Preface. vii 



of estimation ; the latter, to a certain extent, are 

 inevitable in the earliest (1166-8) case, and the 

 method, acceptable or otherwise, is set forth, but 

 as a modus, necessitated by the defect of contem- 

 porary evidences. 



A considerable amount of space is allotted to 

 tabular illustration, and, it is believed, that the 

 mere arithmetical results are free from conspicuous 

 errors, although no attempt has been made to 

 exactly determine long series of fractions ; nor can 

 pages, so largely concerned with mere figures, 

 attempt to compete in interest, for the general 

 reader, with theories, elaborated by verbal art, and 

 displayed in becoming detail. 



A Statistical Index, before the text (the former 

 perhaps also of service in demonstrating any too 

 condensed details of latter), recapitulates and 

 classifies some of the more important data, but 

 rarely repeats those given only in the Tables, 

 a list of which (arranged) precedes it : both, of 

 course, are for convenience of reference, etc., and 

 the former, owing to necessary brevity, does not 

 always quite convey the sense, more precisely given 

 in the pages alluded to. 



Some sort of apology may be esteemed neces- 

 sary in the presentation of pages mainly concerned 



