Application of nucleation theory to the freezing of supercooled insects

r. ins. PhpX.,

1958, Vol. 2, pp. 178 to 186.

Pergamon Press Ltd., London

APPLICATION OF NUCLEATION THEORY TO THE FREEZING OF SUPERCOOLED INSECTS* R. W. SALT?_ Crop

Insect

Section,

Science

Service

Laboratory,

Lethbridge,

Alberta,

Canada

Abstract-The factors affecting freezing in insects are examined and interpreted in terms of their theoretical and observed applications to water itself. The construction of ice-crystal nuclei is of the heterogeneous type (built on a non-aqueous substrate) in most if not all insects. The probability of nucleation is strongly temperaturedependent, the relationship being a composite of probabilities for construction, survival, and growth of incipient nuclei. Time plays a dominant role because nucleation depends on chance favourable molecular orientations. The probability-time relationship is essentially that expressed by the compound interest law. Surfaces influence nucleation by providing sites for heterogeneous nucleation, by restricting molecular motion, by providing areas whose energy values differ from those within a mass of water, and by their modifying effect (e.g. attraction, orientation) on foreign nucleating agents present in the water. Negative pressures produced by sudden impacts can produce freezing in plain water and in insects by momentarily raising the freezing point.

INTRODUCTION

INSECTS that are killed by freezing are dependent on supercooling to protect them For each individual there are limits to the ability against freezing temperatures. to supercool, dependent on several factors. It is the purpose of this paper to examine these factors, which apply to all liquid-to-solid phase changes, and to attempt to interpret their entomological applications. A brief introduction to nucleation concepts has already been presented (SALT, in press). TYPES

OF

NUCLEATION

The events leading up to freezing in a supercooled insect are essentially those occurring in any liquid, A crystal nucleus is built up to critical size by the aggregation of molecules of the liquid alone (homogeneous nucleation) or of molecules of the liquid on a foreign substrate (heterogeneous nucleation). MASON (1956) has ably postulated the freezing of a drop of water as follows: “As the temperature is lowered, the internal structure of the supercooled liquid becomes progressively more and more ice-like as is revealed by X-ray diffraction patterns. In the absence of foreign surfaces, nucleation of the ice phase may occur only by the chance orientation of local group(s) of water molecules into an ice-like configuration. A suitable solid particle, however, may causewatermolecules to become “1ocked”into the ice lattice under * Contribution Ottawa, Canada. i Research

No.

3778, Entomology

Division,

Officer. 178

Science

Service,

Department

of Agriculture,

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the influence of its surface force field. The molecular aggregate will not only be strongly bound to the surface of the particle, but will have only one exposed surface; on both counts it will be less vulnerable to thermal bombardment than will a spontaneously formed aggregate and will therefore have a higher probability of attaining the critical size at which it may nucleate the ice phase. Whether or not a stable ice nucleus is formed must be largely determined by the configuration of the surface force field of the substrate, since this will affect the ability of the water molecules lying within its sphere of influence to form an ice lattice.”

Liquids entirely free from foreign particles or surfaces are rare; thus heterogeneous nucleation is the customary type. In most instances of insect freezing one can be reasonably certain that nucleation is heterogeneous. It is known that most feeding insects supercool much less than non-feeding stages (SALT, 1953). The main cause of decreased supercooling is the presence of foreign particles on the food, for the atmosphere literally teems with dust particles that are generally good nucleating agents (DORSEY, 1938), and food exposed to the air cannot escape them. Unless such foreign matter is modified in the insect’s alimentary tract it will limit supercooling in the tract, and hence in the insect, to a few degrees. In contrast, some piercing and sucking insects, endoparasites, and similar feeders are able to feed without ingesting air-borne dust, and as a result their supercooling is only limited by nucleating agents native to the food or to their own tissues, whichever are the more effective (SALT, in press). Their supercooling is much greater than that of insects eating food contaminated by air-borne particles. The ability of feeding mandibulate endoparasitic insects to supercool much more than similar external feeders indicates that the mastication of the food does not affect the food’s supercooling. Support is thereby given to the idea that contaminants are responsible when present. When there is no feeding, as in eggs and pupae or during a moult, the nucleating agent is presumably contained in the tissues or perhaps in the residue of food often retained in the mid-gut. As pupae usually supercool about the same amount as eggs, their residual gut contents do not seem to be the limiting factor, and hence the tissues themselves are thought to contain the determining nucleating agents. In freshly moulted insects supercooling is greater than that of the preceding feeding stage (SALT, 1953) but does not always attain the level of egg or pupa, suggesting that in these cases at least the foreign matter or food retained in the gut is responsible for nucleation. As the action of a nucleating agent is dependent on its surface, it is to be expected that after ingestion the action may be altered by chemical action or by the coating of its surface with materials having less nucleating efficiency. I tested this idea by feeding nearly mature phytophagous larvae of two species food dusted with hexagonal crystals of silver iodide, which are very effective in nucleating supercooled water and are virtually insoluble. No reduction in supercooling was observed in the ensuing pupae. Unless the crystals were all excreted, those remaining must have been altered or coated. When pupae of Tenebrio molitor L. were injected with a suspension of silver iodide in water coloured with Fast Green dye, their supercooling ability was at first decreased, but after several hours

