864 DE. A. MATTHIESSEN ON THE EXPANSION 



mining the coefficients of expansion ; for although it appears a very simple one, yet it 

 requires, I may say, very gi-eat care to ensure reliable results. 



I. Very often a series was rendered valueless by small hairs or particles of dust falling 

 into the water and attaching themselves to the fine platinum wire, as 0*1 or 0*2 milli- 

 gramme diiference in the weight makes a considerable diflference in the expansion of 

 those metals or alloys which have a loAv coefficient of expansion ; this source of error 

 was carefully guarded against ; in fact, if on taking the cylinder out to reboil the water 

 any particle of dust floated near the wires, the obser\'ations were considered worthless, 

 and fresh ones taken after reboiling the water. 



II. When, for instance, the observations were being made at the highest temperature, 

 if by chance the temperature sunk three or four degrees and giadually rose again, the 

 air absorbed at the lower temperature would be expelled, and an air-bubble would 

 sometimes attach itself to the metal and cause a false weighing. 



III. If the casting were not perfect, or w ere crystalline, and the air could not be com- 

 pletely expelled from the small cavities by boiling, results were obtained which did not 

 agree together, owing to its expansion at the high and partial absoi-ption by the water at 

 the lower temperature. For this reason two series were always made with each metal 

 and alloy, and where possible they were recast. 



The values obtained when weighing the purified metals in water were as follow : — 



Table III. — Cadmium. 



Owing to this metal becoming crystalline at about 80°, four obsei'vations were made 

 between 0° and 100°. It will be seen that this change of molecular condition has no 

 effect on this physical property. 



No, 3. — Cadmium, four times boiled. 



Loss of weight 



V,= 6-28826(l + 10-'0-7991<+10-''x 0-163/=)*, or if Vo=l, then Vto=1-009611. 

 No. 4. — Cadmium varnished, four times boiled. 



V.= 5-90793(l + 10-^0-799U+10-»x0-l63<='), or if Vo=l, then V,oo=l-0096ll. 



• I have employed this method of writing the formulae to prevent mistakes ia the number of the zeros, as 

 well as to show at a glance their number. I have also preferred keeping the exponents constant, adding, instead 

 of altering them, a zero after the decimal point where required. 



