As to results which are not proportional, it is best to take some
imaginary examples, and then to apply the lesson to an actual one. A
series of titrations of a copper solution by means of a solution of
potassic cyanide gave the following results:--

+---------------+---------------+-----------+
| Copper taken. | Cyanide used. | Standard. |
+---------------+---------------+-----------+
| 0.1 gram | 11.9 c.c. | 0.8403 |
| 0.2 " | 23.7 " | 0.8438 |
| 0.3 " | 35.6 " | 0.8426 |
| 0.4 " | 47.6 " | 0.8403 |
+---------------+---------------+-----------+

These are proportional, but by using a larger quantity of acid and
ammonia in the work preliminary to titration, we might have had to use
1 c.c. of cyanide solution more in each case before the finishing point
was reached. The results would then have been:

+---------------+---------------+-----------+
| Copper taken. | Cyanide used. | Standard. |
+---------------+---------------+-----------|
| 0.1 gram | 12.9 c.c. | 0.7752 |
| 0.2 " | 24.7 " | 0.8097 |
| 0.3 " | 36.6 " | 0.8191 |
| 0.4 " | 48.6 " | 0.8230 |
+---------------+---------------+-----------+

It will be noted that the value of the standard increases with the