=

C-CH(C)(C)

is given by the approximate solution of the equation sin (a + t) sin 60° sin (a + B + 2t) (B) In order to arrive at the domains of the various atoms Ingold made use of Traube's determinations of the atomic volumes of carbon (9.9 and hydrogen (3.1). These values are now regarded as incorrect Instead of using particular values of the atomic volumes it is preferable to make use of the well-established ratio (4: 1) between the atomic volumes of carbon and hydrogen, determined from a very large number of compounds 14.

12 13

Although the angles calculated by the different methods are approximately the same, the difference between the two arrangements is shown by the fact that, in the case of the methylene group, the tangent angles are all 56.6° in the second arrangement, whereas in Ingold's arrangement they are 0° and 3.57° when the central carbon atom is small or interpenetrating, and 23.8°, 15.4° and 42.8° when the central carbon atom has its normal volume.

The angles of strain in the cycloparaffins may now be calculated using the alternative

Cyclobutane Cyclopentane

TABLE III.

115.3°

116.6°

...

26.6 12.6

...

28.3 13.3

3.6

...

4.3

It is significant that Ingold's strain angles do not show the maximum strain in the cyclobutane ring which he anticipated, and it is probably for this reason that he has preferred to calculate "by how much " the terminal atoms in n-propane, n-butane, etc., must approach one another in forming a cyclopropane, cyclobutane, etc., ring. It should be noted however, that the approach values (Table IV.) calculated from Baeyer's angle also show a maximum at cyclobutane.

It is obvious that the presence of a gem dimethyl group will facilitate the formation of those rings which are produced by an inward deflection of the normal angle of the carbon valencies, since the amount of approach of the terminal carbon atoms necessary for ring formation will be diminished. The stability of these ring systems containing a gem dimethyl group should also be increased. Kötz15, however, claims that the stability of the trimethylene ring is decreased by the introduction of alkyl groups so that, for example, 1:1 dimethylcyclopropane is less stable that methylcyclopropane. It is therefore clear that the "volume factor" is not always the only one which influences ring stability. Ingold (loc. cit. and subsequent papers), has advanced a considerable amount of evidence in favour of his hypothesis and although it is impossible here to examine the vast amount of experimental results

which he has obtained, a few points may be dealt with.

Ingold has examined the elimination of bromine from bromo dibasic esters, C2H, OOC.CHR (CH2) CR' (Br) COOCH, under two sets of standard conditions (a) using dilute aqueous sodium carbonate (b) using strong methyl alcoholic potassium hydroxide. The main reaction in the first case is the replacement of bromine by hydroxyl, while in the second case a small amount of unsaturated acid is produced, but the main products are the hydroxy acid, and the ring acid, one of which may predominate. By comparing the relative amounts of the hydroxy acid and the ring acid produced, it is claimed that non-steric factors affecting ring formation are eliminated to a large extent, since it is reasonable to suppose that changes in the reactivity of the bromine atom would be approximately equally effective in retarding or stimulating the formation of both these reaction products. The results so obtained are summarised in Table V.

They appear at first sight to favour Ingold's hypothesis, but it is necessary to examine the assumptions involved more fully. It does not necessarily follow that alteration in the reactivity of the bromine atom will influence the formation of the hydroxy-acid and the ring acid to an approximately equal extent, because the activity of the hydrogen atom eliminated in ring formation is also an important factor. An instance in which this factor is operative and which illustrates the insufficiency of the "volume factor" to account for the whole of the phenomena encountered is to be found in the behaviour of the bromo-a methyl glutaric esters. Ingold1 remarks that it is curious that when the isomeric mono-bromination products of a-methylglutaric ester are treated with dilute alkali, they are converted into the hydroxy-acids quantitatively, whereas a-bromoglutaric ester, under the same standard conditions, gives rise to a small quantity of the ring acid as by-product. This is held to be the

