The viscosity of dry air at atmospheric pressure was measured by a capillary-tube method, at about 15°C. The ends of a wide-limbed U tube containing paraffin oil, of density 0.87, were connected by a pair of capillary tubes in series, so as to form a closed system. The oil was initially displaced, and in proceeding towards its equilibrium position it forced air through the capillaries. Care was taken to avoid constant and systematic errors, and two U tubes, two sets of capillaries and two methods of drying the air were used. Assuming that the viscosity increases by 4.93 × 10-7 per °C., the value at 23°C. is (1834.7 ± 0.8) × 10-7 c.g.s. units. The paper includes a summary of the general theory of the capillary-tube method and the correction terms involved, as well as a detailed theory of the present experiments.
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J E Lennard-Jones 1931 Proc. Phys. Soc. 43 461
W N Bond 1937 Proc. Phys. Soc. 49 205
J B Nelson and D P Riley 1945 Proc. Phys. Soc. 57 160
Measurements on X-ray photographs of cylindrical specimens of different absorption and thickness taken in a camera without eccentricity show that the absorption error in the apparent unit-cell dimension a is proportional to cos2θ/sinθ + cos2θ/θ. The plot of a against ½(cos2θ/sinθ + cos2θ/θ) is linear down to θ = 30° for all four specimens used. The extrapolated values for a are in good agreement, and this extrapolation function is accordingly recommended in the case of data from well constructed cameras. Other extrapolation functions are also considered, and the effect of various sources of error discussed. A table of ½(cos2θ/sinθ + cos2θ/θ) is given.
R F Bishop et al 1945 Proc. Phys. Soc. 57 147
A discussion is given of the indentation of ductile materials by cylindrical punches with conical heads. On the experimental side, experiments have been made with work-hardened and with annealed copper, with penetrations up to nine times the diameter of the punch. It is found that the load rises towards a maximum value which is not approached until the base of the cone has travelled four to five diameters into the copper block. Denoting this maximum load by p0A, where A is the area of the cross-section of the punch, it is found that p0 for a lubricated punch is about twice the hardness, or five times the yield stress, of the work-hardened material. A theoretical method is given for calculating p0, as follows: the pressures pc and p8 required to enlarge a cylindrical and a spherical hole in a material showing any kind of strain hardening can be calculated. It is plausible to assume that p0 should be between pc and p8, and since p8 is only slightly greater than pc, an approximate theoretical estimate of p0 is obtained. This is in good agreement with experiment. In the light of these results a qualitative discussion is given of hardness testing, and it is shown both on experimental and on theoretical grounds that with lubricated cones and work-hardened materials the hardness, i.e. load/indentation area, will not depend much on the angle of the cone unless this is less than 10°.
R Peierls 1940 Proc. Phys. Soc. 52 34
Calculations are made of the size of a dislocation and of the critical shear stress for its motion.
Helen D Megaw 1946 Proc. Phys. Soc. 58 133
The cell dimensions of a number of double oxides belonging to the perovskite type have been accurately determined from examination of high-angle lines on x-ray powder photographs. The structures found fall into groups, as follows:
Cubic (ideal perovskite type). This includes SrTiO3, SrSnO3, SrZrO3, BaSnO3, BaZrO3, BaThO3; also BaTiO3 above 120°C.
Tetragonal. This includes the usual form of BaTiO3 at room temperature, PbTiO3, and PbZrO3. The unit cell is derived from the cubic by simple extension or compression along one tetrad axis; and, like the cubic, it contains the formula number of atoms.
Orthorhombic. This includes CaTiO3 (the mineral perovskite), CaSnO3, CaZrO3, and CdTiO3 (fired above 1100° C.). The structure is derived from the cubic by a shear in the (010) plane and a slight extension or compression along the b-axis, giving a monoclinic pseudo-cell with a and c edges equal. The lattice is thus actually orthorhombic, and should be referred to new a and c axes lying at approximately 45° to the old in the same plane. There is an observed doubling of the cell edges, attributable to changes in some of the atomic parameters.
Rhombohedral. BaTiO3 can be prepared in this form, though the conditions are not yet fully established. The pseudo-cell is obtained by a very slight compression of the cubic cell along the cube diagonal; the true cell is a multiple of this
Steric considerations, based on Goldschmidt's ionic radii, are used to account for the occurrence of the different structure modifications.