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regained its normal level. Control specimens pierced with a similar glass capillary needle but not injected recovered their normal supercooling point in about an hour, this being the time required for the wound to form a dry surface. The results indicate gradual suppression of the nucleating ability of silver iodide crystals by the tissues. Nucleation is also heterogeneous when the insect is injured in such a way as to expose a moist surface to the atmosphere, or when environmental water lies in contact with a permeable spot in the cuticle (SALT, in press). Foreign nucleating agents from the environment contaminate the wound or contact water, reducing supercooling in it. When freezing occurs it progresses into the insect, thereby nullifying the greater supercooling ability of the intact tissues (SALT, 1936). It will be shown later that the surface characteristics of the externally exposed water, whether from wounding, regurgitation, secretion, excretion, condensation, or wetting with free water, influence the action of nucleating agents contained in ‘it. Nucleation in non-feeding insects is probably heterogeneous also. The supercooling ability of a non-feeding stage of a species is always greater than that of its feeding stages, and is less variable (SALT,1953). This fact suggests the presence of a specific, characteristic nucleating agent that is a constituent part of the insect. Its physical nature determines its nucleating efficiency, but its chemical and anatomical nature can as yet only be guessed. I have found experimentally, however, that the point of origin of nucleation is not constant in a specific group of insects or in an individual frozen repeatedly; hence the agent is widespread in the body. INFLUENCE OF TEMPERATURE Temperature has the same influence whether water is supercooled in the pure state or in biological tissues. As the temperature falls below the freezing point, or in other words as supercooling increases, the probability of nucleation increases, at least down to -50°C. The effect of time on such nucleation is discussed in a later section. Considering temperature alone, it is well to remember that as the temperature decreases so also does the kinetic energy of the molecules. Solids, particularly crystalline solids, have an orderly, compact molecular arrangement and consequent low energy level as compared to liquids. Hence decreasing the energy level favours the phase change from liquid to solid, though the change can actually take place only at or below the freezing point because of vapour pressure considerations. In terms of molecular movements, greater kinetic energy increases the probability of formation of any given molecular configuration in a given time, but equally favours its destruction. Lower temperatures, or lower kinetic energies, decrease the probability of formation but increase the chance of survival if formation is accomplished. In addition to these two opposing influences of temperature, crystal growth has a positive temperature coefficient. The resulting composite effect for water is a rise in nucleation rate with decreasing temperature down to -50°C at least, and probably lower (HOLLOMON, 1950; MASON, 1956).On the basis of Tammann’s curve for piperine (TAMMANN, 1925; LUYET and GEHENIO,

