Part 21 (2/2)
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Age of Mother
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t
---------+---------+---------+---------+---------
------------
1 1
24 to 25
26 ” 27
6 6
4 1 2
28 ” 29
12 15
2 5 2 1
30 ” 31
21 25
9 5 1 2
32 ” 33
14 18
12 9 5 3 1
34 ” 35
15 25
12 10 4 5 5 2
36 ” 37
14 22
10 15 6 7 2 1
38 ” 39
7 11
3 9 7 7 2 1
40
=================================================
--------------------
Total within outline.
90 123
Total between outline
52 54 24 25 7 9 1
Total beyond outline.
=================================================
=====================
90 123 52 54 24 25 7 9 1
Total.
TABLE II.
----------------------------------------------------------------------
Number of Families
Number of Children
--------+--------------+------------------------
Factory
Agricultural
Factory
Agricultural
Within outline
541
436
903
778
Between outlines
375
476
1233
1562
Beyond outlines
84
88
545
571
=============================================+========================
Total
1000
1000
2681
2911
======================================================================
C -- AN APPARATUS FOR TESTING THE DELICACY WITH WHICH WEIGHTS CAN BE DISCRIMINATED BY HANDLING THEM.
[_Read at the Anthropological Inst.i.tute_, Nov., 1882.]
I submit a simple apparatus that I have designed to measure the delicacy of the sensitivity of different persons, as shown by their skill in discriminating weights, identical in size, form, and colour, but different in specific gravity. Its interest lies in the accordance of the successive test values with the successive graduations of a true scale of sensitivity, in the ease with which the tests are applied, and the fact that the same principle can be made use of in testing the delicacy of smell and taste.
I use test-weights that mount in a series of ”just perceptible differences” to an imaginary person of extreme delicacy of perception, their values being calculated according to Weber's law. The lowest weight is heavy enough to give a decided sense of weight to the hand when handling it, and the heaviest weight can be handled without any sense of fatigue. They therefore conform with close approximation to a geometric series; thus-- _WR0, WR1, WR2, WR3_, etc., and they bear as register-marks the values of the successive indices, 0, 1, 2, 3, etc. It follows that if a person can just distinguish between any particular pair of weights, he can also just distinguish between any other pair of weights whose register-marks differ by the same amount. Example: suppose A can just distinguish between the weights bearing the register-marks 2 and 4, then it follows from the construction of the apparatus that he can just distinguish between those bearing the register-marks 1 and 3, or 3 and 5, or 4 and 6, etc.; the difference being 2 in each case.
There can be but one interpretation of the phrase that the dulness of muscular sense in any person, B, is twice as great as in that of another person, A. It is that B is only capable of perceiving one grade of difference where A can perceive two. We may, of course, state the same fact inversely, and say that the delicacy of muscular sense is in that case twice as great in A as in B. Similarly in all other cases of the kind. Conversely, if having known nothing previously about either A or B, we discover on trial that A can just distinguish between two weights such as those bearing the register-marks 5 and 7, and that B can just distinguish between another pair, say, bearing the register-marks 2 and 6; then since the difference between the marks in the latter case is twice as great as in the former, we know that the dulness of the muscular sense of B is exactly twice that of A. Their relative dulness, or if we prefer to speak in inverse terms, and say their relative sensitivity, is determined quite independently of the particular pair of weights used in testing them.
It will be noted that the conversion of results obtained by the use of one series of test-weights into what would have been given by another series, is a piece of simple arithmetic, the fact ultimately obtained by any apparatus of this kind being the ”just distinguishable” fraction of real weight. In my own apparatus the unit of weight is 2 per cent.; that is, the register-mark 1 means 2 per cent.; but I introduce weights in the earlier part of the scale that deal with half units; that is, with differences of 1 per cent.
In another apparatus the unit of weight might be 3 per cent., then three grades of mine would be equal to two of the other, and mine would be converted to that scale by multiplying them by 2/3. Thus the results obtained by different apparatus are strictly comparable.
A sufficient number of test-weights must be used, or trials made, to eliminate the influence of chance. It might perhaps be thought that by using a series of only five weights, and requiring them to be sorted into their proper order by the sense of touch alone, the chance of accidental success would be too small to be worth consideration. It might be said that there are 5 4 3 2, or 120 different ways in which five weights can be arranged, and as only one is right, it must be 120 to 1 against a lucky hit. But this is many fold too high an estimate, because the 119 possible mistakes are by no means equally probable. When a person is tested, an approximate value for his grade of sensitivity is rapidly found, and the inquiry becomes narrowed to finding out whether he can surely pa.s.s a particular 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 32 = 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, 3, 1, or 3, 2, 1, or 3, 1, 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--
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 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 _WR4_ 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, 3-1/2, 4-1/2, 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.
We are so accustomed to deal with concurrent impressions that it is exceedingly difficult, even with the best intention of good faith, to ignore the influence of any corroborative impression that may be present. It is therefore right to take precautions against this possible cause of inaccuracy. The most perfect way would be to drop the weights, each in a little bag or sheath of light material, so that the operatee could not see the weights, while the ratio between the weights would not be sensibly changed by the additional weight of the bags. I keep little bags for this purpose, inside the box that holds the weights.
_Arrangement of the Weights_.--The weights are placed in sets of threes, each set in a separate shallow tray, and the trays lie in two rows in a box. Each tray bears the register-marks of each of the weights it contains. It is also marked boldly with a Roman numeral showing the difference between the register-marks of the adjacent weights. This difference indicates the grade of sensitivity that the weights in the tray are designed to test. Thus the tray containing the weights _WR0_, _WR3_, _WR6_ is marked as in Fig. 1, and that which contains _WR2_, _WR7_, _WR12_ is marked as in Fig. 2.
[Ill.u.s.tration: Fig. 1.]
[Ill.u.s.tration: Fig. 2.]
The following is the arrangement of the trays in the box. The triplets they contain suffice for ordinary purposes.
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Just
perceptible
Grade of
Sequences
Ratio.
Sensitivity
of Weights
-------------+-------------+-------------
1.020
I.
1, 2, 3
1.030
I.1/2
2, 3-1/2, 5
1.040
II.
3, 5, 7
1.050
II.1/2
2, 4-1/2, 7
1.061
III.
0, 3, 6
1.071
III.1/2
0, 3-1/2, 7
1.082
IV.
1, 5, 9
1.082
IV.1/2
0, 4-1/2, 9
1.104
V.
2, 5, 7
1.127
VI.
0, 6, 12
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But it will be observed that sequences of 1/2 can also be obtained, and again, that it is easy to select doublets of weights for coa.r.s.er tests, up to a maximum difference of XII., which may be useful in cases of morbidly diminished sensitivity.
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