SEQUEL TO THE GENERALIZATION. 375 



problem of the precession; and in 1752, a memoir which, he entitled 

 Discovery of a New Principle of Mechanics, and which contains a 

 solution of the general problem of the alteration of rotary motion by 

 forces. D'Alembert noticed with disapprobation the assumption of 

 priority which this title implied, though allowing the merit of the 

 memoir. Various improvements were made in these solutions; but 

 the final form was given them by Euler ; and they were applied to a 

 o-reat variety of problems in his Theory of the Motion of Solid and 

 Rigid Bodies, which was written" about 1760, and published in 1765. 

 The formulae in this work were much simplified by the use of a dis- 

 covery of Seguer, that every body has 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 attacked as erroneous by Landen in the Philosophical Trans- 

 actions for 1785 ; but I think it is impossible to consider this criticism 

 otherwise than as an example of the inability of the English mathe- 

 maticians of that period to take a steady hold of the analytical general- 

 izations to which the great Continental 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 Moon's Libra- 

 tion ; 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 questions, unconnected 

 with astronomy, were also pursued 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, pub- 

 lished in 1716, had annexed to his work a solution of this problem; 

 obtained on suppositions, limited indeed, but apparently conformable 

 to the most common circumstances of practice. John Bernoulli, in 

 1728, had also treated the same problem. But it assumed an interest 

 altogether new, when, in 1747, D'Alembert published his views on the 

 subject ; in which he maintained that, instead of one kind of curve 

 only, there were an infinite number of different curves, which answered 

 the conditions of the question. The problem, thus put forward by 

 one great mathematician, was, as usual, taken up by the others, whose 

 names the reader is now so familiar with in such an association. In 



11 See the preface to the book. 



