I. THE PRIMARY ACT RADIATION ABSORPTION AND ENERGY LOSS BY PRIMARY AND SECONDARY PARTICLES BY F. W. SPIERS Department of Medical Physics, The University, Leeds Received 14th February, 1952 The processes of absorption of ionizing radiation are reviewed and their relative importance is discussed in terms of quantum energy. Examples of the energies of secondary importance is discussed in terms of quantum energy. Examples of the energies of secondary electrons are given for commonly used radiations. The modes of energy loss by fast charged particles are described and the magnitude of the energy required to produce one ion-pair is discussed in reIation to particle typ:: and speed and the pro- perties of the absorbing medium. Some indication is given of the initial spatial dis- tribution of the ionization.The purpose of this article is to review the processes by which ionizing radi- ation transfers energy to matter and the manner in which secondary electrons dispose of the energy thus acquired. Knowledge of radiation absorption pro- cesses is now very complete and can be translated into forms directly applicable to the problems of radiation chemistry and radiobiology. The theory of the loss of energy by fast charged particles is also well founded and experimentally estab- lished-for example, by accurate a-ray range data. In some directions, however, knowledge is less complete. The stopping powers of various media for electrons are at present deduced from the more precise information on a-particles; the energy lost by an electron in producing one ion-pair in water is inferred from the value for a-rays in water vapour and the partition of this cnergy between ioniz- ation and excitation of the water molecules can only be very roughly estimated.Nevertheless a useful qualitative picture can be given of the initial distribution of ionization in a liquid, which accords with a considerable body of experimental findings on the chemical effects of radiation. A number of excellent reviews have already appeared and, among them, those of Gray 1 and Lea 2 contain most of what is known or can be reasonably surmised about this subject at the present time. INTERACTION OF RADIATION WITH MATTm-When electromagnetic radiation traverses matter it is attenuated by scattering processes and by transference of energy to atomic electrons.For X-rays and y-rays the photon energy may be transferred in whole or in part to an electron, with the result that the latter is set in motion with an energy greatly in excess of its binding energy in the atom or molecule. Unlike the photon, this pro-jected electron has a limited range in liquids and solids and usually dissipates all its energy in the medium in which it arises. For this reason the radiation energy transformed to kinetic energy of secondary electrons is referred to as the real or true energy absorption in the medium. Some of the scattered electromagnetic radiation will be subsequently absorbed in any extended medium and thereby contribute also to its real energy absorption. Factors such as multiple scatter and the extent and shape of the medium make it difficult to calculate the magnitude of this scatter contribution theoretically. The usual and most satisfactory procedure is to measure the 1314 ABSORPTION AND ENERGY LOSS total dose or energy absorption due to both primary and scattered radiation under conditions which accurately simulate those of the experimental irradiation.The energy absorption of a medium is determined by the sum T~ -t ua + K~ of the absorption coefficients which refer respectively to the photoelectric, Compton recoil and pair production processes. Since these depend in different ways on the energy of the radiation, it is of interest to indicate briefly their relative im- portance in the absorption coefficient of water. PHOTOELECTRIC ABSORPTION COEFFICIENT .r,.-This process is important for photon energies below 0-2 MeV and its magnitude varies approximately as $24, Values of T~ may be taken from compilations of experimental results 3, 4 or from empirical formulae.2> 5 The energy given to the electron is the photon energy less the binding energy of the electron which, for water, can never amount to more than 0.5 keV for an electron in the K shell of the oxygen atom.COMPTON RECOIL COEFFICIENT u,.-The magnitude of this coefficient, which gives the fraction of the photon energy imparted to the recoil electron, is cal- culated by the formulae given by KIein and Nishina.6 The mean energy of the recoil electron E is a& liv but the electron energies are continuous over a range given by h where 6A = - (1 - cos 4).The recoil electron energy will therefore vary from mc 0, when the photon is undeflected, to a maximum when SA = ~ for a photon scattered through c,b -- 180". PAIR PRODUCTION COEFFICIENT K,.