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1940), the rate may fall at still lower temperatures, but this has not been established in the case of water. The possibility that nuclei are formed but do not grow to detectable size at such low temperatures must be considered. It will be shown in a later section that nucleation depends on time as well as temperature. For instance, if a specimen freezes within seconds after attaining a temperature of -3O”C, it will also freeze at higher temperatures if given time (SALT, 1950). It may take hours at --25”, weeks at -ZOO, and years at -15”, but some degree of probability of freezing, no matter how low this may be, exists as long as supercooling exists. The probability is largely but not entirely temperaturedependent; it also depends on the presence or absence of nucleating agents, and their efficiency if present. There is thus no difference in the basic influence of temperature in homogeneous and heterogeneous nucleation, even though nucleation will always take place more readily in the presence of nucleating agents than in their absence, when temperature, time, and specimen size are equivalent in each instance. Because of the difficulty of obtaining specimens that are entirely free from foreign matter, known or suspected cases of homogeneous nucleation have been confined to rather small masses (MASON, 1956; BIGG, 1953; MOSSOP, 1955; MEYER and PFAFF, 1935; WYLIE, 1953). Even more important is the fact that supercooling was not maintained for very long, as in all such experiments the temperature was lowered at some arbitrary rate until nucleation was obtained. Had the temperature been maintained at higher levels, freezing would have occurred eventually, as will be shown later. At lower temperatures, however, the rate of homogeneous nucleusformation in water increases abruptly at temperatures below -38°C. HOLLOMON (1950) and MASON (1956) have calculated that in this temperature range the rate increases by a factor of about ten for each degree fall in temperature. Neither faster cooling nor further reduction in specimen size can result in supercooling water much more than -40” because of this rapidly increasing rate of nucleation. INFLUENCE OF SURFACES The importance of the surface of a foreign nucleating agent, especially its similarity of spatial molecular arrangement to that of ice, has already been mentioned. Silver iodide, for example, has a crystal structure that more closely resembles ice than does any other substance, and it is also the most efficient agent known for the freezing of water. Surfaces other than those of crystalline solids may conceivably act as bases for nucleus formation, and in addition enclosing surfaces or interfaces of any kind may influence the action of nucleating agents in or near them. A common natural example of water-air interface is found in cloud droplets, whose freezing has been the target of a great deal of research by meteorologists. It has been established many times in the laboratory that mean supercooling ability increases as the size of water droplets decreases (HEVERLEY,1949; DORSCH and HACKER,1951; HOSLER,1953; BIGG, 1953; MASON, 1956). This is the expected relationship whether nucleation be homogenous or heterogeneous, as a larger mass

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of water contains more molecules to produce homogenous nucleation, or a greater number or variety of foreign nucleating agents to produce heterogeneous nucleation, than a smaller mass. However, surface area, surface curvature, and the extension of surface effects inwards are also related to droplet size, and it is quite likely that one or more of these affect nucleation. Essentially the same problems exist in capillaries, though here the water-air interface is concave whereas in drops it is convex. This difference, and indeed the water-air interfaces themselves, appear to be of little significance in capillaries. The water-capillary wall interface is more important, for all investigations have agreed in showing that amount of supercooling is inversely related to diameter in uniform capillaries. In tapered capillaries, HOSLER and HOSLER (1955) found that the greatest diameter was the determining factor. Volume of liquid must affect nucleation in capillaries for the reasons just set forth for droplets, but volume is not the important parameter. It is probable that surface effects dominate nucleation in both drops and capillaries. In insects, the respiratory tract is capillary in nature throughout most of its length. The tracheolar ends contain an aqueous solution that moves in and out along the tracheoles in response to the oxygen requirements of the cells. Air in contact with the liquid surface may contribute foreign particles, and certainly the liquid must pick up impurities while advancing distally along the tracheoles. Pores through the cuticle present a similar situation. However, the small diameter of tracheoles and cuticular pores ensures a high degree of supercooling, overriding the nucleating ability of foreign particles. Here again the implication is that a surface effect is the important factor. In biological systems water is seldom if ever in a pure state. It contains dissolved ions and molecules, suspended solids and immiscible liquids of various sizes down to colloidal, and is attached to hydrates. Whether the interfacial forces involved in any of these situations affect nucleation is not known. However, BIGG (1953) sus p en de d water drops from 50 microns to 2.5 cm in diameter at the interfaces between several pairs of immiscible liquids (carbon tetrachloride and ethylene dichloride, heavier than water; amyl acetate, toluene, and liquid paraffin, lighter than water). None of these appeared to affect the nucleation of the water. It was stated in a previous section that free water on the surface of an insect, in physical contact with internal moisture, as in a fresh wound, secretion, etc., supercools relatively little and on freezing inoculates the internal tissues. This can now be modified to take into consideration the nature of the water surface involved, particularly its curvature.. When, for example, insects were injured in such a way that haemolymph exuded and formed a flat surface, supercooling was minimal. If the exudate formed a drop, however, supercooling increased; the more convex the droplet surface, the greater was the supercooling. Further evidence is readily provided, perhaps most simply by cutting off appendages of various diameters. In very small insects the removal of an appendage did not raise the supercooling point unless an exudate appeared and spread into a flattened mass. With larger insects, a cut through a wide or thick appendage raised the supercooling point,

