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352 last not hours but years. A " single wave continuously circulating for seven years," Lewis pointed out, " may seem to be a remark- able conclusion; nevertheless, it is one we are now bound to accept."

It is evident that the permanence or impermanence of this circulating wave of excitability depends on the fact that the crest of the wave always finds recovered and so responsive muscular tissue in front of it to revert to the analogy, the advancing crest of the fire always finds new-grown grass to burn. There is thus present, in auricular flutter, a " gap " of recovered or responsive muscle be- tween the refractory or excited portions and the crest of the on- coming wave of excitability. This gap moves round and round the ring just as the wave of excitability does. The grass in fact grows up as quick as it is burnt down there is always a patch of it for the flames. Upon the continued presence and integrity of this gap the permanence of the flutter depends. So long as the gap is there the wave will circulate; so long as there is grass the fire will burn. But if the gap could be closed the flutter would must stop at once.

The same description applies to fibrillation except that the circus movement here is less well defined in its quality and the wave motion more diffuse. It will be seen that the experimental work has led to the door of the sick-room, so to speak, and that Lewis's view of the " gap " is probably justified: " it is a gap which will command the attention of many workers in the near future, for upon our power to influence its length, our success in treating flutter and the closely allied condition, fibrillation, will very largely depend." (R. M. Wl.) HEAT (see 13.135). Progress in the science of heat on the experimental side during 1010-21 was necessarily slow, because time and opportunity were lacking during the World War for the laborious work which solid progress entails. Some valuable researches, for which provision was made before the war, were subsequently brought to a successful conclusion, but many of the minor details, which taken in the aggregate constitute a con- siderable addition to knowledge, had not been made available by 1921 in a digested form suitable for reference. Speculative theories, on the other hand, which require no apparatus or elaborate preparation, have flourished the more abundantly in the absence of effective checks and exact verification. The sum- mary of recent works, given below, is arranged for convenience as far as possible in the order of the earlier articles connected with heat, in the nth ed. of the E.B., as enumerated in 13.157, and references to them are made where necessary.

International Notation. The symbolic notation here adopted is based on that recommended by the International Commission for the Unification of Physico-Chemical Symbols at their meet- ing at Brussels in 1913, as extended by a special Committee of the Physical Society of London under the presidency of Sir J. J. Thomson. Fortunately their recommendations coincide in the main with the notation employed in the nth ed. of the E.B., but a few changes have been made for the sake of uniformity, as indicated in the following list.

'Alphabetic Index of Symbols.

A = i/J, Reciprocal of mechanical equivalent of heat. Numerical factor for reducing PV to heat units.

B, Constant of integration in expressions for E and H.

b, Covolume in characteristic equation of gas.

C, Cooling-effect of Joule and Thomson (see 27.901).

c, Coaggregation volume in gas-equation. E, Intrinsic energy.

G, Gibbs' function, T*-H.

H, Total heat of vapour, E+aPV.

h, Total heat of liquid.

J, Joule's equivalent.

K, k, Thermal Conductivity, and Diffusivity.

L, Latent heat.

M, Mass.

m, Molecular weight or mass-flow.

N, Number of atoms or molecules.

n, Index in formula for c.

P, Pressure generally.

p, Saturation-pressure.

Q, Quantity of heat energy.

R, Gas-constant in PV = RT.

S, Specific heat of vapour; s, of liquid.

T, Absolute temperature; t, from oC.

U, Velocity of motion.

V, Specific volume of vapour; v, of liquid.

W, Work.

X, Cross-section of pipe or nozzle.


 * , Entropy of vapour;, of liquid.

0, Radiation constant in 0v/T.

v. Ratio of specific heats of gas.

A. Velocity of light, 3 X io 10 cms/sec. X, Wave-length; v, frequency. >), Viscosity of gas.

CALORIMETRY

Units of Heat. One of the most fundamental points in the measurement of heat is the relation between the practical units corresponding to the various methods discussed in the earlier article (see 5.60), in which the most important experi- mental evidence then available was described and reviewed. Some of the conclusions reached have since been contested, but additional experimental evidence has been obtained which seems to confirm the views previously maintained.