-The absorption coefficient K for pair production is proportional to 2 2 and increases with increasing photon energy above a threshold energy at 2mc 2 (1.02 MeV). The energy available as kinetic energy of the created electron pair is therefore hv - 27nc2 which, in the most probable distribution, is divided equally between the positron and negatron. The real energy absorption is given by 2h mc Values of K have been calculated by Heitler 7 and values of K~~ for air and of real energy absorption of a number of elements relative to air, have been given by Mayneord.8 If absorption data for any medium and the radiation energy are accurately known then the energy absorption in ergs/g can be deduced from a measurement of the dose in rontgen," at least in the energy range up to 2 MeV.The energy absorption in ergs/g r for water and for a number of values of 2 is shown in fig. 1 over the range 0.01 to 1.0 MeV. At low energies the photoelectric coefficient predominates but above 0-2 MeV the absorption is due almost entirely to the Compton recoil process and depends only on the number of electrons per g. The energy absorption per r for water shows little variation throughout this range of photon energy, a fact which justifies the use of the rontgen as a unit of dose for therapeutic irradiation of the aqueous tissues of the body. Fig. 2 shows the absorption of radiations of high energies above 1 MeV, and indicates the region where pair production is effective.The energy absorption is given relative to water since in this region the rontgen becomes unsuitable as a unit of dose. The * The rontgen is defined as " the quantity of X or y radiation such that the associated corpuscular emission per 0.001293 g of air produces, in air, ions carrying one electro- static unit of quantity of electricity of either sign ". It is equivalent to an energy absorp- tion of 84 ergs in 1 g of air,F. W. SPIERS 15 absorption again becomes dependent on 2, the coefficient increasing with the photon energy. piled in table 1 for a number of photon energies in the range 10 keV and 1-25 MeV, where radiation absorption is due to the photoelectric and recoil processes.Radiations having average photon energies corresponding to the first four lines of table 1 are produced by X-ray tubes operating at approximately twice the listed DATA FOR WATER FOR SOME COMMONLY USED RADIATIONS.-Data are COm- FIG. 1. photon energies with suitably chosen filters. The fifth radiation listed is the mean y-ray energy of the C060 isotope. Proportions of the two types of secondary electron are given, together with the proportions of the dose to which they give rise. Large differences between photoelectron energies and the mean energies of the recoil electrons are evident and corresponding differences exist between their ranges. In these circumstances it becomes difficult to assign to the secondary electrons a mean energy which has much practical significance; still less can the electrons be regarded as having a mean range.TABLE DA DATA FOR WATER * photon energy 10 KeV 25 ? 3 50 ? 3 100 ? ? 1.25 MeV types of electron recoil photo Y ? 3 ) Y Y 9 ) :< numbers ”/, contribu- electron of elcctrons tion to dose energies kV ‘ $ ~ ~ ~ ~ ~ 4.2 95-8 41.0 59.0 84.0 16.0 97.4 2.6 100.0 0.1 99.9 2.9 97.1 30.0 70-0 84.0 16-0 100.0 0.18 9.5 1.1 1 24.5 4.05 49.5 13.7 99-5 600-0 0.006 2.3 0.06 12-1 0.52 42.0 4.35 140.0 2150.0 ion pairs per micron mean for 1160 148 629 74 279 57 112 72 25 - 10 10 _______- mean P and R 147 - 72 - 42 - 0.0 (also pair production < 0.2 %) * W taken as 28 eV per ion pair ; 9 range data from Lea 2 and Siri.10 MEAN ION DENSiTY .-If an electron has an initial energy E in keV and we follow Gray 9 in taking W as 28 eV per ion pair in water, a mean ion density can be calculated as - A = 1000 E/28 R = 35-7 E’/R ion pairs per micron, (3)16 ABSORPTION AND ENERGY LOSS where R is the range in microns of the electron of energy E.Ion densities calculated in this way are listed separately in table 1 for photoelectrons of single energy E p and recoil electrons of average energy ZR. The mean ion densities given in the last column of table 1 have been derived by taking the summated electron energies npEp + n R G and a total range equal to npRp + nRRR, where n p , Ep, R p and F ~ R , ER, RR refer to the numbers, energies and ranges of the photo- and recoil-electrons respectively. The variation of this mean ion density over a range of photon energies from 10 keV to 1.25 MeV is shown in curve J L of fig.3. The broken curve I in this figure is taken from calculations of mean ion densities by Gray l b who used the mean recoil and photoelectron energy and the range cor- responding to it as given by Lea.2 The curves show similar qualitative features but differ in absolute values by a factor of two in the region of photon energies between 30 and 70 keV. The two methods of calculating the mean ion density become identical where only one type of secondary