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whereas a cut through a slender one was not likely to do so. With a tapered femur, for example, supercooling decreased as the diameter of successive cuts increased. These relationships were not precise, of course, because the tissues create irregular patterns, capillary and otherwise, where they are cut. Another observation also points to curvature of water surfaces as important in nucleation. When larvae of Cephus cinctus were supercooled in a room cooled to -2O”C., breathing on them lightly from a distance of about 6 inches had no noticeable effect at first, though supercooled vapour must have condensed on them. After several breaths, however, some insects suddenly froze, and the number increased with further breaths, Cessation of the treatment allowed the moisture to evaporate and freezing from this cause ceased. It appears that successive applications of vapour from the breath built up condensation droplets on the cuticle of the insects, and when a critical size was reached (curvature reduced to a critical value) freezing occurred. The insect freezes along with the droplet if the water of each is connected, as through cuticular pores. In the above experiment foreign particles from the air or on the surface of the insect are apt to be the causative agents in nucleation, but their operational ability at the experimental temperature appears to be determined by some property of the droplets associated with size. Mass alone has some influence, but less than that of curvature, as already explained. Evidence of this was again supplied by observing larvae of C. &ctus supercooled to -20°C. When such larvae were injured so as to present a wound surface larger than capillary size freezing followed almost instantly, whereas injuries of capillary dimensions were without effect. Such observations strongly suggest that entry of foreign nucleating particles into the wounded surface is not responsible for its freezing; they suggest rather that the liquid surface nucleates quickly at -2O”C, when its curvature flattens to a value specific to that temperature. The capillary-sized injured surface does not freeze any sooner than the intact insect, though the chances of an efficient nucleating agent entering it are excellent. In both instances, moreover, the “native” nucleating agents that normally nucleate the insect from within the body are sure to be present at the injured surface. It may perhaps be justifiable to conclude that the flat surface of the large open wound raises the efficiency of these internal nucleating agents so that they are able to cause freezing at -2O”C, and no doubt at somewhat higher temperatures also, rather than at about -27”C, the mean supercooling point of the uninjured insects. If so, the concept that a nucleating agent has a fixed range of efficiency, in terms of temperature of nucleation, is untenable. The effect of time, discussed later, also contributes to make such a concept meaningless. In any case, the surface of the water, particularly its curvature, appears to be a dominant factor in determining the level of efficiency of nucleating agents. INFLUENCE OF TIME Most workers studying nucleation have given some consideration to rate of cooling, thus acknowledging the effect of time. This is natural in view of the assumption that chance collisions of molecules are required to build up an effective

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nucleus. Often the complication introduced by time has been circumvented by adopting a certain rate of cooling, but whenever a variety of rates has been used, the duration of supercooling has been brief. Even when supercooling has been prolonged at constant temperatures, a few hours or days has been considered sufficient. The only work known to the writer in which supercooling has been prolonged for periods up to several months was carried out with insects (SALT, 1950).

01 0

I

I

1

20

I

40

3

60

TIME IN DAYS

FIG. 1. Relationship between freezing and time at a constant temperature. A : Theoretical curve yt = yoewrt when r = 0.13 or 13 per cent. May be transformed to a straight line by plotting y on a logarithmic scale. B : Experimental curve obtained by exposing 200 larvae of Cephus cinctusto -20°C.

If the concept that nucleation results from chance suitable molecular orientations is correct, it allows us to derive the theoretical relationship between freezing and time for ideal conditions. These conditions are, first, a constant amount of supercooling, and second, identical experimental specimens. They impose a constant probability for nucleation and thus, if a certain percentage of the sample freezes in a given unit of time, the same percentage of the remainder will freeze in each ensuing unit of time. As the probability is continuous, nucleation is ideally continuous rather than intermittent, and the relationship is therefore that expressed by the compound interest law when used to calculate its negative counterpart, depreciation. The most convenient form of the formula is:where y1 is the number unfrozen at time t out of an original population yO, e is the base of natural logarithms, and Y is the probability expressed as rate of freezing. Such a curve is shown in Fig. 1 A, with ordinates converted to percentage frozen. Its approach to complete freezing is asymptotic; thus the possibility of a specimen remaining unfrozen always exists, no matter how great are the odds

