66 ALEXANDER VON HUMBOLDT. 



and may with propriety be inserted here, although somewhat 

 interrupting the chronological order of events : 



' I am greatly indebted to you for your letter to Kastner. 

 Your kindness makes me fear that you may have excited in 

 him higher expectations than I with my limited attainments 

 and slender abilities can possibly fulfil. Kastner has invariably 

 received me with the greatest kindness. I have visited him 

 repeatedly, and I find his society most instructive. Who could 

 take offence at externals in a man so truly great ? 



' As I am destined to serve my country in various branches 

 of political economy, I can only follow mathematics as an 

 auxiliary science. Unfortunately, the career I have adopted, 

 otherwise very attractive, requires an acquaintance with so 

 great a variety of subjects botany, mineralogy, chemistry, and 

 statistics among others that one is obliged to exert all one's 

 powers to attain even to something very mediocre. Yet the 

 study of mathematics, as well as that of mechanics, will ever 

 remain the true basis of political economy. How little, how- 

 ever, can mechanics accomplish without the aid of a higher 

 mode of analysis ! Whoever is but slightly acquainted with 

 the machinery used in various manufactures or in mines will 

 not fail to discover, as well from the want of certain contri- 

 vances as from the mode of their application, the value of 

 mathematics, and the mischief , that might be occasioned 

 through ignorance. Boulton's steam-engine and Holl's hy- 

 draulic press appear to me to be the best vindication of theo- 

 retical mechanics, if any were needed. From even the slight 

 acquaintance I have with mathematics, I can well believe how 

 important the study of this science must be to those engaged in 

 the consideration of political economy : all the time, therefore, 

 that I can spare from my numerous occupations I devote to 

 the study of mathematics, and particularly to the differential 

 calculus, in the use of which I feel myself very deficient. I 

 am now going diligently through Tempelhof, a work I had 

 commenced at Berlin. I continue also to prosecute machine 

 drawing and the invention of new constructions, and though I 

 am far from being vain enough to think that I shall ever arrive 

 at any new combination, yet I have found these exercises of 

 essential service in the close reasoning necessary to find the 



