humanfaculty4 - page 274 of 305

mistake. He is little likely to make a mistake of double the amount in question, and it is

almost certain that he will not make a mistake of treble the amount. In other words, he

would never be likely to put one of the test-weights more than one step out of its proper

place. If he had three weights to arrange in their consecutive order, 1, 2, 3, there are 3 x 2

= 6 ways of arranging them; of these, he would be liable to the errors of 1, 3, 2, and of 2,

1, 3, but he would hardly be liable to such gross errors, as 2,

Therefore of the six permutations in which three weights may be arranged three have to be

dismissed from consideration, leaving three cases only to be dealt with, of which two are

wrong and one is right. For the same reason there are only four reasonable chances of error

in arranging four weights, and only six in arranging five weights, instead of the 119 that

were originally supposed. These are—

But exception might be taken to two even of these, namely, those that appear in the third

column, where is found in juxtaposition with 2 in the first case, and 4 with 1 in the second.

So great a difference between two adjacent weights would be almost sure to attract the

notice of the person who was being tested, and make him dissatisfied with the

arrangement. Considering all this, together with the convenience of carriage and

manipulation, I prefer to use trays, each containing only three weights, the trials being

made three or four times in succession. In each trial there are three possibilities and only

one success, therefore in three trials the probabilities against uniform success are as 27 to

1, and in four trials at 81 to 1.

Values of the Weights.—After preparatory trials, I adopted 1000 grains as the value of

W and 1020 as that of R, but I am now inclined to think that 1010 would have been better.

I made the weights by filling blank cartridges with shot, wool, and wads, so as to distribute

the weight equally, and I closed the cartridges with a wad, turning the edges over it with

the instrument well known to sportsmen. I wrote the corresponding value of the index of R

on the wad by which each of them was closed, to serve as a register number. Thus the

cartridge whose weight was WR

was marked 4. The values were so selected that there

should be as few varieties as possible. There are thirty weights in all, but only ten

varieties, whose Register Numbers are respectively 0, 1, 2, 3, 3½, 4½, 5, 6, 7, 9, 12. The

reason of this limitation of varieties was to enable the weights to be interchanged

whenever there became reason to suspect that the eye had begun to recognise the

appearance of any one of them, and that the judgment might be influenced by that

recognition, and cease to be wholly guided by the sense of weight.