The abjad numerals assign each of the twenty-eight letters a value: the first nine letters of the inherited sequence run from one to nine, the next nine from ten to ninety, the next four from one hundred to four hundred, and the six letters Arabic added carry five hundred to one thousand. The system is called hisab al-jummal, and it was the ordinary way of writing numbers in Arabic before the decimal figures now used everywhere displaced it for arithmetic. It survives in dating, in the numbering of sections and verses in some manuscripts, in chronograms, where a phrase is composed so that its letters sum to a year, and in the letter speculation of a range of Sufi and occult writers.
There are two orders, and they do not agree. The eastern or Mashriqi reckoning, standard from Egypt eastward, is the one usually meant when the abjad is cited without qualification, and it is the one recorded here. The western or Maghribi reckoning, used across North Africa and in al-Andalus, assigns several letters different values: sad, fa, qaf, sin, dad, za, ghayn and shin all move. A chronogram composed in Fez and read in Baghdad therefore yields two different years.
This is not a disagreement to be resolved but two conventions that coexisted, each internally consistent and each attested over centuries. The practical consequence is that any numerical reading of an Arabic text has to state which reckoning it uses before it means anything, and a modern numerological claim that does not name its order has not said enough to be checked. The atlas records the eastern values on each letter and records the existence of the western order beside them.