JOSEPH FOURIER. 145 



eiice, it imparted to scieutiflc studies quite a uew direction, wliicli Las 

 been i^roductive of the most important results. In supporting this 

 opinion at some length, I shall acquit myself of a task which Fourier 

 would certainly have imposed upon me, if he could have suspected that 

 with just and eloquent eulogiums of his character and his labors there 

 should mingle within the walls of this apartment, and even emanate 

 from the mouth of one of his successors, sharp critiques of his beloved 

 normal school. 



It is to the normal school that we must inevitably ascend if we would 

 desire to ascertain the earliest public teaching of descriptive geometry, 

 that fine creation of the genius of Monge. It is from this source that it 

 has passed almost without modification to the Polytechnic School, to 

 founderies, to manufactories, and the most humble workshops. 



The establishment of the ]Srormal School accordingly indicates the com- 

 mencement of a veritable revolution in the study of pure mathematics; 

 with it demonstrations, methods, and important theories, buried in 

 academical collections, appeared for the first time before the pupils, and 

 encouraged them to recast upon new bases the works destined for 

 instruction. 



With some rare exceptions, the philosophers engaged in the cultiva- 

 tion of science constituted formerly in France a class totally distinct 

 from that of the professors. By appointing the first geometers, the first 

 philosophers, and the first naturalists of the world to be professors, the 

 convention threw new luster u^^on the profession of teaching, the ad- 

 vantageous influence of which is felt in the present day. In the opinioa 

 of the public at large, a title which a Lagrange, a Laplace, a Monge, a 

 Berthollet, had borne, became a proper mat-ch to the finest titles. If 

 under the empire, the Polytechnic School counted among its active pro- 

 fessors councilors of state, ministers, and the president of the senate, 

 you must look for the explanation of this fact in the impulse given by 

 the Normal School. 



You see in the ancient great colleges professors concealed in some 

 degree behind their portfolios, reading as from a pulpit, amid the indif- 

 ference and inattention of their pupils, discourses prepared beforehand 

 with great labor, and which reappear every year in the same form. 

 Nothing of this kind existed at the Normal School ; oral lessons alone 

 were there permitted. The authorities even went so far as to require of 

 the illustrious savants appointed to the task of instruction the formal 

 promise never to recite any lectures which they might have learned b}^ 

 heart. From that time the chair has become a tribune where the pro- 

 fessor, identified, so to speak, with his audience, sees in their looks, 

 in their gestures, in their countenance, sometimes the necessity for pro- 

 ceeding at greater speed, sometimes, on the contrary, the necessity of 

 retracing his steps, of awakeuiag the attention by some incidental ob- 

 servations, of clothing in a new form the thought which, when first 

 expressed, had left some doubts in the minds of his audience. And do 

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