Composition of Dilute Sulphuric Acid. 



307 



in the last place the arithmetical mean of the corresponding 

 quantities given for two other points of which the abscissas (p) 

 differ by equal amounts from that of the point in question. 



Thus the value of cV'sjdp 1 at 80*5 per cent, is- the mean of 

 the values at 81*5 per cent, and 79*5 per cent. 



' Table II. 



81-5 

 80-5 

 79-5 

 78-5 

 77-5 

 76'5 

 75-5 

 74-5 

 73-5 

 72-5 

 71-0 

 690 

 67-0 

 650 

 630 



dp 2 



X10 |; 



370 

 ■290 

 210 

 140 

 ■ 60 



• 80 

 50 



• 10 



- 10 



- 2 

 53 

 61 

 72 

 80 

 94 



Mean. 



P- 





] 61-0 



-290 



i 59-5 



-215 



58-5 



-135 



57-5 





56-5 





55-5 



- 45 



54-5 





! 53'5 





52 - 5 





51-5 





50-5 



62 



490 



70 



47-0 



83 



450 



91 



430 



d 2 s 

 dp 2 



Xl0 ,; 



102 

 105 

 102 

 105 

 102 

 110 

 108 

 112 

 110 



111 



105 



98 

 88 



Mean. 



99 

 102* 

 105 

 102 

 107 

 105 

 111 

 109 



104 

 96 



* The difference of the two values of ds/d/p, from which this number is ob- 

 tained, is 127. I am not sure whether this discrepancy is due to a mistake or 

 to the supposed existence of a point of discontinuity. 



The intervals from which these mean values are calculated 

 are at least twice as great as those which have to be used in 

 deducing values of ds/dp at points intermediate to those given. 

 Hence the errors introduced are not likely to exceed 2 or 3 

 in the last place. 



I have therefore deduced from the numbers in Mr. Picker- 

 ing's Table II. the readings on his curves at the points 

 corresponding to his experiments. 



In the following Table III., _p and (y-j are the values of 



these quantities given in Mr. Pickering's Table III. The 



percentage at the experimental points is p, andp m = (p +p )/2. 



The second differential atp m is calculated from my Table II. 



above and indicated by ( -y- 2 ) > and by means of this the value 



\dp ) m 



of — at p is deduced. 

 Thus, to give an example. 



If the values of - r - 5 at 

 ap z 



80 



per 



