22 THE COMPRESSIBILITY OF LITHIUM, SODIUM, 



tube, and that when mercury alone was in the tube, was found by simple 

 subtraction. From this remainder was taken further the weight of mer- 

 cury which represented the difference between the change in volume of 

 the kerosene present and that of the mercury it displaced. The remainder, 

 still a weight of mercury, represented the change in volume of the metal 

 minus that mercury which it displaced. To convert this weight of mer- 

 cury into change of volume, it was necessary to divide it by the density of 

 mercury under 500 atmospheres pressure at 20, that is, by 13.57. The 

 resulting volume, upon being divided by 400 times the volume of sodium, 

 yielded as a result the difference between the compressibility of mercury 

 and of sodium. To this was then added the average compressibility of 

 mercury (3.69 X lO' 6 ) for the final result. 



The calculation may be expressed algebraically as follows, causing all 

 weights of mercury to correspond to the pressure-difference of 400 kg. 

 per square centimeter between 100 and 500. Let W = the weight of mer- 

 cury added when the alkali metal and paraffin oil were in the jacket; 

 W = the weight added when mercury alone was in the jacket; Wk = 

 the weight when oil alone was in the jacket; K = the weight of the oil 

 taken in the last case ; K = the weight of oil used in the first case ; A = 

 the weight of the alkali metal, and D = the density of the alkali metal, and 

 ft the compressibility of the metal sought. The density of mercury is 

 assumed to be 13.57, and its average compressibility* between 100 and 500 

 kg. per square centimeter is assumed to be 3.71 X 10~ 6 , then 



B== - -- 1-0.00000371 

 400 X 13.57 A 



W k W 3-096 

 or, more conveniently for the present cases, where ^- z y^j 



(W -0.0721- 0.4387 K)D . 00000371 

 5428 A 



A special example taken at random may make the method yet clearer. 

 In experiment 3 below, at the start, when 6.947 grams of sodium and 1.445 

 grams of kerosene were in the tube, contact was made with the corrected 

 gauge reading at 80. By first adding four successive amounts of mercury, 

 weighing, respectively, 0.377, 0.358, 0.343, and 0.153 gram, and then 

 removing 1.170 grams, f the following corrected pressure-readings were 

 obtained in succession: 200, 325, 449, 508, and 100. The total weights 

 of mercury were then plotted against the pressures as shown in fig. 4, 



*This matter is discussed at length in the third paper of the present series. 

 fThis last figure was observed only to test the work and is not recorded in 

 the table on p. 20. 