electron is involved, but differ when significant numbers of both recoil and photo-electrons of widely different initial energy are produced. FIG. 2. The points B, C and D in fig. 3 are taken from some unpublished work which Prof. H.E. Johns has very kindly allowed me to use. Cormack and Johns 11 have made. detailed calculations of the energy distributions of secondary electrons from a number of commonly used radiations. By using the complete spectral distribution of the radiation, they have derived the numbers of electrons set in motion with energies within successive 5 keV intervals and from these they have calculated mean ion densities in a manner similar to that used by the writer. It will be seen that the mean ion densities obtained for complete spectral ranges by the detailed analyses of Cormack- and Johns are of the same order as the values given in curve IT in fig. 3 by the elementary calculation for photons of single energies. It is reasonable to take curve I1 in fig. 3 as giving the order of the mean ion density in relation to the average photon energy of a heterogeneous radiation.Tt is evident, however, that a mean ion density describes the ioniza- tion more adequately at both low and high photon energies than in the inter- mediate energy range. At low energies photoelectrons predominate arid at high energies the recoil electrons, although not homogeneous, have energies mainly in the region where specific ionization is a slowly varying function of electron energy. Tn the intermediate range of photon energies the interpretation of a radi- ation effect may need to be made in terms of a distribution of ion densities rather than a simple average.F . W . SPIERS 17 FIG. 3. FIG. 4.18 ABSORPTION A N D ENERGY LOSS Some graphical data given by Cormack and Johns illustrate in detail the energy distributions produced by heterogeneous X-rays.Fig. 4 reproduces parts of fig. 1 and 6 of these authors’ paper and shows the spectral distribution of dose for a lightly filtered 200 keV beam (B) and a heavily filtered 200 keV beam (C). Fig. 4 also gives the instantaneous distribution of electron energies at a point in water for these two radiations; the large differences in the character of the photon spectrum are present to a much smaller extent in the electron energy dis- tribution. Fig. 5 gives the distribution of ion densitjes among the secondary electrons for the radiations B and C together with the relative distribution for C060 y-rays (Cormack and Johns,ll parts of fig. 9 and 10). Fig. 5 also gives a FIG.5. representation derived from Cormack and Johns’ data of the dose distributed among the ion density values, which incidentally leads to the evaluation of a mean ion density. The results illustrate very clearly the small range of ion densities for the high energy C060 y-rays (the range is likewise small for Ra y-rays), and the difficulty of assessing the significance of a mean ion density in the intermediate X-ray range from 100 to 200 keV. Another way of arriving at a mean ion density would be to take a mean of the ion densities of the recoil and photoelectrons weighted according to their con- tributions to the dose (Gray, private communication). Values nearer to curve I in fig. 3 are then obtained and such a mean might have more significance for chemical effects.If an average is taken in this way, however, for the distribution shown for Cormack and Johns’ radiation C in fig. 5 , a mean ion density coincident with their value is obtained-i.e. one which is below that given by the various approximations considered.F . W. SPIERS 19 ENERGY LOSS BY CHARGED PARTICLES.-When a charged particle traverses matter it loses energy by inelastic “ collisions ” with atomic electrons in which the atoms may be excited or ionized. The electrical disturbance caused by the passage of the charged particle, and therefore the energy transferred to the atomic electron, depends on the particle’s charge and speed, on the binding energy of the orbital electron and on the closeness of the collision. In general, ejection of an atomic electron, i.e.ionization, will occur in close collisions near the track of the moving particle and excitation of orbital electrons will occur in glancing collisions at greater distances from the track. The loss of energy per unit length of the path of the particle can be written : where N is the number of atoms of atomic number 2 per cm3, z and 7) are the charge and velocity of the particle and e and rn are the charge and mass of the electron. B is the “ stopping number ” of the medium which can be calculated from the theory given by Bethe 12 based on quantum theory. A recent review and statement of this theory has been given by Bohr.13 The Bethe formula for the stopping number for electrons is R == 2 In --- - In (I - /32) - /3*, (23 where E i s the ‘ mean excitation potential ’ of the atom.The