Thus if T is expressed as a quadratic function of U, V, W, P, Q, R, the components of momentum corresponding are dT dT dT (I) = dU + x2=dV, x3 =dW, dT dT dT Yi dp' dQ' y3=dR; but when it is expressed as a quadratic function of xi, 'x2, x3, yi, Y2, Y3, U = d, V= dx, ' w= ax dT Q_ dT dT dy 1 dy2 dy The second system of expression was chosen by Clebsch and adopted by Halphen in his Fonctions elliptiques; and thence the dynamical equations follow X = dt x2 dy +x3 d Y = ..., Z ..., (3) = dt1 -y2?y - '2dx3+x3 ' M =..
See also with reference to this text Louis Halphen, Etude sur les chroniques des comtes d'Anjou et des seigneurs d'Amboise (Paris, 1906).
The above may he supplemented by some valuable annals published by Louis Halphen, Recueil d'annales angevines et vendomoises (Paris, 1903), (in the series Collection de textes pour servir a l'etude et a l'enseignement de l'histoire).
1276 -1310, and the book of Louis Halphen mentioned below.
The 11th century only has been treated in detail by Louis Halphen, in Le Comte d'Anjou au XP siecle (Paris, 1906), which has a preface with bibliography and an introduction dealing with the history of Anjou in the 10th century.
See Louis Halphen, Le Comte' d'Anjou au XI e siecle (Paris, 1906).
See Louis Halphen, Le Comte d'Anjou au XI' siecle (Paris, 1906).