[Illustration:  Fig. 1.]

[Illustration:  Fig. 2.]

The following is the arrangement of the trays in the box.  The triplets they contain suffice for ordinary purposes.

|=========================================|
| 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   |
|=========================================|

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 coarser tests, up to a maximum difference of XII., which may be useful in cases of morbidly diminished sensitivity.

Manipulation.—­A tray is taken out, the three weights that it contains is shuffled by the operator who then passes them on to the experimenter.  The latter sits at ease with his hand in an unconstrained position, and lifts the weights in turn between his finger and thumb, the finger pressing against the top, the thumb against the bottom of the cartridge.  Guided by the touch alone, he arranges them in the tray in what he conceives to be their proper sequence; he then returns the tray to the operator, who notes the result, the operator then reshuffles the weights and repeats the trial.  It is necessary to begin with coarse preparatory tests, to accustom the operatee to the character of the work.  After a minute or two the operator may begin to record results, and the testing may go for several minutes, until the hand begins to tire, the judgment to be confused, and blunders to arise.  Practice does not seem to increase the delicacy of perception after the first few trials, so much as might be expected.

D.—­WHISTLES FOR TESTING THE UPPER LIMITS OF AUDIBLE SOUND IN DIFFERENT INDIVIDUALS.

The base of the inner tube of the whistle is the foremost end of a plug, that admits of being advanced or withdrawn by screwing it out or in; thus the depth of the inner tube of the whistle can be varied at pleasure.  The more nearly the plug is screwed home, the less is the depth of the whistle and the more shrill does its note become, until a point is reached at which, although the air that proceeds from it vibrates as violently as before, as shown by its effect on a sensitive flame, the note ceases to be audible.