function B increases slowly with particle energy and hence dT/dx at first falls as the particle energy rises, owing to the 2.2 term in eqn. (4). This term becomes constant as w approaches the velocity of light and consequently the dT/dx curve passes through a broad minimum and then rises slowly for very high particle energies. The formula, which is derived for a simple hydrogen-like atom, can be applied to other electronic configurations if the mean excitation potential Ecan be deter- mined. This is usually done empirically by adjusting E to fit known energy- range data, Since experimental data of sufficient precision are difficult to obtain with electrons, values of have been deduced by fitting the theoretical formula for a-particles to a-particle range data.Mano 14 has in this way derived values of E which, in the absence of other data, are used in calculating B for electrons. From Mano’s values of 16 eV and 86 eV for H and 0 atoms, a logarithmic mean value of 69 eV is obtained for water, and this figure is used in Lea’s calculations of energy loss and range. Cormack and Johns 11 have used a value of 80 eV for ’E for water in some of their calculations but this makes only a very small difference in the value of dT/dx. The variation of energy loss of fast electrons in water is shown by the full curve A in fig. 6. The formula for B is not valid when the particle velocity approaches that of the orbital electrons of the atoms of the medium, and B is zero for velocities below the lowest velocity of the atomic elec- trons.The energy loss therefore follows the familiar Bragg type of curve showing a maximum and then a sharp fall to zero at low energies. Fermi 15 modified the Bethe formula to allow for polarization of the medium by the field of the moving particle which effectively reduces the value of B. Halpern and Hall 16 have elaborated this idea, replacing Fermi’s single frequency model of the absorbing atom by a multiple frequency model and deriving cor- rections which are illustrated in fig. 6. For water, Halpern and Hall’s correction begins to show at energies above 1 MeV, and when applied to the collision losses calculated on Bethe’s formula, gives the broken curve B in fig. 6, which only departs significantly from A at high energies. The insert in fig.6 relates to carbon, for which the corrections suggested by Halpern and Hall amount to a decrease in the stopping power of some 10 %, even at low electron energies.20 ABSORPTION AND ENERGY LOSS Halpern and Hall find thcir value of the stopping power of carbon for 10 MV /3 particles to be in good agreement with measured values at this energy. A careful comparison by Gray Ic of the ionization produced by Ra y-rays in a carbon- walled ionization chamber and in a gelatin-walled chamber did not reveal any differences of the magnitude suggested by Halpern and Hall’s theory for carbon as against water. Besides energy losses by collision, a charged particle can be accelerated in the field of the nucleus and lose energy by emitting radiation. This radiative process-the production of Bremsstrahlung-is insignificant for heavy particles but becomes important for electrons at energies greater than 2 MeV. The curve C in fig.6 indicates the incidence of radiative loss by electrons in water. The energy loss in this process increases roughly in proportion to the particle energy and is proportional to the square of the atomic number of the medium traversed. The expression for the stopping number B of light elements for a-particles can be simplified by omission of the relativity corrections necessary for P-particles. Since corrections for the Fermi effect depend on the particle’s speed and arise only for very high energies, the collision loss for cc-particles can be written dx 112 L.2 In (y), (6) d T 4re4z2NZ _. - - ___ where the symbols have the same meaning as in eqn.(4) and (5). Since the charge z is now twice that of the electron, the energy loss of the v,-particle is four times that of an electron of the same speed. The a-particle, however, has a mass some 7000 times greater than the electron and consequently much greater energy for the same speed. An cc-particle having the same energy as an electron has a much lower velocity and an energy dissipation of the order of 1000 times that of the electron. The formula (6) is not precise below 1 MeV because the cc-particle velocity is then comparable with the velocity of the orbital electrons in the absorbing atoms. A comprehensive review of the stopping powers of gases and liquids for a- particles has been given by Gray lL7 in which substantial evidence is presentedF .W. SPIERS 21 for the validity of the Bragg additive law of atomic stopping power. The stopping power of water, as measured by Michl17 and by Philipp,lS was greater, however, than the value for water vapour which itself followed the Bragg law. The only recent