Lagrange's Memoirs. 67 



inconsistent with themselves : Lagrange so demonstrated. Lagrange 

 founded his new researches on the known laws of dynamics ; by 

 considering in the air only the particles found in a straight line, he 

 reduced this problem to that of vibrating cords, about which the 

 greatest geometers were divided ; he showed that their calculations 

 were insufficient to decide the question : he undertook a general so- 

 lution by an analysis as new as interesting, since it permits of resolv- 

 ing at once an indefinite number of equations, and since it extends 

 even upon discontinued functions : he established more firmly the 

 theory of the mixture of the simple and regular vibrations of D. 

 Bernouilli : he shows the limits between which this theory is exact, 

 and beyond which it is defective ; then he arrives to the construction 

 given by Euler, a true construction, although the author had arrived 

 to it only by calculations which were not sufficiently rigorous : he 

 answers objections raised by D'Alembert ; he demonstrates that 

 whatever figure we give to the cord, the duration of oscillations will 

 be always the same, a truth of which for experiment D'Alembert 

 had judged the demonstration very difficult or even impossible; he 

 passes to the propagation of sound; treats of simple and compound 

 echoes, of the mixture of sounds, of the possibility that they spread 

 in the same space without disturbing one another, and demonstrates 

 rigorously the generation of harmonical sounds ; he announces in fine, 

 that his object is to destroy the prejudices of those who still doubt if 

 mathematics could ever shed true light in physics. 



We have given the above extent to the extract of this memoir, be- 

 cause it is the first by which Lagrange became known. If its anal- 

 ysis is of the most transcendent kind, the object at least has some 

 thing in reality. It recalls names and facts, which are not foreign to 

 the greater part of the audience. We have done so, because it is 

 surprising that such had been the commencement of a young man. 

 He it was, that, seizing upon a subject treated by Newton, Taylor, 

 Bernoulli, D'Alembert and Euler, appeared suddenly in the midst of 

 these great geometers, as their equal ; as an umpire too, who, to put 

 an end to a difficult case, showed to each of them wherein he was 

 right and wherein he was wrong ; judged them, reformed them, 

 and gave to them the true solution, which they had seen faintly, 

 without being able to attain to it. 



Still, however, solid and well grounded as his calculations appear- 

 ed to him, the author avows that they render only an imperfect ac- 

 count of phenomena observed, so far as concerns the theory of wind 



