A. M. Mayer — Determination of the coefficient, etc. 323 



Fe 93-39 



Ni - - 5-62 



Co -. -58 



P -31 



99-90 



The iron is the mean of three fairly agreeing determinations, 

 the nickel of two determinations, 5 6.1 and 5*63, the cobalt of 

 two determinations, and the phosphorus is a single determina- 

 tion. 



We take great pleasure in thanking Professor Eugene A. 

 Smith for his assistance in obtaining the iron, and Professor F. 

 P. Yenable for furnishing the analysis. 



Art. XLIII. — On the determination of the coefficient of cu- 

 bical expansion of a solid from the observation of the 

 temperature at which water, in a vessel made of this solid, 

 has the same apparent volume as it has at 0°C; and on 

 the coefficient of cubical expansion of a substance deter- 

 mined by means of a hydrometer made of this substance ; 

 by Alfred M. Mayer. 



[Read before the National Academy of Sciences, at Washington, April 21, 1886.] 



The curve W of Fig. 1 shows the absolute expansion of 

 water. The unit of abscissae of this and the other curves is 

 1° C, the unit of ordinates is yo^-o^ of the unit of volume of 

 the water, this unit of volume being at 0° C. The curve 

 G shows the apparent expansion of water in a glass vessel, and 

 curves S, C, B and Z are the respective curves of the apparent 

 expansion of water in steel, copper, brass and zinc vessels. 

 The curve W cuts the axis of X at 8° 4 centigrade ; G at 

 ll°-7 ; S at 12°-8 ;C at 15°-3; B at 16° 3 ; Z at 21°-5. These 

 points of intersection correspond to the following coefficients 

 of cubical expansion ; for G, '000025 ; for S, -000033 ; for C, 

 •00005 ; for B, 000056 ; for Z, -00009. 



Let us consider the curve G. The curve goes below W be- 

 cause water contracts from 0° to 4°, and the glass vessel by 

 expanding adds to this fall of the water. Beyond 4° the water 

 expands more than the glass and at 11°"7 the expansion of 

 the water from 0° to ll°-7 equals the expansion of the glass 

 through the same range of temperature, and the curve G cuts 

 the axis of X at 11°'7. Therefore, to obtain the cubical 

 expansion of the glass, or of any other substance forming the 

 vessel, we have merely to determine the temperature at which 

 water has the same apparent volume that it has at 0° C, and 



