MEASUREMENT OF VARIABLE PROPERTIES 153 



increase of the weight precip., since this cannot exceed looo 

 mgr. 



Therefore the variation curve of the weight precip. does not 

 coincide with the curve of the committed errors. The series 

 of committed errors (from 984 to io-i6 c.c.) being divided into 

 eleven groups (intervals ; compare p. 145), and the relative 

 number of mixtures of each group being represented by a 

 vertical ordinate, a sjonmetrical curve of errors (Fig. 19) is 

 obtained similar to Fig. 18, p. 146. In the six groups A,B, C, 

 D, E, F the weight precip. increases from A to F. In F it 

 reaches the value of 1000 mgr. In the groups G, H, I, J, K the 

 maximal value 1000 mgr. is invariable. Therefore if the varia- 

 tion curve of the weight precip. {observed effects) is constructed, the 

 frequencies G, H, I, J, K are added to the frequency F, and the 

 curve ABCDEL (Fig. 19) is obtained (FL = G + H + 1 + J + K). 



The causes which have produced in the present example a 

 unilateral variation curve LEDCBA are exactly the same as 

 those which resulted in a symmetrical curve {ABCDEFGHIJK, 

 Fig. 19) in the fourteenth example (10 + 10 c.c. water, § no). 

 The diference between the two ciu-ves does not depend on a 

 difference in the causes, but merely on a difference in the 

 specific energy of the measured properties (volume ; precipitate) 

 of the mixtures. 



REMARK : Comparing the fourteenth, fifteenth and sixteenth examples, 

 we see that the same causes may produce : (i) continuous variation, expressed 

 by a symmetrical curve ; (2) discontinuous variation ; (3) continuous variation 

 expressed by a unilateral curve. 



In the sixteenth example the maximal value {weight precip. 

 1000 mgr.) has a preponderant importance ; it is, as it were, a 

 measure of the resultant of the two simple causes (10 c.c. 

 solution a + 10 c.c. solution b) which have acted simultaneously. 

 The minimal limit, on the contrary, is indefinite. From aU the 

 observed figures a mean value may be easily calculated, and it 

 might be possible to find a mathematical expression of the 

 (rather complicated) relation between this mean value and the 

 maximum. The significance of the mean value is, however, 

 rather a fictitious one, at least for the naturalist. 



We see from this example that a unilateral variation curve 

 may be simply a product of chance acting through a certain 

 machinery, without the intervention of any peculiar cause. 

 (Compare § 102, Example (B), p. 129.) 



§ 114.— THE FOURTEENTH, FIFTEENTH AND SIX- 

 TEENTH EXAMPLES MODIFIED BY A UNIFORM 

 INCREASE OF PIPETTE B.—ln the mentioned examples 

 (§§ no. III and 113) there is question of a mixture of two 

 liquids a and b, 10 c.c. of each being measured respectively by 



