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The aims of the study were to explore the effects of teaching heuristics in a calculus course and to generate hypotheses about related changes in heuristic usage and problem solving performance. Thirty college students in two classes participated and a Solomon four-group research design was used. Students from one group in each class were interviewed individually and asked to solve word problems aloud, then an instructional program was given in which one class received heuristic-oriented instruction while the other class did not. A second diagnostic observation was held. Results indicate that heuristic subjects exhibited superior performance on approach, plan, and result; showed less difficulty in terms of hesitation and reading the problem; and exhibited slightly decreased solution time and markedly increased time in checking the results than the control group. (Author/DT)

Persons whose economic position is poor and who have had little or no economic security in the past; persons who have health problems and physical complaints; those who live alone and who lack personal relationships with a spouse, friends, relatives, or close friends; those who do not participate in social or organizational activities; and those with low morale are likely to be poorly adjusted in old age. Confidence in these findings was afforded by performing identical research procedures in two cities. No differences in the degree of adjustment were found between three socioeconomic strata.

From an experimental investigation of superfluid film transfer in narrow beakers in helium II it emerges that there are probably two kinds of film. A ‘normal’ film is formed by superfluid creep over a dry substrate. A ‘thick’ film remains when liquid has drained from a substrate that has previously been immersed in the liquid helium bath. A comparison has been made of the superfluid flow between the two types of film. Scatter of values of transfer rate associated with a normal film is attributed to third sound generated by bath waves impinging on the meniscus at the base of the film. The thick film shows an enhanced rate of transfer which can persist for long periods of time in quiet conditions, but which can be abruptly diminished by disturbances such as bath surface agitation. There is a maximum stable length for a thick film exhibiting the full enhanced rate. The enhanced rate can be as much as 60% greater than the normal rate at 1° K, but the difference between the two rates of transfer disappears above 1.8 °K. No enhanced rate of transfer at any temperature is observed in beakers as large as 8 mm diameter.

The velocity fields of heliumn have been studied in a short, wide tunnel in which a heat current can be made to flow. A fine quartz fibre suspended from the tunnel roof and carrying a small weight at its lower end is used as a probe. The random motion of the fibre measures the intensity of turbulence in the normal fluid, while its response to short heat pulses, either alone or superimposed on a heat current, is related to the superfluid circulation about the fibre. From the size, direction and rate of change of this circulation the state of vorticity of the superfluid can be deduced. At 1*3 °K three flow regimes are found. In low or zero heat currents the normal-fluid flow is laminar; observed circulations are of the order of one quantum and persist for many seconds. It is believed that they are created by the measurement process (the heat pulse) itself, so that in this régime the superfluid is essentially undisturbed. In the second regime, which occurs above an onset heat current determined by the geometry, the observed circulations are smaller and more variable. It is argued that this results from superfluid vorticity associated with secondary flow. In the third regime random motion of the fibre occurs. It is shown that this motion cannot be due to superfluid turbulence alone: the normal fluid must be turbulent, and probably the superfluid also. The régime occurs when a modified Reynolds number, based on the normal-fluid viscosity and mean velocity, the mean tunnel diameter and the total density of the helium, exceeds a critical value of about 1350. The onset of the third regime is the analogue for heliumn of the classical transition from laminar to turbulent flow. The behaviour at higher temperatures is similar but less clear cut. It is concluded that, while the behaviour of the measured circulations about the fibre is consistent with the quantization of superfluid circulation, the critical velocities observed in heat currents in wide channels are directly related not to the creation of quantized vortex lines, but to the quasi-classical effects, secondary flow and turbulence.

The unusual characteristics of heat transfer in liquid He II have been reported in several recent papers. The very high thermal conductivity of the low-temperature modification of liquid helium was first noted by Keesom and Keesom (1935). It was then found by Allen, Peierls and Uddin (1937) and subsequently verified by Keesom, Keesom and Saris (1938) that the rate of transfer of heat varied with the temperature gradient. The discovery of the momentum transfer accompanying heat flow in He II which was made by Allen and Jones (1938) and the work on mobile surface films of the liquid done by Daunt and Mendelssohn (1938) show that a large part of the heat must be carried by some form of mass transfer. Several ideas and theories to explain the phenomena have been put forward by Kapitza (1938), Jones (1938), Michels, Bijl and de Boer (1938), Tisza (1938) and Keesom and Taconis (1938). The experimental evidence is as yet too meagre to prove or disprove any of the theories. It was with the intention of adding to the data already known concerning the properties of liquid He II that the present research was undertaken. The apparatus which was used is shown in fig. 1. The thermal conductivity was measured by a standard method. A constant supply of heat was supplied to one end of a long capillary containing liquid He II, and the other end was maintained at the constant temperature of the He II bath. Temperatures were observed at two points along the capillary.

The problem of the viscosity of liquid He ll has been the subject of several recent investigations. In their experiments, Misener, Burton and others at Toronto (1935 a, b ) and later MacWood (1938) at Leiden used the methods of oscillating cylinder and disk respectively. Kapitza (1938) employed radial flow between parallel plates, and Giauque, Stout and Barieau (1938), Burton (1938), and the present authors (1938 a, b ) have used the method of flow through capillaries. There has been wide disagreement among the investigators with regard to the magnitude of the viscosity, and the determination of the value by the different investigators varies from an upper limit of 5 × 10 -9 c.g.s. units, as found by Kapitza (1938), to a value of 10 -5 c.g.s. units, as observed by Burton (1938). In addition to this the present authors reported (1938 a ) that, at least for long, narrow capillaries, the flow of liquid He ll appeared to be non-classical in that the velocity of flow bore a relation to the pressure, which corresponded neither to laminar nor turbulent conditions. Flow is classically defined as laminar when the average velocity over the cross-section of the tube is directly proportional to the hydrostatic pressure which produces the flow. At sufficiently high velocity, the flow ceases to be laminar; it becomes turbulent and the velocity is then proportional to the square root of the pressure. It was observed that for He ll in long, narrow capillaries the velocity became almost independent of pressure and the suggestion was advanced that this might be attributed to slip on the walls of the capillary.