210 [Assembly 



solidity is half the square root of three, viz: the decimal .866-|-j 

 and the diagonal line in numbers is the square root ot three, 

 viz: 1 .732-|-, which is just double the former number ; that is, 

 diametc r being one the diagonal line in numbers is double the 

 solid, and it proved exactly the same in cubic quantity, for taking 

 an octahedron of one inch diameter, tilling it twice and pouring 

 it into the diagonal, just filled the diagonal. In the octahedron 

 whose diameter is two, this proportion was exactly reversed. If 

 computed in numbers, the diagonal line is the square root of 

 twelve, viz: 3.464-}-, and the solid in numbers is 6.928-|-, just 

 double the former number, and the contents of the octahedron, 

 two inches in diameter, poured into its diagonal just filled it 

 twice. To mention a single example of pouring surfaces into 

 lines, if the tetrahedron, whose diameter is one, be calculated in 

 numbers, the surface is found to be 10.392-}-; and in the octahe- 

 dron, whose diameter is six, calculated in numbers, the diagonal 

 line is found to be 10 . 392-}-. Mr. Smith took the surface pans of 

 the tetrahedron, which was one inch in diameter, filled and 

 poured them into the diagonal line of the octahedron, which was 

 six inches in diameter, and the surface was found to be exactly 

 equal to the diagonal line in cubic quantity, as it is in numbers. 



In conclusion Mr. Smith called upon teachers and scientific 

 men to give this important subject a fair and full examination, 

 and if the principles and demonstrations are found to be correct, 

 to give the world the benefit of the new truth. 



ON FOOD. 



[Communicated by a Member.] 



The preservation of our general health depends upon a proper 

 selection of food, as well as the most judicious modes of prepar- 

 ing it. All our organs are daily experiencing waste, and re- 

 quire a fresh supply of materials to replace it, so great is this 

 waste, that probably it only takes a few years to change the sub- 

 stance of which we are formed entirely. It is to supply this de- 

 cay that God has given us an instinctive desire for food ; this foo 



