kanolt: melting points of fire bricks 337 



In the proof which was given that /3 6 = e bl3 , a method was 

 introduced which afterwards proved effective in demonstrating 

 the Exponential Theorem. It consists in restoring the original 

 powers from which a reduced expression was derived : 



/3 6 = cos 6-/3°+ sin b-^ /2 



-1-5+5-}' 



+ K-, + S-k; 



2! 3! 4! 



= e b ^ /2 



PHYSICS. — The melting points of fire bricks. C. W. Kanolt. 

 Communicated by C. W. Waidner. To appear in the Bulletin 

 of the Bureau of Standards. 



We are accustomed to thinking of a melting point as a tempera- 

 ture at which a substance changes from a rigid to a fluid condi- 

 tion, but a melting point can be precisely and rationally defined 

 only as the temperature at which a crystalline or anisotropic 

 phase and an amorphous or isotropic phase of the same composi- 

 tion can exist in contact in equilibrium. While this definition 

 is satisfactory for pure substances, so complex a mixture as an 

 ordinary fire brick usually has no single definite melting point 

 according to this definition, since several anisotropic phases may be 

 present, all differing in composition from the isotropic phase pro- 

 duced by fusion. We can then only select the temperature at 

 which the transition from a rigid to a fluid state seems most dis- 

 tinct, and can call this the melting point only by apology. In the 

 case of fire bricks, the transition temperatures so found are for- 

 tunately sufficiently distinct. I have taken as the melting point 

 the lowest temperature at which a small piece of the brick could 

 be distinctly seen to flow. 



The experiments were conducted in an Arsem graphite resist- 

 ance vacuum furnace. The samples were usually inclosed in a 

 refractory tube made of a mixture of kaolin and alumina in the 



