* 225, 226] Tobias Mayer 283 



Much more important, however, were his lunar theory 

 and the tables based on it. The intrinsic mathematical 

 interest of the problem of the motion of the moon, and its 

 practical importance for the determination of longitude, had 

 caused a great deal of attention to be given to the subject 

 by the astronomers of the i8th century. A funher stimulus 

 was also furnished by the prizes offered by the British 

 Government in 1713 for a method of finding the longitude 

 at sea, viz. 20,000 for a method reliable to within half 

 a degree, and smaller amounts for methods of less accuracy. 



All the great mathematicians of the period made attempts 

 at deducing the moon's motions from gravitational principles. 

 Mayer worked out a theory in accordance with methods 

 used by Euler (chapter XL, 233), but made a much more 

 liberal and also more skilful use of observations to determine 

 various numerical quantities, which pure theory gave either 

 not at all or with considerable uncertainty. He accordingly 

 succeeded in calculating tables of the moon (published with 

 those of the sun in 1753) which were a notable improve- 

 ment on those of any earlier writer. After making further 

 improvements, he sent them in 1755 to England. Bradley, 

 to whom the Admiralty submitted them for criticism, re- 

 ported favourably of their accuracy ; and a few years later, 

 after making some alterations in the tables on the basis of 

 his own observations, he recommended to the Admiralty a 

 longitude method based on their use which he estimated 

 to be in general capable of giving the longitude within 

 about half a degree. 



Before anything definite was done, Mayer died at the 

 early age of 39, leaving behind him a new set of tables, 

 which were also sent to England. Ultimately ,3,000 was 

 paid to his widow in 1765 ; and both his Theory of the 

 Moon * and his improved Solar and Lunar Tables were 

 published in 1770 at the expense of the Board of Longitude. 

 A later edition, improved by Bradley's former assistant 

 Charles Mason (1730-1787), appeared in 1787. 



A prize was also given to Euler for his theoretical work ; 

 while ,3,000 and subsequently 10,000 more were awarded 

 to John Harrison for improvements in the chronometer, 



* The title-page is dated 1767 ; but it is known not to have been 

 actually published till three years later. 