more remarkable when count is taken of the lability which tertiary hydrogen usually displays as compared with secondary hydrogen in an otherwise similar situation, examples of which are given. Now, if we exclude steric hindrance as a factor influencing the chemical reactivity of an atom, the relative activity of an atom (in the same or different compounds) in the same type of reaction will depend upon the alternate and general polar influences exercised upon it by the other atoms in the compound. (Lapworth", Robinson 18 19.) It is therefore clear that a tertiary hydrogen atom may be more or less "reactive" than a secondary hydrogen atom according to the nature of such influences. In the examples quoted by Ingold the tertiary hydrogen atoms are under polar influences which render them "reactive" than the secondary hydrogen atoms. In view of the fact that Ingold himself had shown that a-methyl glutaric chloride yields on bromination the y-bromo derivative almost exclusively, the isomeric a-bromo compound being formed in very small amount, it is not surprising that the tertiary hydrogen atom which is replaced by bromine with such difficulty also shows a reluctance to unite with bromine and produce the ring acid.

more

99

The results of a brilliant series o finvestigations by Thorpe, Ingold and their coworkers", which led to the discovery of ring-chain tautomerism, seem to indicate that a larger deflection of the " methylene carbon valency angle is produced by the gem-diethyl, gem-dipropyl and similar groups than by the bem-dimethyl group, and at the same time constitute the most weighty evidence for the "volume effect " that has so far been brought forward. It is difficult to see how the values of the deflected angles could be calculated by the method adopted by Ingold for the calculation of the "methylene " carbon valency angle. The tangent method," however, should allow these angles to be calculated to a first approximation.

66

II.

RUZICKA'S MODIFICATION OF THE BAEYER STRAIN THEORY.

During the preparation of this paper for publication the author received the current number of the Helvitica Chimica Acta, containing a paper on the Baeyer strain theory by Ruzicka and his co-workers'. Some of

the conclusions arrived at by these authors are identical with those here recorded.

an

Ruzicka considers that the relative ease of formation of carbon rings containing up to ten atoms is governed by two factors (a) the ease of formation of an intramolecular C-to-C bond (main factor), and (b) the strain in the ring compound formed (subsidiary factor). The ease with which intramolecular carbon-to-carbon bond is formed is assumed to decrease continuously with increasing separation in the chain of the carbon atoms concerned. The ring strain decreases from dimethylene to pentamethylene and then remains approximately constant. The result of these two factors is to produce a large decrease in ease of formation in passing from dimethylene to trimethylene and a sharp rise in passing from tetramethylene to pentamethylene.

It

The factor (a) is a measure of the influence of the starting materials upon the ease of ring formation, and, so far as it goes, is a recognition of a general polar effect. cannot be claimed, however, that the reactivity will always fall off continuously as the length of the chain is increased. This was recognised many years ago by Michael21 and at the present time it is stil luncertain whether part of the general polar effect may not be transmitted directly through space and so produce an irregular increase (or decrease) in activity in certain cases. (Compare Lewis22.) The presence of strongly polar groups (Lapworth and Robinson, loc. cit.) will also render Ruzicka's assumption untenable in many cases, for, although such effects are not transmitted through a chain of more than two saturated carbon atoms, a hydrogen atom at one end of the chain may be "activated" by a neighbouring polar group and will then be more likely to be eliminated with a bromine atom (at the other end of the chain) than will a hydrogen atom nearer the bromine atom but in a less "activated condition.

Experimental results obtained by Ingold show that Ruzicka's assertion that a double bond is more easily formed than any other ring system is not valid in all cases. Thus, by the action of alcoholic potash upon ethyl a-bromoglutarate results in the formation of 16% of a-hydroxyglutaric acid, 47% of cyclopropane dicarboxylic acid and only 3% of glutaconic acid. That is, in spite of the considerable steric hindrance to be overcome in the formation of the cyclo

(b) The relative ease of formation of carbon rings is not directly proportional to their relative stabilities. Thus, the cyclobutane ring is more stable than the cyclopropane ring, but the latter is frequently more easily formed.

