412 PROCEEDINGS OF THE AMERICAN ACADEMY 



calculus, in its ordinary form, are identical with those of this other so 

 far as the latter apply to zero and unity, because every class, in its 

 first intention, is either without any extension (that is, is nothing), or 

 belongs essentially to that rank to which every class belongs, whether 

 divisible or not. 



These considerations, together with those advanced on page 293 

 (§ 12) of this volume, will, I hope, put the relations of logic and 

 arithmetic in a somewhat clearer light than heretofore. 



Five liuiidred and eiglity-sixtli Meeting. 



October 8, 1867. — Monthly Meeting. 



The Corresponding Secretary in the chair. 



The Corresponding Secretary read letters relative to ex- 

 changes ; also a letter from Major-General Sabine in acknowl- 

 edgment of his election as Foreign Honorary Member of the 

 Academy. 



The Corresponding Secretary announced the recent decease 

 of Hon. Charles G. Loring, of the Resident Fellows. 



Dr. C. G. Putnam presented the meteorological observations 

 of the late Dr. Jackson. 



Professor Levering presented for Professor Treadwell the 

 following paper : — 



Corrections to a Paper " On the Comparative Streno;th of Can- 

 non of Modern Construction,^^ published in Vol. YH. of the 

 Proceedings of the Academy. By Daniel Treadwell. 



In a paper " On the Comparative Strength of Cannon of Modern 

 Construction," written by me in January, 1866, communicated to the 

 Academy in September of the same year, and published in the last 

 volume (the seventh) of our Proceedings, I, by some inadvertence 

 for which I am now unable to account, in computing the force of the 

 600 pounder, or 13-3-inch coil gun, as constructed by Armstrong, de- 

 scribed it as capable of bearing a charge of 100 pounds of powder. 



Although tliis quantity of powder was no doubt fired in it, I know 

 not how many times, yet it ought not by any means to be rated as its 

 service charge ; and I recognize it as an oversight in me to have taken 



