OF ARTS AND SCIENCES. 187 



Twenty-three years after the death of Laplace, Biot confided to the 

 Academy of Paris these interesting reminiscences of him. " Every 

 one," he says, " will understand how valuable to a young man were 

 these familiar and intimate interviews with a genius so powerful and 

 so comprehensive. But what he might not imagine were the senti- 

 ments of affectionate and paternal delicacy which attended them, 

 unless he himself had been the object of them. Shortly after I was 

 permitted to approach him, I had the good fortune to take a step, 

 which seemed to me new and unexpected, in a field of mathematics 

 hitherto scarcely invaded. In 1766, Euler had treated a peculiar class 

 of geometrical questions by an indirect method in a paper entitled JJe 

 inslgni promotione methodi tangentium inversce.* Subsequently, he 

 attacked a more difficult problem of the same kind, to which he re- 

 peatedly returned with different solutions, but always indirect. The 

 singularity of the problem originated in the nature of the curve, the 

 geometrical characters being of different orders, — some belonging 

 to points infinitely near, others to distant points separated by finite 

 differences. I succeeded in rendering a complete statement of the 

 problem in analytical language, applying to each part appropriate 

 symbols. The realization of this idea surpassed my expectations. f 



" After I had found the key to a solution of the problem, I spoke to 

 Laplace about it. He listened with attention and with some surprise, 

 and then said, ' It seems all very well ; come to-morrow morning 

 and bring your memoir ; I shall be glad to see it.' After hearing it, 

 discussing it, and suggesting certain omissions, he told me to present it 

 to the Academy the next day, and, after the session, come and dine 

 with him. 'Now,' said he, 'let us lunch.'" 



Biot communicated his paper to the Academy in the presence of 

 Monge, Lagrange, Laplace, and of Bonaparte who had just returned 

 from Egypt. Bonaparte pretended to recognize the diagrams, though 

 no one had ever seen them before except Laplace. " I had more fear 

 of Lagrange," said Biot, "than of Bonaparte, with all his military 

 glory." 



After Biot had read his paper, and received the congratulations of 

 the Academicians, he accompanied Laplace home. As soon as they 

 had entered the house, Laplace took Biot into his study, unlocked a 

 closet, took out a copy-book, yellow with age, and showed him all 



* Nov. Comment. Petrop., x. 



t Considerations sur les equations aux differences mdlfes j Mem. Saratlta 



Etrangeres, i 296-328. 



