The number of writings dealt with here is very slightly in excess of the number under the same heading for the period 1880–1900, and there is also little alteration in the general character of them. The bigradient which still receives most attention is that resulting from Sylvester's dialytic method of elimination, and others are close relatives of it.

Researches of recent years have shown that the intercorrelations which exist among the measures of mental qualities are connected in a particular way, from which it has been sought to deduce facts concerning the nature of the mental structure on which the various qualities depend. If we take any four such qualities, there are six correlation coefficients, r12, r13, r14, etc., and it is found that the quantity F = r13r24 — r14r23 is in practice approximately zero. Since the observed correlations are vitiated by errors due to measuring a sample of the population instead of the whole it is legitimate to think that the value of F throughout a set of mental qualities is truly zero.

1. Integrals of the form where ψ(x) is a function with a limited number of turning-points in the range of integration and k is a constant which may take up large values, frequently occur in investigations in mathematical physics, and their computation by quadratures is often desirable.

The Fulcher Bands of Hydrogen have recently been arranged by Richardson. An examination of Richardson's arrangement in the light of recent accurate measurements of the hydrogen spectrum by Gale, Monk, and Lee, while strongly confirming Richardson's allocation of the Q branches, has failed to yield confirmation of the remaining branches which he gives.

The present paper gives a number of combination relations which have been found to hold between the lines of the Fulcher Bands. These indicate that there are three main branches in each band, designated the R', Q, and P' branches, the Q branch being identical with that of Richardson. The R' and P' branches have a common initial level differing from that of the Q branch, while all three branches have a common final level. The arrangement yields term differences consistent throughout the bands.

As far as these term differences have been investigated, they have been found to be in agreement with the new mechanics.

The present investigation was suggested to me by Prof. H. Stanley Allen of St Andrews, and my warmest thanks are due to him for constant encouragement and helpful criticisms and suggestions.

The attempt to extract information from correlation coefficients concerning possible common factors among measured variables presents serious difficulties, since common factors are not determinate functions of the original variables. It is indeed possible, by the assumption of specific, group (common to some), and general (common to all) factors, to construct various hypothetical correlated variables which will produce correlations of a given magnitude. If it is required, for instance, to construct three variables to produce three given positive correlations, we may choose among various ways to produce the correlations by means of a triple factor (common to three variables) or dual factors (common to two), or both in co-operation. We are faced by a certain restriction, however, for whereas correlations of any magnitude can be produced by using a triple factor with or without dual factors, yet with dual factors unaided by a triple factor certain magnitudes are unattainable. The condition expressing this restriction is known as a “boundary condition.”

1. Let x1, x2, x3 represent three mental activities; r12 the correlation coefficient of x1 and x2; r23 that of x2 and x3; r31 that of x3 and x1.

J. Ridley Thompson has shown (Brit. Journ. Psychol., 1919, vol. ix, p. 335) that if

F(r)≡r122 + r232 + r312 + 2r12r23r31

be greater than 1, a “general factor” is undoubtedly present in the three activities.

1. A problem of considerable importance in the theory of statistics is the determination of the accuracy with which a given sample of observations determines the characteristics of the population from which it is derived. Any parameter of this distribution can only in practice be estimated from the sample, and the degree of latitude in our choice of the right function enables considerations of suitability and efficiency of the particular moment statistic to be taken into account. As well as this, however, the probable errors of such frequency constants, or, to be more complete, the distribution of the constants in all possible samples, must be determined. These problems were formulated many years ago by Karl Pearson (1), and his important researches have stimulated and suggested much subsequent work.

(1) In accordance with theoretical considerations, it is proved experimentally that hydrogen and bromine combine to a small extent when exposed to the light of the aluminium spark, which radiates strongly at λ=185 μμ. At equilibrium the vapour pressure of hydrobromic acid is 1·4 to 1·8 per cent, that of the bromine, and the equilibrium state is rapidly reached.

(2) The absorption coefficient of bromine increases slowly with decreasing wave-length for wave-lengths shorter than 254 μμ, but the gas is still very transparent even at 185 μμ.

The authors wish to acknowledge their indebtedness to Professor Sir James Walker and Professor Kendall for their interest and very helpful advice during the progress of the work, and also to Imperial Chemical Industries, Ltd., for a grant covering the expense of some of the apparatus used.