(c) The main factors which control the relative ease of formation of carbon-rings are (i) the "activities " of the atoms eliminated (in ring formation) as influenced by general and alternating polar effects produced by polar atoms; (ii) the spatial proximity of the polar atoms eliminated in ring formation. In cases where the production and fission of the ring is reversible under the conditions of the synthesis, the strain in the ring would obviously exert a modifying influence. The most satisfactory measure of factor (ii) is afforded by the "approach values" calculated by employing the value of the "normal" deduced by the tangent method.

angle

In some cases factor (i) will exert a predominating influence and in others factor (ii) will be the more powerful. In no case, however, may factor (i) be entirely disregarded. (This point will be discussed in a subsequent paper.)

(d) The stability of a carbon ring system is measured approximately by the angle of strain and, except in extreme cases where strongly polar groups are present, polar conditions in the ring will not exert a powerful influence on the relative ease of ring fission.

The equations (A) and (B), for the tangent arrangement were deduced by Professor D. M. Y. Sommerville, of Victoria College, Wellngton. The author's thanks are due to him both for these equations and for checking other mathematical expressions used in the course of this investigation. My thanks are also due to Professor Worley for his interest in this work. University College,

Auckland,

New Zealand.

1

BIBLIOGRAPHY.

1 Baeyer, Ber., 1885, XVIII., 2277. 2 Sachse, Ber., 1890, XXIII., 1363; Zeit. phys. Chem., 1892 X., 203; 1893, XI., 185.

3

4

Mohr, J. pr. Chem., 1918, XCVIII., 315; 1922, CIII., 316; 1924 CVII., 391; Ber., 1922, LV., 230.

Hückel, Nach. K. Ges. Wiss. Göttingen, 1923, 43; Ann., 1925, CDXLI., 1. 5 Meerwein, Kiel, Klösgen and Schach, J. pr. Chem., 1922 CIV., 161. Baker and Ingold, T., 1923, CXXIII., 123; Dickens, Horton and Thorpe, T., 1924, CXXV., 1833.

7 Ruzicka, Brugger, Pfeiffer, Schinz and Stoll, Helv. Chim Acta, 1926, IX., 499.

8

Ingold, T., 1921, CXIX., 305. "Stohmann and Kleber, J. pr. Chem., 1892, XLV, 475.

10

Hückel, Ber., 1920, LIII., 1277.

11 Beesley, Ingold and Thorpe, T., 1915, CVII., 1080.

12 Smiles' Chemical

Constitution

and

Some Physical Properties (1910), pp. 145-6.

13 Le Bas' Molecular Volumes (1915) pp. vii-viii.

14 Le Bas' loc. cit., pp. 19 and 21.

15 Kötz, J. pr. Chem., 1903, LXVIII.,

174.

16 Ingold, T., 1925, CXXVII., 387.

17 Lapworth, Mem. Manchester Phil. Soc., 1920, LXIV., ii., 1; T., 1922, CXXI., 416.

18

Robinson, Mem. Manchester Phil. Soc., 1920, LXIV., ii., 17.

19 Kermack and Robinson, T., 1922, CXXI., 427.

Allan, Oxford, Robinson and Smith,
T., 1926, CXXIX., 401.

20 Thorpe, Ingold and Co-workers, T., 1922, CXXI., 1178, 1430, 1821; 1923, CXXIII., 113, 1206, 1683.

12 Michael, J. pr. Chem., 1899, LX., 286. 22 Lewis, J. Amer. Chem. Soc., 1916, XXXVIII., 762; Valence, 84, 139,

143.

THE ENERGY OF HIGH VELOCITY ELECTRONS.

By MARSH W. WHITE. Precision determination of the energy of high velocity electrons. The total heat generated in an x-ray tube operated at rotentials up to 25,000 volts was measured by immersing a Coolidge x-ray tube of the water-cooled type in an oil bath and noting the temperature rise of the oil for a precisely measured energy input. The current

39

was

and voltage furnished to the tube by a high potential d.c. source were kept constant and were continuously measured by potentiometers. The heat energy given up to the oil by this" high potential "source compared with that developed by the same quantity of "low potential energy by taking alternate runs wherein the same potentiometers measured the current and voltage supplied from a storage battery to a heating coil immersed in the oil. The data proved with a probable error of about 0.2 per cent., that, up to 25,000 volts, all of the energy input into a Coolidge tube is ultimately transformed into heat and that any sources or sinks of energy which may exist have a smaller effect than 0.2 per cent. Ionisation, photographic and pyrometric methods were used to test for the presence of radiations involving an absorption of energy at the cathode. No appreciable quantity of such energy could be detected. The results of these experiments indicate that all of the input energy must go into the energy of the moving electrons and their fields. It also follows that only a negligible portion of the current in a Coolidge tube is furnished by positive ions which actually reach the cathode, for otherwise the cathode would be heated.