determination of the stopping power of water for a-particles, made by Appleyard,lg has confirmed the earlier experiments and gives a value about 12 % greater than that for water vapour. Gray 1" has pointed out that evidence of discrepancies for other liquids is not entirely convincing and until more extensive experimental data are available it is safest to assume the validity of the Bragg law in calculating the stopping powers of gaseous and liquid compounds. expended in creating one ion pair in air has been well established as 32.5 eV for electrons and 35.1 eV for cc-particles.1" The value of W for electrons is dependent on the electron energy only at energies below 10 keV.According to a formula given by Gerbes,zo W increases by 1 % as the energy decreases from 100 keV to 10 keV, and by amounts given in table 2 for energies less than 10 keV. TOTAL ENERGY EXPENDED IN THE FORMATION OF ONE ION PAIR.-The energy w electron energy in keV TABLE 2 10 5 3 2 1 % increment in W over value for fast electrons 1 3 5 8 17 Appleyard 21 has recently compared the mean energies expended per ion pair by a-particles traversing air and water vapour, and finds the value of Wfor water vapour to be only 88% of that for air. Applying the same ratio to ionization by electrons the value of W for electrons traversing water vapour would be 28 eV.This lower value would appear to be in closer accord with inferences from chemical experiments and has been used in calculating the specific ionizations given earlier in the paper. The mean energy expended per ion pair formed is also of the order of 30-35 eV For many gases in spite of great variation in the ionization potentials of the mole- cules concerned. Fano 22 has pointed out, however, certain complementary aspects of the partition of energy between ionization and excitation. In atoms having rather loosely attached electrons and low ionization potentials, the value of W is maintained by the considerably greater proportion of energy which then goes in exciting electrons to oscillate intensely in states of low excitation.If the electrons are stiffly bound and the ionization potential is high, excitation is less probable and less energy is expended in that process. Hence although W is nearly constant, the proportions of the energy appearing as ionization and excitation will vary with the type of atom or molecule irradiated. The value of W determines the number of ions formed by a given dose and this, for some substances at least, will be roughly constant. On Fano's view, however, the accompanying number of excitations may differ considerably from one substance to another. SPATIAL DISTRIBUTION OF THE IoNs.-The ion pairs created by the fast particle are not uniformly distributed along its track ; they occur discontinuously in groups or clusters of varying size.Lea 2 calculated the distribution of cluster size along electron tracks and also derived the contributions made by branch tracks, or delta rays, which arise both from electron and heavy particle tracks. Gray 9 has set out the presumed distribution of ions on the present available evidence and the salient features only of the distribution will be mentioned here. Less than half the clusters formed along an electron track contain one ion pair, 5 % of the clusters may contain as many as 16 ion pairs and the average cluster has 3 ion pairs. If a &ray track is produced by the electron, its characteristics will be similar to those of the primary particle and need not, in this case, receive special attention. The average cluster spacing can be derived simply from the mean ion demity as S =z 3,'E microns.The mean cluster spacings for the secondary electrons produced by the photon energies between 10 and 1000 keV, -22 ABSORPTION AND ENERGY LOSS are shown in fig. 7 ; they relate to the data used in table 1, and are derived from curve I1 in fig. 3. Since the positive ions probably lie within a few mp of the track, and the negative ions (produced by the ejected electrons) are some 15 mp from the track, it is evident that only at photon energies below 8 keV are the cluster separations of the same order as the cluster dimensions. At 1.5 keV the cluster spacing is the same as the mean separation of the positive ions and there is a more or less uniform distribution of positive ions along the track.The mean ion densities for a-rays in water are of the order of 3500 to 4500 ions/,u and the density of positive ions along the track is several times greater than that for a 1 keV electron. The conditions close to the track are such that dissociation of the positive ion H20f into H+ and OH leaves a very high concentra- tion of OH radicals, which can form H202, and a central region of positive charge which may well produce electric fields high enough to affect the spacing and movement of the negative ions surrounding it.23 With the exception of reactions