COLLEGE LIFE. 67 



means for accomplishing a certain end. I have often laughed 

 heartily with Fischer at the astonishment he evinced at the 

 first sight of my designs, and his subsequent dismay on finding 

 that, by the multiplicity of the combinations, power and weight 

 had been brought to bear on one and the same point, and had 

 thus become locked. 



6 But though I am compelled to renounce all claim to me- 

 chanical invention, I yet feel bound to acknowledge that I have 

 made a discovery in another branch of mathematics, which 

 (when is a young man ever dissatisfied with himself?) has 

 afforded me some amount of pleasure. But however pre- 

 sumptuous it may seem to commence a correspondence with 

 you, my esteemed friend, by a letter of such unusual length, I 

 am yet going to trespass so far upon your time as will suffice 

 for a preliminary explanation. The subject interests me so 

 deeply. In my limited labours in algebra I keenly felt on 

 one occasion the inconvenience in equations, where various 

 sums and factors occur, of not being able to arrive at the 

 precise value by means of logarithms. I thought over the 

 possibility of remedying this evil, and discovered two ways for 

 the accomplishment of my object either to reduce all the sums 

 and differences of two quantities into products, or to find a 

 new kind of logarithm, which might be made available either 

 for addition or subtraction.' 



Humboldt adds some additional particulars in regard to the 

 two methods, and begs his friend's permission to lay before 

 him, at some future time, a more complete statement of his 

 system of logarithms. Although neither method was com- 

 pletely successful in solving this problem, the solution of 

 which was accomplished by Grauss twenty years later, yet it is 

 evident from this communication that Alexander von Hum- 

 boldt had already gained a great insight into the principles of 

 mathematics, and had proposed to himself severer problems 

 than were to be expected from a student in political economy > 

 who was upon the point of entering only his second collegiate 

 term. 



The following letter to Wegener describes his journey to 

 Gottingen : 



' We left Berlin, I think, on the 10th of April. I spent five 



F 2 



