[ARCHIBALD] MATHEMATICAL INSTRUCTION IN FRANCE 109 
departments of the faculty of science.' The instructors in French 
universities are of six classes. The chaires magistrales are held by 
professeurs titulaires; no less than eleven of these at the Sorbonne, are 
in the departments of mathematics. Then there are professeurs 
adjoints (of whom there may not be a number greater than one third 
of the chaires magistrales), chargés de cours, maitres de conférences, 
chargés de conférences and maitres de conférences adjoints. Just what 
scholastic status or state recognition is implied in these titles I shall 
consider later; but it may be remarked here that all professeurs, although 
theoretically appointed only till the age when the law requires them 
to be pensioned off, are in reality appointed for life. Those at the 
Sorbonne, at least, are known the world over, because of their eminence 
in research and exposition. Here are the names of the chaires, of the 
incumbents and of the courses offered during the past year:— 
Gone Ne sUperieurer à. in. or ON ee ae RONA Darboux. 
I Semester.—30 lectures of 1 hour. “Theory of triply orthogonal systems.” 
Largely as in the new edition of Darboux’s work on this subject and 
as in selected parts of his Théorie des Surfaces. 
2°—Analvse supérieure et algèbre supérieure................. Picard. 
II Semester.—30 lectures of 1 hour. ‘Determination of integrals of 
partial differential equations of the second order with various condi- 
tions as to limits.” 
3°—Calcul differentiel et calcul intégral. ......... ............Goursat. 
I and IT Semesters.—60 lectures of 70 minutes. This course is practically 
that given in Goursat’s Cours d’Analyse Mathématiques, Tomes I-II, 
new edition. 
4°_Applications de l’analyse à la géométrie................. Raffy 
I Semester.—30 lectures of 75 minutes. This course is a slight expansion of 
Raffy’s book on the subject. 
Je PN COMER ES donc HONS (ie MU LU LL 2 RL Use RE Te Borel 
I Semester.—15 lectures of 1 hour. The announced subject of this course 
was “Definite Integrals and some of their Applications,” but the 
treatment was more of series. 
6°—Astronomie mathématique et mécanique céleste.. ..... Poincaré. 
I Semester.—30 lectures of 1 hour. ‘‘Movement of the Celestial Bodies 
about their centre of Gravity.” 
Pa RULOnOMIe physique: WO mene, Lien AY CRE Sta Andoyer. 
II Semester.—30 lectures. 
8°—Physique mathématique et calcul de probabilités ... Boussinesq. 
I Semester.—30 lectures of 1 hour. “Mechanical Theory of Light.” 
II Semester.—30 lectures of 1 hour. ‘Reflection and refraction of a 
pencil of light at the limit common to two homogeneous media.” 

1 The total number of students at all the universities in France, in January 
1910, was 41,044 as compared with 52,456 in Germany. 