A J C Wilson 1941 Proc. Phys. Soc. 53 235
The lattice spacing of aluminium has been measured as a function of temperature by means of a high-temperature Debye-Scherrer X-ray camera. The coefficient of expansion has been deduced. The results are:
Temp. | 0° | 100° | 200° | 300° | 400° | 500° | 600° | 650° C. |
---|---|---|---|---|---|---|---|---|
d | 4.0391 | 4.0486 | 4.0592 | 4.0701 | 4.0820 | 4.0947 | 4.1087 | 4.1162 |
106 α | 22.0 | 25.4 | 26.5 | 27.8 | 29.9 | 32.5 | 35.5 | 37.2 |
The systematic and random errors in d are each about 0.0001 A., the error in α from 1 to 2 per cent.
N F Mott and R Peierls 1937 Proc. Phys. Soc. 49 72
C N Davies 1945 Proc. Phys. Soc. 57 259
For calculation of terminal velocities it is convenient to express the Reynolds' number, Re, of a moving sphere as a function of the dimensionless group ψRe2, where ψ is the drag coefficient. The following equations have been fitted by the method of least squares to critically selected data from a number of experimenters:
Re = ψRe2/24 -0.00023363(ψRe2)2 + 0.0000020154(ψRe2)3 - 0.0000000069105(ψRe2)4 for Re<4 or ψRe2<140. This tends to Stokes' law for low values ofRe. It is specially suited to calculation of the sedimentation of air-borne particles. The upper limit corresponds to a sphere weighing 1.5 μg. falling in the normal atmosphere, that is, one having a diameter of 142 μ for unit density.
logRe=-1.29536+0.986 (logψRe2)-0.046677 (logψRe2)2+0.0011235 (logψRe2)3 for 3<Re<10,000 or 100<ψRe2<4.5.107.
Correction for slip in gases should be applied to Stokes' law by the following expression, based on the best results available:
1 + l/a[1.257 + 0.400exp(-1.10a/l)],
where the mean free path l is given by η/0.499σc.
This conveniently transforms to the following for the sedimentation of particles in air at pressure p cm. mercury
1 + l/pa[6.32.10-4 + 2.01.10-4exp(-2190ap)]
A R Stokes and A J C Wilson 1944 Proc. Phys. Soc. 56 174
Broadening of the Debye-Scherrer lines in x-ray photographs of cold-worked metals has been attributed (i) to breaking up of the crystals into " crystallites " whose linear dimensions are less, similar10-5 cm., (ii) to the presence of crystal grains of different lattice parameters, and (iii) to distortion of comparatively large crystal grains. The broadening to be expected on the last hypothesis is worked out approximately. It is found that the " apparent strain " is given by ηidentical withβ cot Θ=2/Φhkl(0), where β is the (corrected) integral breadth of the hkl reflection, Θ is the Bragg angle, and Φhhl(e)de is the fraction of the crystal for which the tensile strain in the hkl direction is between e and e+de.
To relate η with the internal stresses requires some approximations. In cubic crystals fairly plausible assumptions lead to the equation η2=A+BH, where A and B are constants involving the elastic moduli and the mean square values of the direct and shear stresses, and Hidentical with(k2l2 + l2h2 + h2k2)/(h2 + k2 + l2)2. This equation is verified within the rather large experimental error for metal filings and wire. Details of the experimental work will be published elsewhere.
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R E Belin 1948 Proc. Phys. Soc. 61 571
Corrections to 1948 Proc. Phys. Soc. 60 381.
R B R-Shersby-Harvie 1948 Proc. Phys. Soc. 61 571
Corrections to 1948 Proc. Phys. Soc. 61 255.
F K Goward and J J Wilkins 1948 Proc. Phys. Soc. 61 580
Mary P Lord 1948 Proc. Phys. Soc. 61 489
A critical survey of previous work on the measurement of fixation eye movements shows that none of it has satisfied all the conditions: (i) possibility of detection of movements of magnitude one minute of arc; (ii) little interference with the natural state of the eye; (iii) satisfactory treatment of the head movement problem.
A technique which more nearly meets these requirements is described. Photoelectric recording of the movements of an ultraviolet beam reflected from the surface of the cornea enables the first and second conditions to be satisfied. The reflected beam is divided into two parts, one of which falls on a horizontal straight edge, the other on a vertical straight edge. In each case more or less of the radiation passes the straight edge as the eye moves, and is focused on an electron multiplier phototube. The output of each multiplier is amplified and fed to a cathode-ray oscillograph, the time-base of which is suppressed. The oscillograph beams are thus arranged to give vertical traces only, and these are photographed simultaneously on a continuously moving film travelling in the horizontal direction. The eye movements can be deduced from the two records on the film. In an attempt to meet the third requirement the subject is placed in the prone position, in which the movements of the ultraviolet beam due to head movements are smaller than for other positions of the subject.
No attempt at analysis of the observations has yet been made.