450 Mr, S. U. Pickering on the Recognition of 



experimental error determined by the graphic method was 

 0'0021°; and a two-curve drawing, such as that shown in 

 fig. 2, AB, gives a mean apparent error, and also total error, 

 of almost exactly this amount, namely, '0020 (column x., Table 

 VIII. ), but an attempt to represent the results as a single 

 curve increases the apparent error to 5 times, and the total 

 error to 219 times the known experimental error. 



The examination by the mathematical method shows that 

 two parabolas will represent the results with nearly as close 

 an agreement with the experimental error (1*5 times this 

 error*) as two bent-lath curves do, but that a single para- 

 bola is even more inapplicable than a single bent-lath curve, 

 the total apparent error according to it being no less than 

 3380 times greater than the experimental error. 



Some little doubt was entertained at first as to the exact 

 position of the break in this case, chiefly owing to the difficulty 

 of getting a lath of a flexibility, and sectional paper of a size 

 and accuracy, suited to the curvature of the figure and to the 

 experimental error, so the values were manipulated in a 

 variety of ways, and the results form a striking illustration of 

 how independent the recognition of a true break is of the 

 nature of the ordinates and abscissas selected for the plotting, 

 for all the figures illustrated in fig. 2 concur in placing a 

 break at the same point, - 8°, in spite of the great dissimi- 

 larity of their general form. The various plottings are : — 



AB. Depression against molecular composition. 

 Depression against percentage composition gives a veri- 

 similar figure. 



AC. Depression minus the readings of a selected parabola 

 against molecular composition. (A depression of 8° 

 becomes 0° according to this plotting.) 



DE. Depression against the reciprocal of the molecular 



composition. 

 F G. Depression against the logarithm of the molecular 



composition. 

 H I. Half the square of the depression against the molecular 



composition. 

 J K. Depression against the square root of the molecular 



composition. 



The numbers given at the top of the figure refer to A B and 

 A C only. In the case of H I only should there, I think, be 



* The excess in this case may be due to some, small error, of which 

 there are indications, but which I cannot locate, in the equation for 

 the second portion of the result. 



