The scale of the instrument having for its unit the two-hundred-and- fiftieth part of an inch, it follows that the number of vibrations in the note of the whistle is to be found by dividing (13440 x 250)/4 or 84,000, by the graduations read off on its scale. A short table is annexed, giving the number of vibrations calculated by this formula, for different depths, bearing in mind that the earlier entries cannot be relied upon unless the whistle has a very minute bore, and consequently a very feeble note. =================================== | Scale Readings | Corresponding | | (one division | Number of | | = 1/250 | Vibrations | | of an inch). | per Second | |----------------+----------------| | 10 | 84,000 | | 15 | 56,000 | | 20 | 42,000 | | 25 | 33,600 | | 30 | 28,000 | | 35 | 24,000 | | 40 | 21,000 | | 45 | 28,666 | | 50 | 16,800 | | 55 | 15,273 | | 60 | 14,000 | | 65 | 12,923 | | 70 | 12,000 | | 75 | 11,200 | | 80 | 10,500 | | 85 | 9,882 | | 90 | 9,333 | | 95 | 8,842 | | 100 | 8,400 | | 105 | 8,000 | | 110 | 7,591 | | 115 | 7,305 | | 120 | 7,000 | | 125 | 6,720 | | 130 | 6,461 | =================================== [Footnote 28: Mr. Hawksley, surgical instrument maker 307 Oxford Street also makes these.] The largest whistles suitable for experiments on the human ear, have an inner tube of about 0.16 inches in diameter, which is equal to 40 units of the scale. Consequently in these instruments the theory of closed pipes ceases to be trustworthy when the depth of the whistle is less than about 60 units. In short, we cannot be sure of sounding with them a higher note than one of 14,000 vibrations to the second, unless we use tubes of still smaller bore. In some of my experiments I was driven to use very fine tubes indeed, not wider than those little glass tubes that hold the smallest leads for Mordan's pencils. I have tried without much success to produce a note that should be both shrill and powerful, and correspond to a battery of small whistles, by flattening a piece of brass tube, and passing another sheet of brass up it, and thus forming a whistle the whole width of the sheet, but of very small diameter from front to back. It made a powerful note, but not a very pure one. I also constructed an annular whistle by means of three cylinders, one sliding within the other two, and graduated as before.