400 D'ALEMBERT. 



strate directly many propositions which had never before 

 been satisfactorily investigated. It is equally unde- 

 niable that much remained after all his efforts incapable 

 of a complete solution, partly owing to the inherent 

 difficulties of the subject from our ignorance of the 

 internal structure and motions of fluids, and partly 

 owing to the imperfect state in which all our progress 

 in analytical science still has left us, the differential 

 equations to which our inquiries lead having, in very 

 many cases, been found to resist all the resources of 

 the integral calculus. 



This remark applies with still greater force to his 

 next work. In 1752, he published his Essay on a new 

 theory of the Resistance of Fluids. The great merit of 

 this admirable work is that it makes no assumption, 

 save one to which none can object, because it is in- 

 volved in every view which can well be taken of the 

 nature of a fluid ; namely, that it is a body composed 

 of very minute particles, separate from each other, and 

 capable of free motions in all directions. He applies 

 the general dynamical principle to the consideration of 

 resistance in all its views and relations, and he applies 

 the calculus to the solution of the various problems 

 with infinite skill. It is in this work that he makes 

 the most use of that refinement in the integral calculus 

 of which we shall presently have occasion to speak more 

 at large, as having first been applied by D'Alembert to 

 physical investigation, if it was not his own invention. 

 But the interval between 1744 and 1752 was not passed 

 without other important contributions to physical and 

 analytical science. In 1746, he gave his Memoir on 

 the general theory of Winds, which was crowned by 

 the Eoyal Academy of Berlin. The foundation of this 

 able and interesting inquiry is the influence of the sun 

 and moon upon the atmosphere, the aerial tides, as it 

 were, which the gravitation towards these bodies pro- 

 duces ; for he dismisses all other causes of aerial cur- 

 rents as too little depending upon any definite opera- 