sensitive to H202 this concentration of ionization is too great to be very efficient chemically and, in one case at least, the chemical action of radiation has been FIG. 7. accounted for wholly by effects outside the immediate vicinity of the cc-particle track.Thus Dale, Gray and Meredith24 showed that %rays, arising from the main track and carrying ionization out to distances of 1 to 2 p from it, could account for the observed x-ray inactivation of the enzyme carboxypeptidase. The proportions of the total ionization produced outside the a-ray column, re- garded as having a radius of 0.015 p, were given as below. initial or-particle energy TABLE 3 2 4 6 8 MeV proportion of dose beyond Y = 0.015 p 2.5 6 9 11 % The highest ion densities which can be produced are those along the tracks of atomic particles and fission fragments, the latter producing values as high as 130,000 ionslp. These ionizing particles do not lend themselves readily, however, to chemical experiments.Nevertheless, a very wide range of ion densities lies between the low ion densities associated with y- and hard X-rays and the high ion densities produced by ct-rays. Conditions in and near the track of the densely ionizing a-particle differ not merely in degree but in character from those associ- ated with fast electrons. Transition from the low to the high ion density condition might be expected when the cluster spacing along the track is of the same order as the separation of the positive ions in the cluster. = 4 mp This would occur atF . W . SPIERS 23 for electrons produced by 1.5 keV X-radiation. Effects which depend on the distribution of ions within the cluster would not be expected to vary much with mean ion density until 3 approaches values of the order of 15 mp.Little can be reported of the spatial distribution of excitations except that it will be unlikely to differ considerably from that of the ionizations. Although the excitations will be likely to occur farther from the track of the particle than the positive ions, the majority will still be within a few millimicrons of the centre of the track. The spacing of excitations along the track is probably very similar to the linear distribution of ions. If the In (Z,nv2/E) term in eqn. ( 5 ) and (6) is replaced by two separate terms in Ei and ze, for the mean ionization and mean excitation potentials respectively, the value & might be expected to be perhaps 10 times less than E . Since the terms are logarithmic, the excitation term might then be twice the ionization term at low particle energies.Over most of the 20 $0 6 0 80 FIG. 8. particle range, the difference in the separate log terms would not be great and consequently the effect on dT/dx, and therefore on &, would be small. APPENDIX.-h addition to the data given in table 1 and fig. 3, the method of Cormack and Johns 11 has been applied to the radiation spectrum of an X-ray tube operating at 100 keV. The mean photon energy of this beam is then derived as 53 keV and the numbers of recoil and photoelectrons generated in water are respectively 78 % and 22 %. The complete distributions of the secondary electrons are shown in fig. 8 where they are compared with the single recoil and photo- electron energies used to compile the data for the 50 keV photons in table 1. The mean ion densities, computed by methods I1 and I11 in fig. 3, are 61 and 105 ion pairs/micron and these lie respectively close to curve 11 and a little below curve I11 in fig, 6 .24 GASEOUS IONS AND THEIR REACTIONS 1 (a) Gray, Proc. Camb. Phil. SOC., 1944, 40, 72. (b) Gray, Brit. J. Rad., suppl. 1, 2 Lea, Actions of Radiations on Living Cells (Cambridge University Press, 1946). 3 Allen, Compton and Allison, X-ray in Theory and Experiment (Macmillan & Co., 4 Victoreen, J. Appl. Plzysics, 1943, 14, 95. 5 Walter, Fortsch. Geb. Roentgen, 1927, 35, 929. 6 Klein and Nishina, 2. Physik, 1929, 52, 853. 7 Heitler, Tlie Quantum Tlteory of Radiation (Oxford University Press, 1936). 8 Mayneord, Brit. J. Rad., suppl. 2, 1950, 138. 9 Gray, J. Chim. Phys., 1951, 48, 172. 1947, 7. (c) Gray, Brit. J . Rad., 1949, 22, 677. 1935). 10 Siri, Isotopic Tracers arid Nuclear Radiations, (McGraw-Hill Book Co., 1949). 11 Cormack and Johns, Brit. J . Racl. (in press). 12 Bethe, Handb. Physik, 1933, 24 (i), 273. 13 Bohr, Det. Kgl. Dattske Vidensk. Selskub, Math-fys. Meddel., 1948, 18, 8. 14 Mano, J . Physique Rad., 1934, 5, 628. 15 Fernii, Physic. Rev., 1940, 57, 485. 16 Halpern and Hall, Physic. Rev., 1948, 73, 477. 17 Michl, A k d Wiss. Wien., 1914, 123, 1965. 18 Philipp, 2. Physik., 1923, 17, 23. 19 Appleyard, Proc. Canib. Phil. SOC., 1950, 47, 443. 20 Gerbes, Ann. Physik, 1935, 23, 648. 21 Appleyard, Nature, 1949, 164, 838. 22 Fano, Physic. Rev., 1946, 52, 44. 23 Read, Brit. J . Rad., 1949, 22, 366 ; 1951, 24, 345. 24 Dale, Gray and Meredith, Phil. Trans. Roy. Sue. A , 1949, 242, 33.