+-------------+---------------+----------+ | Weight. | Volume found. | Standard | +-------------+---------------+----------+ | 0.2160 gram | 72.9 c.c. | 0.2963 | | 0.2185 " | 73.9 " | 0.2957 | | 0.2365 " | 79.9 " | 0.2959 | | 0.2440 " | 82.3 " | 0.2964 | | 0.2555 " | 85.9 " | 0.2974 | +-------------+---------------+----------+ Any inclination that may be felt for obtaining an appearance of greater accuracy by ignoring the last result must be resisted. For, although it would make no practical difference whether the mean standard is taken as 0.2961 or 0.2963, it is well not to ignore the possibility that an error of 0.4 c.c. may arise. A result should only be ignored when the cause of its variation is known. In this series the results are proportional, but the range of weights (0.216-0.2555 gram) is small. All processes yield fairly proportional results if the quantities vary within narrow limits. 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 weight of metal used; and calculations from the mean standard will be incorrect. By subtracting the lowest standardising from the highest, a third result is got free from any error common to the other two; thus:-- 0.4 gram = 48.6 c.c. "cyanide." 0.1 " = 12.9 " " --- ---- 0.3 " = 35.7 " " And the standard calculated from this corrected result is 0.8404. Further, if 0.3 gram requires 35.7 c.c., then 0.1 gram should require 11.9 c.c., or 1.0 c.c. less than that actually found.