1. Fertility tests of eight partially castrated cocks and three controls show that within quite wide limits of fertility and of testis size the fertility of the male fowl is not in any way dependent upon size of the testis.

2. The average density of sperm suspension was found to be approximately four million spermatozoa per cubic millimetre for the thirty-six samples examined from ten males.

3. The variations in the average density of sperm suspension from different birds ranged from 825,000 to over 7,000,000 cells per cu. mm., but within this range the density of sperm suspension bore no relation to fertility.

4. The number of sperm per cubic millimetre of semen appears to be entirely independent of the size of the testes within the ranges covered by this experiment.

5. Compensatory hypertrophy to a degree approximating to the normal weight of both testes was observed in the retained right testes of cocks castrated unilaterally on the left side at one week of age.

6. Exceptions to the rule of compensatory hypertrophy included birds with subcutaneous testis grafts and two in which one whole testis and part of the other had been removed.

7. It is suggested that fertility in the male fowl is dependent upon the physiological efficiency of the spermatozoa rather than upon their quantitative production.

1. An examination has been made of 11,797 eggs which had failed to hatch, among which were 5050 embryos which had died after the eighteenth day.

2. Four major malpositions of the chick embryo are described and the frequency of each given.

3. It is concluded that one of these, in which the head is buried between the legs, definitely prevents hatching. In the material examined, this abnormality was responsible for 9·25 per cent. of the mortality among embryos of eighteen days or over.

4. It is suggested that the other three malpositions usually result fatally, by reason of their preventing pulmonary respiration in the embryo as well as by mechanical hindrance.

5. Of the embryos over eighteen days, nearly 56 per cent. were in one or another of the four major malpositions.

6. Possible causes are discussed, and the suggestion made that some of the abnormal positions result from an incorrect orientation of the embryo established early in cleavage.

1. Among 7135 chick embryos of nine days or over, obtained from unhatched eggs from three poultry farms, 112 cases of chondrodystrophy were observed. From 1900 eggs set at this Department, 124 chondrodystrophic embryos were obtained.

2. The mortality caused by this condition varied in different flocks from 0.80 to 7.96 per cent. of the embryos dying after the eighth day; at this Department it was responsible for loss of 6.5 per cent. of the eggs set.

3 The incidence of chondrodystrophic embryos was found to be greatest in January and February, and to decline steadily thereafter to an almost complete absence in June.

4. The occurrence of chondrodystrophy appears to be independent of breed of fowl, sex of embryo, and age of dam.

5. The number of these abnormal embryos produced by individual hens ranged from 1 to 28.

6. Evidence is advanced in support of the theory that the causal agency is an hereditary physiological abnormality in the dam which, under certain unfavourable conditions, results in the production of chondrodystrophy in the embryo.

7. It is shown that the incidence of chondrodystrophy appears to be inversely proportional to the amount of sunshine, and the suggestion is made that lack of direct sunlight is a factor in the etiology of the abnormality.

In an examination of 11,797 eggs which had failed to hatch, 433 specimens exhibiting teratological abnormalities were obtained.

The various types of monsters observed are briefly described and the frequency of each given.

The most common types were characterised by various degrees of abnormality either in the brain, cranium, or eyes, or in two of these structures, or in all three. Hyperencephaly, exencephaly, and microphthalmia constituted 93 per cent. of all the monsters observed.

Other teratological abnormalities encountered included prognathia, duplicity, ectopia, cyclopia, otocephaly, malformed limbs, and absence of premaxillæ.

Monsters accounted for at least 3·6 per cent, of all mortality in the material examined.Since this material included many embryos too decomposed for detection of teratological abnormality, the actual loss is probably considerably higher.

No significant deviations from the normal sex-ratio were evident in any class of monsters.

A decline in the frequency of such abnormalities from February to April was evident.

Evidence is adduced from Stockard's experimental teratology in fish eggs, to show that a very probable cause of the production of monsters in the chick is an arrest of development of the embryo at a critical stage.Presumably such a condition results from the chilling of those eggs laid in the early stages of gastrulation.

Some evidence to indicate the possibility of an hereditary tendency to produce monsters is briefly discussed.

In a former paper (Ludlam and West, Proc. Roy. Soc. Edin., xliv, 185) the emission spectra of the halogens in the ultra-violet region were described and discussed. In connection with the work at that time the flame produced by the union of hydrogen and chlorine was photographed in the hope of gaining some insight into the processes involved and the nature of the energy changes attending the combination. The photograph obtained showed a continuous spectrum in the visible fading rapidly in the violet.

