which the sequence 1, 4, 10, ..., 348, 415, 450 is successively subtracted, while the sequence 282, 348, 415, ..., 663, 660, ... is successively added, giving rise to the sequence 715, 996, 1340, ....
Harriot makes an error in this column, adding 633 instead of 670 after subtracting 165, but this is rectified in the rightmost column.]