The problem of the amount of independence possessed by the units which go to make up the nervous system is one which has long occupied the attention of neuro-pathologists, and is still far from solved. That degenerative changes, as the result of peripheral injury, may extend across several intermediate neurons is indicated by the work of many investigators, notably v. Monakow, Campbell, Bolton, etc. Thus after enucleation of the eyeball changes have been met with in the visual cortex, showing that degeneration has travelled over the neurons situated at the basal ganglia of the cerebrum to the neurons in the visual cortex itself. Interruption of the sensory conduction path affects the integrity of themore centrally placed neurons. The question of the stability of the peripheral neurons under similar conditions has not received attention. Birch-Hirschfeld in 1900 published the results of a large series of experiments upon the retina, including a few cases of the effects of experimental section of the optic nerve.

No subject in the domain of preventive medicine is attracting greater attention at present than that of the prevention of tuberculosis, more especially that of tuberculosis of the lungs. The fact that this disease is one of the largest contributors to the death-rate makes the question pressing, and the great diminution of the mortality from it that has already taken place in most civilised countries makes the prospect of still greater diminution most hopeful.

The paper discusses the effects of errors in linear and angular measurements on the accuracy of surveys, and is divided into six sections, thus:—

Section I. The Sum of Vector Errors.

Section II. The Average Error due to Imperfect Centring.

Section III. The Relative Effects of Errors in Centring and those of Sighting and Reading.

Section IV. The Propagation of Errors in Traversing.

Section V. The Propagation of Errors in Minor Triangulation.

Section VI. A Summary of Results.

In a paper read before the Royal Society of Edinburgh (Proc. Roy. Soc. Edin., xxviii., part v., p. 382 (1908); Zeit. phys. Chem., lxiv. 5) I described a new type of concentration cell, in which the one platinum electrode was surrounded by a solution of ·025 molecules of KI containing ·001 molecules of iodine dissolved in absolute alcohol, and the other electrode was surrounded by ·025 molecules of KI and ·001 molecules of iodine, dissolved in water. This cell developed a considerable E.M.F. of ·198 volts at 25° C. in the direction which would transfer the iodine from water to alcohol and potassium iodide from alcohol to water.

This investigation was begun as a result of certain observations made by Dr T. Graham Brown, on reflexes in the guinea-pig (45). In various experiments he removed parts of the cerebral cortex and found that little if any disturbance, either motor or sensory, ensued. It was thereupon suggested that an examination should be made of the cortex histologically and by electrical stimulation in order to locate the position of the various areas.

A careful determination of g by means of the ordinary type of Atwood's machine does not, as a rule, lead the average student in a Physical Laboratory to a better result than 930 or 940 cm/sec2. From the point of view of successful teaching, it is somewhat unfortunate that, after bestowing reasonable care and attention to his work, a student should be unable to obtain a result approximating satisfactorily to what he knows to be the correct figure. Not unnaturally he takes it for granted that the actual numerical result obtained from his experimental labours is quite immaterial as long as the processes involved are clearly comprehended, and to him Experimental Physics is anything but an exact science. On the other hand, to set before the ordinary student a complicated apparatus specially designed for reaching an accuracy of 0·1 per cent, would be proceeding to the other extreme, and one could hardly expect much benefit to be derived from its use.

In the determination of the law of decrease of torsional oscillations of an iron wire, when the range of oscillation is large in comparison with the palpable limits of elasticity, an equation of the form

yn (x + a)= b

has been shown by Dr Peddie (Phil. Mag., July 1894) to give close representation of results where—

y = the range of oscillation.

x = the number of oscillations since the commencement of observations.

n, a, b = quantities, constant for any one experiment, depending on the initial conditions of the experiment and the previous treatment of the wire.

In the preceding paper the law of torsional oscillation

yn(x + a) = b,

where y = range of oscillation, x = number of oscillations since start of experiment, and n, a, b constants for any one experiment, is considered with reference to wires of various materials, together with the effects produced on the constants of that empirical equation, and in particular on the constant n, by altering the initial conditions of the experiment. The wires were subjected to changes of length, diameter, temperature, and rigidity, and the resultant changes in the values of n, a, and b were given in detail.