The pressure of ethylene in equilibrium with solid iodine and solid ethylene di-iodide was measured at temperatures between 10°C and 65°C.

The vapour pressure of undissociated ethylene di-iodide was measured at four temperatures between 15°C and 55° C.

From these results and the known vapour pressure of iodine equilibrium constants were calculated.

Some experiments were made on the rate of formation and decomposition of ethylene di-iodide.

We desire to thank Professor Sir James Walker and Professor Kendall for their interest in our work, and Imperial Chemical Industries, Ltd., for a grant towards the cost of apparatus.

1. When a suspension of a large number of small rigid spheres in a viscous fluid is allowed to sediment under the action of gravity the rate of fall of any of the particles in the body of the suspension is

U = U0(1 – κΦ), where U0 is the rate of fall of an isolated single particle calculated according to Stokes' law , where α is the radius of the particle, η the viscosity of the fluid, ρ the density of the particle, σ the density of the fluid, and g the constant of gravity. Φ is the volume of suspended material per unit volume of the suspension, and κ is a constant whose value according to theory is 5·5 + c, where c is probably in the neighbourhood of 1·6.

1. When the univalent anions (of potassium salts) are arranged according to their precipitation concentration for a ferric hydroxide sol the sequence is lyotrope:

A, CNS, Cl, Br, NO3, ClO3, I.

The concentrations range from 0·01 for acetate to 0·093 for iodide; thiocyanate alone is in an unusual position.

The order for kations is also lyotrope:

Li, Na, Mg, K, Rb, NH4, Ca. The concentration range is much smaller, from 0·037 for lithium to 0·055 for ammonium.

2. The pairs of univalent-bivalent kations—Li. and Mg¨, K. and Ca¨—show no trace of antagonistic action in the precipitation of Fe(OH)3 sol—the results being strictly ADDITIVE.

3. The pair of univalent-bivalent anions—ClO3′ and SO4″—on the contrary, show a well-marked ADJUVANT action, which amounts to 50 per cent.

4. The effect of salts on the opalescence temperature of a phenol-water system (10 to 11 per cent, phenol) is lyotrope, and is very marked at a concentration of 0·04 n. The order is—

Anions … C1, Br, NO3, I, CNS

Kations ‥ Na, Li, K, NH4

The effect of the valency of the ion is slight, or non-existent.

5. A preliminary account is given of a method which promises to provide a simple and reliable means of determining the amount of “free” and “bound” water in a solution (applicable to electrolytes and nonelectrolytes, and apparently to colloidal solutions, as e.g. gum arabic).

6. An explanation of the Lyotrope Effect is put forward.

An asymptotic formula has recently been given for the characteristic numbers of the Mathieu equation

From tabular values, it will be seen that the formula provides good numerical approximations to the characteristic numbers of integral order; but as pointed out by Ince, it provides better approximations to the characteristic numbers of order (m + ½), where m is a positive integer or zero. In this paper we shall first attempt to find out why this should be so, and then go on to show that the formula is probably an asymptotic expansion, in the Poincaré sense, for any characteristic number. A new asymptotic formula is then found for the difference between two characteristic numbers.

The elaborate system of molecules, atoms, ions, and electrons modern chemistry and physics have constructed to meet their needs invites the biologist to inquire into the problem of material particles as bearers of life. Leaving aside all questions of finality in the organism touching the vexed problem of purpose in our world, which science has also not been able to solve in lifeless matter (1), we may try to get glimpses of the construction of living material by different methods of attack.

In his investigations on colour blindness, Dr. Houstoun produced two identical patches of colour on a screen; one of these patches was gradually altered until a difference in tint could just be observed. These two patches were at a distance of 8 mms. apart on the screen, and Dr. Houstoun suggested that if these patches were juxtaposed the observer's colour sensitivity might be improved. The following communication records the results of investigations carried out under that suggested condition.

The 33S→23S system of Richardson and Das is extended, the band previously given as the null band (00) now being taken as (20), while two additional vibrational levels are added on the infra-red side. An analysis of the system based on the new mechanics is given, and various tests are applied to prove the correctness of the new arrangement. A Table giving the constants of the 23S and 33S states is appended.

My thanks are due to Professor H. Stanley Allen of St Andrews for encouragement and helpful criticisms.