The experiments of Rowland by the mechanical method, agreeing closely with those of Joule when reduced to the scale of the gas thermometer, showed that the gram-calorie at 2OC. (defined as the quantity of heat required to raise the temperature of I gram of water at 2OC. under atmospheric pressure by I C. on the scale of the hydrogen thermometer) was equivalent to 4-180 joules of mechanical energy. Those of Reynolds and Moorby between o and IOOC. gave the equivalent of the gram-calorie as 4-1832 joules for the mean of the whole range, showing that the mean calorie was nearly the same as the calorie at 2OC., in contradic- tion to the results of earlier experimentalists who had obtained much higher values for the mean calorie. The best of the previous results by the method of mixtures for the variation of the specific heat of water between o and iooC. were those of Ltidin (see 5.64, fig. 6), which gave a somewhat improbable curve for the variation, indicating a value 4-206 joules for the equivalent of the mean calorie, if the calorie at 2OC. was equivalent to 4-180. Most of the older results for the mean calorie, e.g. those of Dieterici (Wied. Ann., 33, p. 417, 1888), giving 4;244 by an electrical method with an ice-calorimeter, were much higher than Liidin's. On the other hand, the continuous electrical method (see 5.65), in which platinum thermometers were employed in place of mercury thermometers, while agreeing very closely with Rowland's results from 5 to 3OC., gave a much slower rate of increase than Liidin's for the specific heat between 40 and iooC., and a value 4-186 joules for the mean calorie, confirming Reynolds and Moorby.

The later experiments of Dieterici, by the method of the ice- calorimeter employing a io times smaller current with a coil of higher resistance in order to reduce the uncertain errors of the electrical measurement, gave an equivalent 4-192 joules for the mean calorie. He also redetermined the constant of the ice-calorim- eter, using water at looC. sealed in thin bulbs of quartz-glass, and obtained a value 15-491 milligrams of mercury per mean calorie, appreciably higher than the value 15-44 previously employed. This has since been confirmed by E. Griffiths (Proc. Phys. Soc., 26, p. I, 1913) who found the value 15-486 for a mean calorie of 4-184 joules. Owing to the smallness of the quantities of heat available for measurement at low temperatures, the ice-calorimeter is unsuit- able for investigating the variation of specific heat in the neigh- bourhood of the freezing-point, but the observations of Dieterici at temperatures above IOOC. by the same method gave a rate of increase of the specific heat of water slightly exceeding that found by Regnault, which could not be reconciled with Liidin's curve showing a maximum of specific heat at 87C. On the other hand, Messrs. W. R. and W. E. Bousfield (Phil. Trans., A, 21 r, pp. 199- 251, 1911) succeeded in reproducing Liidin's results with remark- able fidelity by a most ingenious method of electric heating with a vacuum-jacket calorimeter. The heating-coil consisted of a long spiral of small-bore glass tubing filled with mercury, the expansion of which in a capillary tube was made to indicate the actual tem- perature of the mercury at any time when traversed by the electric current. The observers were thus enabled to avoid the. source of error due to the superheating of the conductor above the tempera- ture of the calorimeter. The uncertainty of heat-loss by evapora- tion from the surface of the water was minimized by protecting the surface with a cover in the form of a metal box maintained as nearly as possible at the same temperature as the water during an experi- ment. The rise of temperature over predetermined ranges, o 13, l3-27, etc. was observed with suitable mercury thermometers of limited scale, standardized at the National Physical Laboratory. The corresponding quantities of electrical energy supplied, when corrected for external heat-loss and for the thermal capacity of the calorimeter, gave the increase of total heat of water, or the mean specific heat over each range. By adding the increments of total heat for each range, the variation of the total heat h, or the small difference h t, could be obtained at each of the points of observa- tion, as in the following table:

Temperature C..

13

27

40

55

73

80

100

Bousfield

<>-(>5S

0-058

0-059

0-124

0-242

0-306

Liidin

0-057

0-059

0-064

0-119

0-285

o-37i

0-633

Formula (i)

0-070

0-072

0-054

0-038

0-046

0-062

0-159

Dieterici

O-OIO

O-OII

o-on

O-O^I

0-090

0-128

0-303