AMERICAN INSTITUTE. 493 



plenty of water in — it exploded ! I think that the heat drove off the water 

 below, the iron became red hot, formed gas, and so exploded it. 



Mr. Garbanati. — We require a uniform strength — a test that docs not 

 overstrain the boiler, for that over exertion often spoils a man I 



Mr. Stetson. — To sustain Mr. Simson's case, I have known plasters of 

 thick brown paper over a weak spot in a boiler, bear the pressure of (said) 

 30 lbs. per square inch ! while other boilers, perfectly new and strong, ex- 

 plode ! So some buildings, soon after having sustained great crowds of 

 people, have tumbled down when empty ! I say, dogmatically, that a 

 boiler can be made which will not burst ! Cast iron won't do ! Electro- 

 type cannot answer, because when deposited thick it is uneven ! 



Mr. Garbanati. — The u-eak spots, such as shoulders, &c., may be fortified. 



The committee on questions, give the following for next meeting, viz : 

 '• Materials for boilers," and " Dentistr}'." 



Adjourned. H. MEIGS, Secretary. 



April 6, 1859. 



Present — Messrs. Pell, Tillman, Pierce, Butler, Scoville, Judge Liv- 

 ingston, Prof. Hedrick, John Joknsoa, Bruce. Garbanati, Haskell, Nash, 

 Breisach, Stetson, Finell, Cohen, Everitt, Seeley, Griffith, Bradford, and 

 others — 38 in all. 



Robert L. Pell in the chair. H. Meigs, Secretary. 



•Mfemoires De La Societe Imperiale Des Sciences Naturelles De Cherbourg. Tome IV, 1856. 



Presented by the Society to the American Institute, March, 1859. 



Extracts tra7islated by H Meigs, for the Polytechnic Association. 

 CHARACTER OF DIVISIBILITY IN WHOLE NUMBERS. 



The celebrated calculating Pastor of Touraine, Henry Mondeux, when 

 he was last in Cherbourg, in February, 1856, sold a pamphlet in which he 

 exhibited the character of the divisibility of whole numbers by the values 

 comprised between 1 and 50. His formula) are extensively ingenious, bvit 

 unaccompanied by any theory, and attest at the same time the marvellous 

 aptitude with which the author is endowed by nature. In fact the former 

 professor of Mondeux, M. Jacobi, in the preface of this pamphlet says : 

 " That his scholar had no knowledge of the principles on which those for- 

 mulae depend, and admits it with all humility." 



We found it interesting to find them out. We shall find how the four 

 first rules of arithmetic prove this divisibility. 



The committee on arts and sciences reported that Professor Cyrus 

 Mason, of Poughkeepsie, had been elected as Chairman, and Henry Meigs 

 Secretary, of the Polytechnic Association for the ensuing year. The 

 Society by a unanimous vote approved of the appointments, 



Mr. S. D. Tillman remarked that the extract read by the Secretary, re. 

 lating to mathematics, reminded him of a curious relation of numbers he 

 had discovered. It was doubtless known already to many mathematicians, 

 although he had not met it in print, yet he inferred that Babbage made 



