208 Miscellanies. 



" For the ordinary purposes of mensuration, the circumference 

 will be determined with sufficient precision by multiplying the diam- 

 eter by twenty-two and dividing the product by seven, which is the 

 approximation discovered by Archimedes."* 



To the popular reader it may be interesting to know that the Dif- 

 ferential and Integral Calculus, teach the analytical methods of pro- 

 ceeding in the pure mathematics, analogous to Algebra, the calcula- 

 tions are divided into constant and variable quantities, in place of the 

 known and unknown quantities of Algebra. The differential calcu- 

 lus determines the effect produced by a given cause ; the integral 

 shows how to determine the cause which produced a known effect." 

 The calculations proceed by methods and expressions similar to the 

 algebraical notations and processes. 



It is the author's aim to furnish the scholar with a complete view of 

 modern analytical science, and to free this higher order of mathemat- 

 ical research from the contradictory theories, and exceptionable prin- 

 ciples, which have pervaded every preceding book on the Calculus, 

 harassing and obstructing the progress of the student, and discourag- 

 ing him with inconsistencies. 



It is believed that the author has succeeded in perfecting " this 

 most powerful instrument which the modern analysis places in the 

 hands of the mathematician," and the student may be cheered by the 

 guide thus afforded him, amidst the difficulties of a laborious but sub- 

 lime and elevating career of enquiry. 

 New Yprk, August, 1833. 



22. On the Cashmere-Angora Shawl Goat. 



TO PROFESSOK SILLIMAN. 



Dear Sir — Many attempts have been made in Europe, to domes- 

 ticate the Cashmere goat, "the down" of that animal being the ma- 

 terial from which are fabricated the most beautiful and costly shawls 

 that are brought from the East. This down is considered the most 

 precious and "the most beautiful filaceous material known," com- 

 bining the fineness and softness of down, and the warmth of wool, 

 with the lustre of silk. 



The following facts are derived principally from the Transactions 

 of the (British) " Society for the Encouragement of Arts, Manu- 

 factures, and Commerce," for 1831-32. 



* See p. 140 Elem. Geom. 



