First Principles of the Differential Calculus, §c. 269 
cle of M. Will’s concerning M. Reizet’s experiments upon the 
new method of estimating the nitrogen of organic bodies. M. 
Will has not been able to obtain an appreciable quantity of ni- 
trogen from the combustion of sugar and other organic substan- 
ces free from nitrogen. 
1.214 gram. sugar candy, burnt with the soda and lime, gave 
0.00086 gram. nitrogen, which represents 0.07 per cent. of the 
sugar used. 
0.386 gram. stearic acid gave 0.00028 gram. nitrogen. 
Numerous other experiments were made with a larger quantity 
of the same and other substances, with similar results, and he 
accounts for M. Reizet obtaining ammonia from sugar, by suppo- 
sing that his mixture of soda and lime contained a nitrate, prob- 
ably the nitrate of potash. 
Dr. Fownes has also been testing the experiments of M. Reizet, 
and finds them incorrect, substantiating those of M. Will. 10 grs. 
crystallized tartaric acid gave him 0.127 ip c. nitrogen, a quantity 
too small to be considered. 
M. Constantin Zwenger, in his article on Elaterin, (Ann. der 
Chem. und Phar. Sept. 1842,) states that this substance contains 
no nitrogen, having satisfied himself of that fact by MM. Varren- 
trapp and Will’s method, the substance being constituted as fol- 
lows, C2° H!4 05. 
T have also examined a specimen of animal charcoal that gave 
M. Laurent by the old method 2.5 per cent. of nitrogen, which 
when burnt with the soda and lime gave me 2.6 per cent. 
Yours, &c. J. Lawrence Smiru. 
Charleston, June 9, 1843. 
Arr. VI.—Remarks on the First Principles of the Differential 
Calculus, together with a new investigation of Taylor's The- 
orem; by Prof. '’Hropore Srrone. 
Ler ¢x denote any function of x, and suppose that x is chang- 
ed tor+h, then gx becomes 9(¢+h), which it is our object to 
express in a series ; considering z and / as indeterminate quanti- 
ties, which are independent of each other. 
We may evidently assume 9(2+h)=92+(A+B)yhA, (1), (a 
finite expression ;) and suppose that A is a function of @ and in- 