1. In two memoirs on the “Theory of Probabilities,” Boole was led to the consideration of a peculiarly interesting form of determinant which has only positive terms in its final form of development, and which in the case of the fourth order may be written

V standing therein for

In the first of the two memoirs the determinant is not explicitly referred to, but in the second it receives considerable attention, Boole, indeed, there saying that the memoir “involves discussions relating to the properties of a certain functional determinant, and to the possible solutions of a system of algebraical equations of peculiar form, discussions which will, I trust, be thought to possess a value as contributions to mathematical analysis, independent of their present application.”

These experiments were made in the Physical Institute of the University of Leipzig at the suggestion of Professor Des Coudres, who very kindly placed at my disposal for the purpose a compression-cylinder suitable for high temperature work, which I shall describe later. The original description by Professor Des Coudres appeared recently in the Berichte der mathematisch-physischen Klasse der Königlichen Sächsischen Gesellschaft der Wissenschaften zu Leipzig, vol. lxii., 18th July 1910.

There was some difficulty in deciding what the title of this paper should be. It ought to have been “The Abnormal Dust Readings at Kingairloch” but as that would convey no suggestion of its contents, it was thought better to make the paper a continuation of a previous one under the above title, as the Kingairloch abnormal readings are a particular case of the same subject.

In 1907 I had the honour of reading a paper before this Society in which a new genus of iron-bacteria was described. This organism was first discovered in Renfrew, near Glasgow, and subsequently observed in various samples of iron-water from different parts of the country. At Renfrew this organism was at the time of its discovery the sole bacterial occupant of the ironwaters of this neighbourhood. In most samples of these waters—and I have examined hundreds—only the remains of iron-bacteria can be obtained, but occasionally the samples are found to contain iron-bacteria in process of growth and multiplication. After a little experience, it is possible to ascertain which streams contain iron-bacteria in this favourable condition. At Renfrew such streams were then common, and so gave me an opportunity of tracing the life-history of this species. The results of this investigation seemed to me to justify the conclusion that I had obtained a new genus of iron-bacteria.

1. Experiments of Hopkinson, Curie, and D. K. Morris.

2. Precautions necessary in magnetic testing. If the temperature of a test-specimen is changed, the specimen must be rendered neutral at the new temperature previous to carrying out the test.

3. The effect of increasing the temperature of a specimen of cast iron from 15° C. to 190° C. is to improve its magnetic quality for moderate values of the magnetising force; from 190° C. to 260° C. the magnetic quality falls off, after which there is a further improvement. Finally the specimen becomes non-magnetic at the critical temperature. These results indicate the presence of a transformation point for carbon alloys of iron in the neighbourhood of 200° C.

4. Steel containing 1·64 per cent, of carbon resembles cast iron in its behaviour. The set-back in magnetic quality takes place at much the same temperature as that which occurs in cast iron, the magnitude of the set-back being much the same for both.

5. Steel containing 0·8 per cent, of carbon exhibits the transformation point, but in a less marked degree. The first maximum point in the susceptibility curve occurs at 180° C, and the first minimum point at 220° C.

6. Low carbon steel containing 0·3 per cent, of carbon shows the transformation point; it is, however, very much less marked than in the case of the steels containing the higher percentages of carbon.

7. The susceptibility-temperature curve of a specimen of soft iron containing 0·06 per cent, of carbon exhibits no turning points in the neighbourhood of 200° C. for fields lying between 2 and 15 c.g.s. units.

In the course of some work in this laboratory a determination of the radius of gyration of an Atwood's machine pulley was necessary. The radius was found by using a bifilar suspension. Having been unable to find any published record of the method, which is capable of giving fairly accurate results, and as the measurement of moment of inertia or of radius of gyration is a frequently occurring and ill-understood exercise in a physical laboratory, it seemed to me that the following details might be of interest.

