AN AUTOBIOGKAPHICAL SKETCH. 281 



known methods I had gradually to hand over -to the 

 pupils in my laboratory, and for my own part turn to 

 more difficult researches, where success was uncertain, 

 where general methods left the investigator in the 

 lurch, or where the method itself had to be worked 

 out. 



In those regions also which come nearer the boun- 

 daries of our knowledge I have succeeded in many 

 things experimental and mechanical I do not know if 

 I may add philosophical. In respect of the former, 

 like any one who has attacked many experimental 

 problems, I had become a person of experience, who was 

 acquainted with many plans and devices, and I had 

 changed my youthful habit of considering things geo- 

 metrically into a kind of mechanical mode of view. I 

 felt, intuitively as it were, how strains and stresses 

 were distributed in any mechanical arrangement, a 

 faculty also met with in experienced mechanicians and 

 machine constructors. But I had the advantage over 

 them of being able to make complicated and specially 

 important relations perspicuous, by means of theoretical 

 analysis. 



I have also been in a position to solve several 

 mathematical physical problems, and some, indeed, on 

 which the great mathematicians, since the time of Euler, 

 had in vain occupied themselves ; for example, questions 

 as to vortex motion and the discontinuity of motion in 



