( 38i ) 

 Par exemple, en posant comme ci-dessus 



U = wjr vz , V = uz wx , W = vx uy, 



on trouvera 



[S, U] = j[S, tv]-z[S, v] + w[S, y]-v[S, ], 



puis, en substituant successivement S les six variables' 



x, y, z, , v, w, 

 et ayant gard aux formules 



- 

 [ar, f]==o, [x, w] = o, [y, >] = o, [y, ]=o, [z, u] = o, [z, v}= o, 



[ar, m] = I , [y, v] sa 1 ! , [z, w] = i ; 



on obtiendra les quations 



[x, U] = o, O, U] = - z, [z, U] = j, 



[a, U] = o, [y, U] == ,, [w, O] a= y. 



On trouvera de mme 



[x, V] =. z, [y, V] = o, [z, V] = _ x, 



[, V] a w, (V, V] = o, [w, V] = u; 



et 



[x, W] == y, |>,W] = z, [z, W] = o, 



[u, W] = I, (V, W] = w, [V, W] = o. 



Enfin , si dans la formule 



[U, S] = j [w. S] - *[*>, S] + w [j, S] - [*, S] 



on remplace S par V, on trouvera 



[U, V] = VX - ujr = W, 





et l'on tablira de la mme manire chacune des trois quations 



[V, W] = U, [W, U]=V, [U, V] = W. 



C. li., ii*4o, a SemeUre. (T. XI, N9.) 52 



