§ 88 Properties of Threads.
A large number of experiments on the numerical values of the elastic constants of quartz threads have been made by Mr. Boys and his students, and by the writer. As the methods employed were quite distinct and the results wholly independent, and yet in good agreement with each other, a rounded average may be accepted with considerable confidence.
| TENACITY OF QUARTZ FIBRES (BOYS). | |||
| Diameter of Thread. | Tenacity in Tons’ Weight per Square Inch of Section. | Tenacity in Dynes per Square Centimetre. | |
| Inches | Centimetres | ||
| 0.00069 | 0.00175 | 51.7 | 8 X 109 |
| 0.00019 | 0.00048 | 74.5 | 11.5 X 109 |
| Rounded mean of Boys’ and Threlfall’s results: | |
| Young’s Modulus at 20° C., | 5.6 X 1011 C.G.S. |
| Modulus of Simple Rigidity at 20° C., | 2.65 X 1011 C.G.S. |
| Modulus of Incompressibility, | 1.4 X 1011 C.G.S. |
| Modulus of Torsion, | 3.7 X 1011 C.G.S. |
Approximate coefficient of linear expansion of quartz per degree between 80° C. and 30° C. is 0.0000017 (Threlfall = loc. cit.).
This must be regarded with some suspicion, as the data were not concordant. There is no doubt, however, about the extreme inexpansibility of quartz.
Temperature coefficient of modulus of torsional rigidity per degree centigrade, 22° to 98° C., 0.000133
Ditto, absolute simple rigidity, 0.000128 (Threlfall).
Limit of allowable rate of twist in round numbers is, one-third turn per centimetre, in a fibre 0.01 cm. diameter.
The limiting rate is probably roughly inversely as the diameter.
Attention must be called to the rapid increase in the torsional rigidity of these threads as the temperature rises. A quartz spiral spring-balance will be appreciably stronger in hot weather.
§ 89. In the majority of instances in which quartz threads are applied in the laboratory, it is desirable to keep the coefficient of torsion as small as possible, and hence threads are used as fine as possible.
It is convenient to remember that a thread 0.0014 cm. or 0.0007 inch in diameter breaks with a weight of about ten grammes, and may conveniently be employed to carry, say, five grammes. With threads three times finer the breaking strength per unit area increases, say, 50 per cent. In ordinary practice — galvanometric work for instance — where it is desirable to use a thread as fine and short as possible to sustain a weight up to, say, half a gramme, it will be found that fibres five centimetres long or over give no trouble through defect of elastic properties. A factor of safety of two is a fair allowance when loading threads.
No difficulty will be experienced in mounting threads having a diameter of 0.0002 inch or over. With finer threads it is necessary to employ very dark backgrounds (Mr. Boys uses the darkness of a slightly opened drawer), or the threads cannot be sufficiently well seen.
In the case of instruments in which threads remain highly twisted for long periods of time, the above rule as to the safe limit of twist does not allow of a sufficient margin; it is only applicable to galvanometric and similar purposes.
The cause of the increase in tenacity as the diameter diminishes is at present unknown. It is due neither to an effect of annealing (annealed threads are rotten), nor is it a skin effect, nor is it due to the cooling of the thread under higher capillary pressure. It is, however, possible that it may be associated with some kind of permanent set taken by the fibres during the stage of passage from the liquid to the solid state.