A HISTORY OF SCIENCE 



matics; but in 1766 he returned to St. Petersburg. 

 Towards the close of his life he became virtually blind, 

 being obliged to dictate his thoughts, sometimes to 

 persons entirely ignorant of the subject in hand. 

 Nevertheless, his remarkable memory, still further 

 heightened by his blindness, enabled him to carry out 

 the elaborate computations frequently involved. 



Euler 's first memoir, transmitted to the Academy of 

 Sciences of Paris in 1747, was on the planetary per- 

 turbations. This memoir carried off the prize that 

 had been offered for the analytical theory of the mo- 

 tions of Jupiter and Saturn. Other memoirs followed, 

 one in 1749 and another in 1750, with further expan- 

 sions of the same subject. As some slight errors were 

 found in these, such as a mistake in some of the for- 

 mulas expressing the secular and periodic inequalities, 

 the academy proposed the same subject for the prize 

 of 1752. Euler again competed, and won this prize 

 also. The contents of this memoir laid the founda- 

 tion for the subsequent demonstration of the perma- 

 nent stability of the planetary system by Laplace and 

 Lagrange. 



It was Euler also who demonstrated that within 

 certain fixed limits the eccentricities and places of the 

 aphelia of Saturn and Jupiter are subject to constant 

 variation, and he calculated that after a lapse of about 

 thirty thousand years the elements of the orbits of 

 these two planets recover their original values. 