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against it. The curve may closely approach its limit almost at once or only after a very long time, depending on the probability rate. For practical purposes, therefore, it is best to impose an arbitrary limit short of total freezing, e.g., 90 per cent, or 99 per cent frozen. The two ideal conditions assumed for the purpose of determining the type of relationship between nucleation and time are of course unattainable in practice. Heterogeneity of experimental material is inevitable and especially so when it is biological. Even if chosen for apparent uniformity, biological specimens will possess different probabilities for nucleation, quite apart from that imposed by temperature, resulting from differences in size, moisture content and its distribution, number or efficiency of nucleating agents, freezing point, etc. Under a constant amount of supercooling, then, individuals having greater nucleation probabilities will tend to freeze before those having less. With the passage of time, consequently, the rate of nucleation decreases, and the curve departs from the theoretical more and more in the direction of delayed nucleation. It is of interest to note in this connexion that abrupt or extensive irregularities reflect major heterogeneities in the population, and may give clues as to the nature of these. Insects constitute excellent material for experiments of this kind, particularly because supercooling can be maintained for long periods. The only drawback, in fact, lies in desiccation, which may become appreciable after several weeks or months in even the more resistant insects. Desiccation delays nucleation by lowering the freezing point, thereby reducing the amount of supercooling while the temperature is held constant. It also reduces the mass*of water and thereby the probability of nucleation; in addition it may reduce the probability through the increase in viscosity of the protoplasm. Desiccation is difficult to prevent in supercooled biological specimens because the vapour pressure of supercooled water is much greater than that of ice at the same temperature. However, it is possible to select species relatively resistant to desiccation which will provide satisfactory data for periods of several weeks or months. Hibernating larvae of Cephws cirzctus are suitable in this respect and also because they are available in large numbers, freezing produces a readily detectable whitening, and they possess a fairly uniform and narrow range of supercooling points. This last term applies to the temperatures at which freezing takes place when the insects are continuously cooled at a particular rate (SALT, 1950, 1956). For C. cinctus larvae such supercooling points lie a degree or two below -25°C ; hence time-to-freeze experiments were carried out at constant temperatures above this level. Adequate samples of larvae were exposed and the numbers frozen were periodically recorded. When the accumulative numbers or percentages of frozen insects were plotted against time the curves were of the form shown in Fig. 1 B. The deviations from the theoretical curve, Fig. 1 A, are as predicted, i.e. the probability decreases with time. The choice of 13 per cent for the probability rate, Y, in curve A is arbitrary, to fit curve B at the ii-day point. Actually the rate of curve B started out much higher than this (e.g. 20.5 per cent at one day) and fell to a much lower level. The section of the curve between 20 and 60 days corresponds closely to a rate of 0.168 per cent

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starting at the 20-day point. In practice the values of Y are of little use, since they are continually and irregularly decreasing. It is of interest to note that the deviation from the theoretical curve is typical also of physical systems when individual specimens are not identical. POUND(1952) froze a sample composed of an estimated log tin droplets of 2.5 to 5 micron diameter in a dilatometer at various constant temperatures. His data follow paths very similar to that of Fig. 1 B, and are readily explainable on the basis of droplet size. The larger droplets froze first and the smaller ones later during the 4.5 hour exposure, thus accounting for the decreasing nucleation rate. INFLUENCE OF TIME AND TEMPERATURE TOGETHER Comparisons of the progress of freezing at a series of constant temperatures are best made on the basis of the exposure times necessary to freeze 50 per cent of each sample (ET5,,). These values may be obtained in several ways, the most dependable being from a plot of probit of percentage frozen against logarithm of time. As this curve is usually close to linear between 30 and 70 per cent, the 50 per cent point is readily determined. Whichever way the data are plotted, gross irregularities indicate that the experimental population contains segments having distinctly different ranges of freezing probability. In practice such curves tell much about the nature and distribution of these differences. TABLE 1-EXPOSURRS NECESSARYTO FREEZE50 PER CENT OF C. cinctus TEMPERATURESBETWEEN - 15 AND - 26°C Temperature

Number

ET,,

I of tests 1 -15°C

3

-18°C -20°C -22°C -23°C -24°C -25°C -26°C

15 1 :

range (hr)

2100

-2800

20 -12:: 1 - 110 0.3 2.8 0.130.9 0.090.4 0.050.15

:: 8

I

LARVAE AT CONSTANT

I

Table 1 gives the ranges of median time-to-freeze values as experimentally determined for hibernating larvae of C. cinctus. Plotting time against temperature on various scales does not indicate any clear-cut relationship, although it is approximately linear when temperature is plotted against the logarithm of the logarithm of time. The ET,, values increase by a factor between 1.5 to 5 for each degree rise in temperature, with one exception. However, no trend is suggested by such ratios. INFLUENCE OF MECHANICAL FACTORS Friction and shock have been shown to induce freezing in water at high subzero temperatures. WYLIE (1953) discusses this aspect in some detail, and states that

