42 DYNAMICAL PBINCIPLE. 



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 pre- 

 sently 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 contribu- 

 tions to physical and analytical science. In 1746, he gave his 

 Memoir on the general theory of Winds, which was crowned 

 by the Royal 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 produces; for he dis- 

 misses all other causes of aerial currents as too little depend- 

 ing upon any definite operation, or too much depending upon 

 various circumstances that furnish no precise data, to be 

 capable of analytical investigation. The Memoir consists of 

 three parts. In the first he calculates the oscillations caused 

 by the two heavenly bodies supposing them at rest, or the 

 earth at rest in respect of them. In the second, he investigates 

 their operation on the supposition of their motion. In the 

 third, he endeavours to trace the effects produced upon the 

 oscillations by terrestrial objects. The paper is closed with 

 ramarks upon the effects of temperature. The whole inquiry 

 is conducted with reference to the general dynamical prin- 

 ciple which he had so happily applied to the equilibrium and 

 pressure of fluids, in his first work upon that difficult subject. 

 In treating of Hydrodynamics, D'Alembert had found the 

 ordinary calculus insufficient, and was under the necessity of 

 making an important addition to its processes and its powers, 

 already so much extended by the great improvements which 

 Euler had introduced. This was rendered still more neces- 

 sary when, in 1746, he came to treat of the winds, and in the 

 following year when he handled the very difficult subject of 

 the vibration of cords, hitherto most imperfectly investigated 



