SEQUEL TO THE GENERALIZATION. Ill 



that every body had three axes which were called 

 Principal Axes, about which alone (in general) it 

 would permanently revolve. The equations which 

 Euler and other writers had obtained, were at- 

 tacked as erroneous by Landen in the Philosophical 

 Transactions for 1 785 ; but I think it is impossible 

 to consider this criticism otherwise than as an 

 example of the inability of the English mathema- 

 ticians of that period to take a steady hold of the 

 analytical generalizations to which the great conti- 

 nental authors had been led. Perhaps one of the 

 most remarkable calculations of the motion of a 

 rigid body is that which Lagrange performed with 

 regard to the Moons Libration ; and by which he 

 showed that the Nodes of the Moon's Equator and 

 those of her Orbit must always coincide. 



10. Vibrating Strings. Other mechanical ques- 

 tions, unconnected with astronomy, were also pur- 

 sued with great zeal and success. Among these 

 was the problem of a vibrating string, stretched 

 between two fixed points. There is not much 

 complexity in the mechanical conceptions which 

 belong to this case, but considerable difficulty in 

 reducing them to analysis. Taylor, in his Method 

 of Increments, published in 1716, had annexed to 

 his work a solution of this problem; obtained on 

 suppositions, limited indeed, but apparently con- 

 formable to the most common circumstances of 

 practice. John Bernoulli, in 1728, had also treated 

 the same problem. But it assumed an interest 



