76 PHILOSOPHICAL TRANSACTIONS. [ANN0]684. 



tropics was ^ of the meridian circle, or 47-11° (Ptolemy's Magna Syntaxis), 

 which is only -%. of a second less than Ptolemy's. — But Eratosthenes's number, 

 according to Cleomedes, as derived by Riccioli, was 23° 46'. And the same, as 

 corrected by Riccioli, is 23° 3 1' 5". 



Hipparchus, anno 140, before Christ, has retained the obliquity of Eratos- 

 thenes, viz. 23° 51' ig" 31'". Yet the Chovaresmic tables, composed 830 years 

 after Christ, exhibit the canonic obliquity of the Alexandrians, according to a 

 Latin manuscript of D. Hatton, as 23° 51'. 



Pytheas Massiliensis, 324 years before Christ, in Riccioli, makes it 23° 52' 41*. 



ArJstarchus, anno 280, before Christ, by Savil's calculation, 23° 51' 20"; but 

 as deduced by Riccioli 23° 30'. 



Strabo, the geographer, anno 30, after Christ, makes it -^ of the circle, or 

 24°. And the same is stated by Geminus in Christ's time; by Tatius, by Pro- 

 clus, by the astrologers, according to Noddam the Arabian, by Abraham Abe- 

 nesdra, &c. But Noddam, the astronomer, who flourished about anno Dom. 

 1200, remarks that the obliquity was never observed greater than 24°, nor less 

 than 23° 33 ', though it continually decreases. 



CI. Ptolemy, anno 1 40, after Christ, having often tried it with his ring and 

 his table, always found it nearly the same with Eratosthenes, or 23° 5 1' 20"; 



cient mathematicians ; a specimen of which he printed in Greek and Latin ; he also drew up a synopsis 

 or view of the whole, afterwards published by Dr. Smith, entitled, Veterum Mathematicorum Grae- 

 corum, Latinorum, etArabum, Synopsis. In consequence of this plan, first enjoined by Sir Henry 

 Savilie, Dr. Halley published his edition of the works of Apollonius, and Dr. D. Gregory those of 

 Euclid. Mr. Bernard undertook also an edition of the Parva Syntaxis Alexandrina; in which, besides 

 Euclid, are contained the small treatises of Theodosius, Menelaus, Aristarchus, and Hipsicles; but 

 it was never published. In 1676 Mr. Bernard was sent to France as tutor to the Dukes of Grafton 

 and Northumberland, sons of King Charles the 2d, by the Duchess of Cleveland, who then lived 

 with her mother at Paris ; but the simplicity of his manners not suiting the gaiety of her family, he 

 soon returned to the pursuit of his studies at Oxford. In 1691, being presented to the rectory of 

 Brightwell in Berkshire, he quitted his professorship at^Oxford, in which he was succeeded by Dr. 

 David Gregory, from Edinburgh. 



Toward tlie latter end of his life, as often happens to studious men, he was much afflicted with the 

 stone ; yet notwithstanding this and other infirmities, he encountered another voyage to Holland to 

 attend the sale of Golius's manuscripts, as he had once before done at the sale of Heinsius's library. 

 On his return to England, he fell into a languishing consumption, which put a period to his life in Ja- 

 nuary 1696, in the 58th year of his age. 



Mr. Bernard seems to have been more distinguished by a talent for a laborious research among the 

 intricacies of old books and writings, than for clearness of perception or skill in composition. Besides 

 his works already mentioned, and two papers in the Philosophical Transactions, the one above printed 

 on the obliquity of the ecliptic, and a former on tlje places of 23 fixed stars, he was author of many 

 other compositions. As, 1. A Treatise on the Ancient Weights and Measures. 2. Chronologioe 

 Samaritanae Synopsis, &c, with many manuscripts left at his death. 



