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'It should be mentioned that nowhere in the nearly 675 sheets relevant to these mer-parts does Harriot explain any step he takes.' (Pepper, 1968, 838)
For a detailed analysis of Harriot's tables of meridional parts and the supporting calculations, see the article quoted above:
Jon Pepper, 'Harriot's calculations of the meridional parts as logarithimic tangents', Archive for History of Exact Sciences, 4 (1968), 359–413.
The mapping presented here is based on Pepper's analysis but goes into greater detail, particularly under 'Spirals' and 'Direct calculations' .