Bauhaus-Universität Weimar

250 Appendix 
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, i, 2, 3, there are 3x2 = 6 ways of 
arranging them ; of these, he would be liable to the errors of 1, 
3, 2, and of 2, i, 3, but he would hardly be liable to such gross 
errors as 2, 3, 1, or 3, 2, 1, or 3, 1, 2. Therefore of the six per¬ 
mutations 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- 
12354 13245 13254 
21345 21354 21435 
But exception might be taken to two even of these, namely, 
those that appear in the third column, where 5 is found in juxta¬ 
position 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. Con¬ 
sidering 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 I, and in four trials at 81 to 1. 
Vahies 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 instru¬ 
ment 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 WRi 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 o, 1, 2, 3, 3J, 4J, 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 recog¬ 
nition, and cease to be wholly guided by the sense of weight.
        

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