These experiments indicate that all of the energy input into an x-ray tube goes into the moving electrons and their fields. Furthermore, it is shown that, within 0.2 per cent. or less, this energy is as completely given up when the electrons are arrested, i.e., that Vit = JH for electrons moving with velocities up to 25,000 equivalent volts. This shows, within the limits mentioned, that there are no atomic molecular changes involving a source or sink of energy in a Coolidge tube at 25 kv. It also follows that only a negligible part of the current in a Coolidge tube is furnished by positive ions reaching the cathode, for otherwise the cathode would be heated a measurable amount. The heat received at the target of a water-cooled Coolidge tube may be only from 75 to 97 per cent. of the total energy input, the remainder of the energy being dissipated at the walls of the tube as a result of their bombardment by "reflected" electrons.-Extract from the Physical

Death, sudden and wholly unforeseen, has stepped between this Section and the President of its choice. Professor Bateson had presided over the whole Association at its meeting in Australia, and partly on that account he had been selected for the chair of this Section in Oxford. From him we might have expected a broad outlook upon biological science. His address would have been instinct with wide experience in both of the branches of living things, the interests of which interweave in enthralling and often most perplexing ways. We should have heard a fearless statement of his mature views. Something constructive would certainly have justified the congratulations with which some of us had already welcomed his nomination. A great figure has been taken from the arena of biological science. A career still full of promise of further achievement has closed prematurely.

1860.

I need not remind you of the fact that the meeting in Oxford of 1860, the year after the publication of the Origin of Species,' witnessed the clash between the new view and the opposition it was certain to arouse. The story has been often told of the aggresive attack and the crushing retort. But it is not sufficiently recognised that, though Huxley bore the first brunt of the fight, a large part in the contest was taken by Hooker. The meeting closed after he had spoken, and in his own words he was congratulated and thanked by the blackest coats and the whitest socks in Oxford.'

Two generations have passed since the Oxford meeting of 1860; and still the Origin of Species' holds its place as a great philosophical pronouncement. As the methods of research passed into greater detail, the area of fact has been extended through the labours of an ever-growing

army of inquirers, and naturally divergences of view have arisen. Some authors appear to demand that for all time the Origin' must cover every new aspect of biological inquiry, or else the whole theory crumbles. That is to demand a prophetic vision for its author. We need not for the moment follow these or other criticisms, but rather recognise that the theory rested essentially on facts of heritable variation, without defining their magnitude, limitations, or origin; and that it explained a means of their summation so as to produce progressive morphological results. As an index of current opinion on the validity of Darwin's theory as a whole, I would draw your attention to three British works on evolution, all published within the last two years. In 1924 Dr. Scott concludes his volume on Extinct Plants and Problems of Evolution' with the judicious sentence: 'I may venture . . . to maintain that a consideration of all the evidence . . . is on the whole favourable to the old, truly Darwinian conception of an orderly and gradual evolution without sudden and explicable leaps, an evolution in harmony with the uniformitarian principles established by Lyell.' But he remarks that he does not favour any exaggerated ideas such as the so-called 'omnipotence of natural selection.'

In the present year Professor Graham Kerr,in his volume on 'Evolution,' also adopts a distinctly Darwinion position, but with greater stress laid upon the potency of natural selection; this might be expected from one who spent some of his most im pressionable years in the wild surroundings of the Gran Chaco. He speaks from experience of the effect of selection as being in actual fact enormous,' and he holds that the attempts that have been made to minimise its importance are to a great extent fallacious. He sees in the recognition of the