bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the Generalization of Josephus' Problem
Authors: Tait  
Published: June 2019

In the third Book of The Wars of the Jews, Chap. VIII. § 7, we are told that Josephus managed to save himself and a companion out of a total of 41 men, the majority of whom had resolved on self-extermination (to avoid falling into the hands of Vespasian) provided their leader died with them. The passage is very obscure, and in a sense self-contradictory, but it obviously suggests deliberate fraud of some kind on Josephus' part.“And now,” said he, “since it is resolved among you that you will die, come on, let us commit our mutual deaths to determination by lot. He whom the lot falls to first, let him be killed by him that hath the second lot, and thus fortune shall make its progress through us all; nor shall any of us perish by his own right hand, for it would be unfair if, when the rest are gone, some-body should repent and save himself.” Whiston, Works of Flavius Josephus, IV. 39.Bachet, in No. XXIII. of his Problèmes plaisants et délectables, makes a definite hypothesis as to the possible nature of the lot here spoken of; so that the problem, as we have it, is really his.“Supposons qu'il ordonna que comptant de 3 en 3 on tuerait toujours le troisième, …. il faut que Josèphe se mît le trenteunième après celui par lequel on commençait a compter, au cas qu'il visât à demeurer en vie lui tout seul.
Some Contributions to the Spectroscopy of Hæmoglobin and its Derivatives
Authors: Harris David Fraser 
Published: June 2019

1. Apparatus.—The following are needed:—Electric or lime light; standard hæmatinometer (i.e., of 1 cm. between the parallel sides) entirely of glass (for many pigments white glass flat-sided stoppered bottles do perfectly well); large direct-vision spectroscope (Messrs Hilger), or a Tollen's carbon-disulphide glass prism (base 5 inches, refracting angle 45°); a well-stretched dead-white screen to receive the spectrum 4 feet long at least, about 12 feet from the lantern.Following Preyer (1), one can with such apparatus first of all demonstrate the different spectroscopic appearance according as blood is or is not diluted. Placing blood newly received from the slaughter-house (defibrinated blood) in the hæmatinometer, we show that it is opaque in a thick layer, no light passes to the prism at all, there is no spectrum, we can say that the percentage of HbO2 is, at least, greater than 7·3. Dilute with pure cold water until a faint gleam of red light appears at the extreme left, the concentration of HbO2 is now not less than 1 per cent.; continue the dilution until the first glimmer of extra-linear green appears, the percentage is now about ·9 per cent.; dilute until the first glimmer of intra-linear green appears, when the percentage is now ·7; add to this its own volume of water, making the percentage fall to ·35. From this point further dilution caused progressive faintness of the two bands, until the vanishing point of the fainter β band is just reached when the hæmoglobin is ·01 per cent.; continue the attenuation until the α band is alone visible, at which point the percentage can be stated to be certainly less than ·01 per cent.
Note on the Effect of Mixed Diet as Regards Salivary Digestion
Authors: Robertson W. G. Aitchison 
Published: June 2019

The following research was made with the object of determining whether the digestion of starch is affected favourably or unfavourably by its admixture with other articles of food.As regards the quantity of saliva secreted per twenty-four hours, this is stated to vary from 200 to 1500 grammes. Investigating this in my own case I found that the average amount was 400 grammes.Method of Investigation.—Ten grammes of each of the various foods as prepared for the table were accurately weighed out, placed in a large tube, and heated to 38° C. Two cubic centimetres of mixed human saliva were then added. A series of these tubes were prepared, and the whole was placed on a water-bath kept at a uniform temperature of 38° C. At intervals a tube was removed, and the condition of its contents noted.
The Strains produced in Iron, Steel, Nickel, and Cobalt Tubes in the Magnetic Field. Part II
Authors: Knott C. G. 
Published: June 2019

AbstractThe most important part of the paper has to do with the behaviour of certain iron and nickel tubes, considerably shorter and narrower than those discussed in Part I. Two iron bars, A and B (A being twice the length of B), and a nickel bar, B, were bored out by successive stages, so as to give three series of tubes of increasing bore. Each tube was subjected to four distinct experiments. These were—1. Measurements in various magnetic fields of the corresponding changes of volume of bore.2. Measurements in the same fields of changes of length.3. Measurements in the same fields of changes of volume of the material of the tube.4. Measurements in the same fields of apparent external changes of volume, the tube being plugged and treated as a bar.
Note on Finding the Logarithmic Sines and Tangents of Small Arcs
Authors: Burgess J. 
Published: June 2019

In geodetical and astronomical computations it frequently happens that we have to use the logarithmic sines or tangents of small arcs, or to find the small angles corresponding to their artificial sines or tangents; and in all trigonometrical tables directions are given to guide the learner in these operations. It might seem, then, superfluous to refer to such a matter. A variety of methods in the solution of a simple problem has, however, sometimes advantages, and the method I have been in the habit of using, though obvious enough, is not usually given.In Vega's great Thesaurus Logarithmorum Completus (1794), based on A. Vlack's Tables, the rules for the functions of small arcs make use of second differences; and the 7th and later editions of Hutton's Tables (1830, 10th ed., 1846) follow the same method.
Note on Dew Bows
Authors: Knott C. G. , Lundie R. A. 
Published: June 2019