We have shown that calomel vapour contains no measurable amount of Hg2Cl2 or of HgCl, and consists wholly of the dissociation products, mercury and mercuric chloride. According to chemical theory, therefore, when, by the removal of all moisture, the dissociation is prevented, the vapour pressure of the dry substance should be equal only to the partial pressure of the undissociated molecules of the undried vapour; that is to say, it should be negligibly small. Brereton Baker, however, was able to measure the vapour density of such dry calomel, finding it to be almost double the ordinary density. Since the measurement was made by the V. Meyer method, at 445°, it follows that this dry calomel must have possessed a vapour pressure approximating, if not exceeding, one atmosphere.

The present article is intended to be the first of a series on the absorption of light by solutions of inorganic salts of different elements. With a few scattered exceptions all the work hitherto done on the absorption spectra of inorganic salts has been merely qualitative and has been confined to the visible spectrum. Kayser in his Spectroscopie, vol. iii. p. 45, states that in this field there is work for years and for numerous observers. E. C. C. Baly states in his Spectroscopy, p. 407, that not much is known about the absorption of light in inorganic salts. Merely for its own sake, then, an accurate determination of the molecular extinction coefficient for as many salts under as many different conditions of temperature and concentration, and for as many wave-lengths as possible, would be very valuable.

As in the case of the work in the infra-red, the salts experimented on were the nitrate, sulphate, chloride, bromide, fluoride, and iodide, and they were obtained from Kahlbaum. Very little trouble was experienced with the sulphate, nitrate, and chloride. The salts were supplied as CoSo47H2O, Co(NO3)26H2O, CoCl26H2O. The fluoride was a pinkish powder sparingly soluble in water. It dissolved with formation of insoluble oxyfluoride which seemed to increase on standing. By heating the salt and driving off the water of crystallisation, it was found to be Cof22H2O. The iodide was an extremely deliquescent green powder. A slight insoluble chocolate-coloured residue remained in the solution and was filtered off. By heating the salt it was found to have the composition CoI2H2O. The bromide consisted of very deliquescent crimson lumps, and was found to have the composition CoBr26H2O.

The methods and the apparatus were the same as in the two previous articles of the series and hence need not be described, the only change being in connection with the galvanometer. Previously it had rested on the table, but when half the results in the infra-red recorded in this paper were obtained, the arrangement was changed; it was suspended by three iron wires each about one and a half metres long from a bracket in the wall and hung with its three levelling screws clearing the table by about one centimetre. Between the table and levelling screws were placed loose wads of cotton wool for the purpose of damping any vibrations that might arise. With this arrangement the zero is very much less sensitive to vibration. With the lamp and scale at one and a half metres—the distance at which they are ordinarily used now–vibrations of the laboratory rarely cause the zero to move mm. either way.

In Kayser's Spectroscopie, vol. iii. pp. 45–49, an account is given of all the different methods that have hitherto been employed for photometry in the ultra-violet part of the spectrum. Photography, phosphorescent plates, selenium cells, and the ionising effect of ultra-violet light have all been used, but with limited success, and Professor Kayser considers that the only really practical method is that which has been recently introduced by Pfluger. Pfliiger has discovered that there is relatively an enormous amount of energy in the ultra-violet spectrum of the electric spark produced by the discharge of a condenser between metal electrodes. He therefore uses the electric spark as a source, and takes the deflections with a thermopile and galvanometer, just as in the infra-red. He finds the deflections to be wonderfully steady, considering the inconstant nature of the spark.

§1. Pringsheim has recently reopened the question as to the circumstances under which Fourier's repeated integral exists and represents the function to which it corresponds. In its simplest form the theorem concerning this integral asserts that, with provisos to be specified—

ƒ( + 0) being the unique limit, supposed to exist, of ƒ(u) as u approaches the value zero. From this equation, indeed, the remainder of the theory follows immediately. If it is to be true, certain conditions must be satisfied at the origin, at infinity, and in the finite part of the range of values of the independent variable. Till Pringsheim's paper appeared, the only condition known to be sufficient at infinity was of a very special character, requiring no less than the absolute integrability of the function at infinity.