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“YOUNG and SICKLEN(1913) found that water could be induced to freeze by the very violent impact of a hard steel point on a steel surface. These workers, by forcing the freezing temperature well above -5°C were able to find a well-defined relationship between the violence of the impact and the highest temperature at which it was effective in producing freezing. Their most violent impacts initiated freezing at temperatures above -0~1°C.” WYLIE calculated approximately the negative pressures necessary to raise the freezing point sufficiently to “cause true self-nucleation with a high probability”, and decided that “large instantaneous negative pressures are responsible for the ability of violent mechanical pressures to nucleate freezing in supercooled water.” DORSEY (1948) found that gentle rubbing of two solids in supercooled water, and a certain type of splashing, raised the temperature. at which spontaneous freezing occurred. The writer was unsuccessful in attempts to induce freezing by means of various vibrations in larvae of C. cinctus supercooled at -20°C. However, when these larvae and other insects supercooled a similar amount were shaken in a glass flask, impact with the container walls produced freezing. Some froze with little shaking, and within a few minutes all were frozen. When the insects were supercooled only to -15°C shaking was less effective. No damage was caused the larvae by the shaking, for when they were thawed and replaced at -20 or -15”, they resisted freezing as long as untreated controls. This evidence thus supports the hypothesis that negative pressures can raise the freezing point sufficiently to nucleate quickly at temperatures that otherwise would offer a low probability of nucleation. Acknowledgements-Criticisms of the manuscript by Drs. C. V. LUSENAand W. H. COOK of the Division of Applied Biology, National Research Council, Ottawa, and by several staff members of the Science Service Laboratory, Lethbridge, are gratefully acknowledged. I am especially indebted to Mr. NORMAN S. CHURCH of this laboratory, whose critical judgment led to the clarification of several interpretative aspects of the paper. REFERENCES BIGG E. K. (1953) The supercooling of water. Proc. phys. Sot. Lond. (B) 66, 688-694. DORXH R. G. and HACKER P. T. (1950) Photomicrographic investigation of spontaneous freezing temperatures of supercooled water droplets. Nut. Adv. Corn. for Aeronautics, Tech. Note 2142. DORSEY N. E. (1948) The freezing of supercooled water. Trans. Amer. Phil. Sot. 38,247-328. HEVERLEY J. R. (1949) Supercooling and crystallization. Trans. Amer. geophys. Un. 30, 205-210. HOLLOMON J. H. (1950) Heterogeneous nucleation. 1n Thermodynamics in physical metallurgy. Amer. Sot. Metals, 161-177. HOSLER C. L. (1954) Factors governing the temperature of ice-crystal formation in clouds. Proc. Toronto Met. Conf. 1953 (Roy. Met. Sot.), 253-261. HOSLER C. L. and HOSLER C. R. (1955) An investigation of the freezing of water in capillaries. Trans. Amer. geophys. Un. 36, 126-132. LUYFT B. J. and GEHENIO P. M. (1940) Life and death at low temperatures. Biodynamics. Normandy, MO., U.S.A. MASON B. J. (1956) The nucleation of supercooled water clouds. Sci. Progr. 44, 479-499. MEYER J. and PFAFF W. (1935) Crystallization of melts. 2. anorg. Chem. 224 305-314.

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MOSSOP S. C. (1955) The freezing of supercooled water. Proc. phys. Sot. Lond. (B) 68, 193-208. POUNDG. M. (1952) Liquid and crystal nucleations. Industr. Engng. Chem. (Industr.) 44, 1278-1283. SALT R. W. (1936) Studies on the freezing process in insects. Tech. Bull. Minn. Agric. Exp. Stu. 116. SALT R. W. (1950) Time as a factor in the freezing of undercooled insects. Cunad. J. Res. (D) 28, 285-291. SALT R. W. (1953) The influence of food on the cold-hardiness of insects. Cunad. Ent. 85, 261-269. SALT R. W. (1956) Influence of moisture content and temperature on cold-hardiness of hibernating insects. Canad. J. Zool. 34, 283-294. SALT R. W. Cold-hardiness of insects. Proc. Tenth Int. Congr. Ent. In press. TAMMANNG. (1925) (translated by Mehl) The States of Aggregation. D. Van Nostrand Co., N.Y. WYLIE R. G. (1953) The freezing of supercooled water in glass. Proc. phys. Sot. Lond. (B) 66, 241-254. YOUNG S. W. and VAN SICKLENW. J. (1913) The mechanical stimulus to crystallization. J. Amer. chem. Sot. 35, 1067-1078.