10 ENERGY CHANGES INVOLVED IN DILUTION OF AMALGAMS. 



Upon this basis the value of R is 



76.00 X I3-596 X 9 8 - 6 X 22,412 



R = = = 8.316 mayers. 



273.08 X 10,000,000 



It should be noted that barometric height and the acceleration of gravity 

 are quantities difficult to determine accurately, but they can hardly be in such 

 serious doubt as V. 



In applying the formula ttvF = RTln ^-, the above value of R is multi- 



C 2 



plied by T, the temperature of the cell, referred to the hydrogen scale. 

 Over that part of the scale used in the following work these readings are 

 essentially comparable with the corresponding thermodynamical tempera- 

 tures. Hence no uncertainty is occasioned by the introduction of this 

 factor into the formula. The experimental determination of temperature 



7" 1 



within one one-hundredth of a degree would fix the value assigned to -~ 



within 1 part in 30,000. This is far greater accuracy than can be attained 

 in the determination of the rest of the data from which ir is calculated. 



The most serious experimental uncertainty lies in the ratio ^- ; this may 



be written as equal to -p? if V x and V 2 are respective volumes occupied by 



a gram molecule of the dissolved metal in the two amalgams. No refer- 

 ence is made to the number of gram molecules of mercury involved in either 

 case. 



Since -n-, in volts, = 0.029 log 'approximately, at 20 , 



log^ 



k c - volts. 



34 



If the concentration ratio recorded for a given cell had been 0.1 per cent 

 too small, the true value of ir should have been found from the equation 



c c 



log 1. 001 -^ log 1 T _ 

 d _ c, .lo g i-ooi 



34 34 34 



Since log 1.001 = 0.00044 



c 



^g c 



TT '" 5 C 4- O.OOOO I VOlt. 



34 



Hence the calculated value of tt will be in error 0.00001 volt if the concen- 

 tration ratio is 0.1 per cent in error. Some serious obstacles to the determi- 

 nation of the ratio with this degree of precision will now be considered. 