A dew bow differs from a fog bow in being formed by minute globules of water resting on the ground; but these globules may or may not have been produced by the usual process of dew formation. In the Proceedings of the Society (vol. vii., 1870), Clerk Maxwell has published a note on a bow seen on ice. With the exception of this record, we have been unable to find any distinct account of observations of the phenomenon, although no doubt it must have been occasionally observed soon after sunrise.The peculiarity of the bows we observed was that they were seen by night, the sources of light being the gas lamps and electric lights of the city. It was on the evening of Friday, November 11, after several days of thick foggy weather. The tiny fog particles seem to have gradually settled down in the still air, the fog steadily clearing the whole time. These globules, in spite of their contact with the damp ground, must have retained their spherical form almost perfectly; for they were able to throw back to the eye, with a rainbow deviation of approximately 42°, the light incident upon them.In the neighbourhood of every lamp where the surface of the ground had been undisturbed by traffic the bows were seen as bright streaks, which shifted position with the observer. Any disturbance of the surface, a wheelmark, a footprint, a finger drawn across the pavement, obliterated the bright streak; and it was not seen on the surface of puddles.
On the Eliminant of a Set of Quadrics, Ternary or Quaternary
Authors: Nanson E. J. 
Published: June 2019

1. There are two methods for expressing in determinant form the eliminant of three ternary quadrics. If u, v, w are the quadrics and J their Jacobian we may eliminate dialytically the ten quantities x3, y3, z3, y2zyz2, z2x, zx2, x2y, xy2, xyz from the ten cubics xu, yu, zu, xv, yv, zv, xw, yw, zw, J. This is in effect the process given by Sylvester in 1841. The other method is to eliminate dialytically the six quantities x2, y2, z2, yz, zx, xy from u, v, w and the three differentials of the Jacobian.2. The eliminant of four quaternary quadrics may be found in determinant form by a process having points in common with each of these two methods. Multiplying each of the quadrics by the variables x, y, z, w in turn we get sixteen quaternary cubics, and we have also the four differentials of the Jacobian. Thus we have in all twenty quaternary cubics, or just sufficient to eliminate dialytically the twenty expressions x3, …, x2y, … xyz, … The result is a determinant of order 20, and of the correct degree, viz., 8, in the coefficient of each quadric.It does not appear to be possible to extend this process so as to obtain, in determinant form, free from extraneous factors, the eliminant of a set of quadrics in more than four variables.
Note on the Compressibility of Solutions of Sugar
Authors: Tait  
Published: June 2019

In continuation of former investigations of the alteration of compressibility of water, which is produced by dissolving various salts in it, I was led to imagine that some instructive results might be furnished by solutions such as those of sugar, whose bulk is nearly the sum of the bulks of their constituents:—for, in them, we might expect little change in compressibility from that of water itself; i.e. in accordance with my hypothetical formula, little change in the term regarded as representing the molecular pressure.The following preliminary results have recently been obtained for me by Mr Shand, Nichol Foundationer, who employed the Fraser gun and the Amagat gauge procured for my “Challenger” work:—and a new set of piezometers of the same (Ford's) glass as that whose compressibility I had determined to be 0·0000026. These have been carefully gauged, but have not as yet been directly compared with those formerly employed.The solutions experimented on were prepared, in Dr Crum Brown's Laboratory, by Mr W. W. Taylor, M.A., B.Sc., and contained respectively 5, 10, 15, 20 parts, by weight, of sugar to 100 of water. The temperature varied but slightly from 12°·4 C. during the whole course of the experiments.
Dust Figures of Electrostatic Lines of Force
Authors: Robertson David 
Published: June 2019

When lecturing on Electrostatics at the Glasgow and West of Scotland Technical College, the author endeavoured to impress upon his students the identity of the laws of force for magnetism and electricity at rest. He thought it would further this idea if he could get pictures of electrostatic lines analogous to those obtained from magnets by means of iron filings, and an analysis of the difference of the conditions in the two cases led to the conclusion that there was no reason why this should not be done.When we shower iron filings upon a glass plate, or a sheet of paper, under which a magnet is placed, unlike poles are induced at the ends of each filing, and it becomes for the time being a little compass needle. Since it is very short, the total action upon it will be a couple turning it into the direction of the force at its centre, unless it be close to the magnet, in which case there will be, in addition, a translation along a line of force. This latter effect causes the filings to crowd towards the edges of the magnet.Now, in electrostatics we also have an inductive action, opposite charges being induced in the near and far ends of each particle as it comes into the field, but we have the important difference, that whereas the magnetic poles are attached to the filing and cannot be separated from it, the electric charges will leave a body if they have an opportunity of doing so.
On some Oceanographic Problems
Authors: Makaroff Vice-Admiral S. 
Published: June 2019

I am very glad to embrace the opportunity of addressing the Fellows of the Royal Society of Edinburgh, many of whose members have contributed much to our knowledge of Oceanography. For instance, your President, Lord Kelvin, besides his researches on the tides, is well known to practical seamen from his excellent compasses and sounding machines; your Secretary, Prof. Tait, is well known from his researches on the pressure errors of deep-sea thermometers; Dr Alexander Buchan has a world-wide reputation in the department of oceanic meteorology; the late Prof. Dittmar was a great authority on the chemistry of sea water. It is enough to say that Sir Wyville Thomson, Mr J. Y. Buchanan, and Sir John Murray, were members of the “Challenger” Expedition, which has given the world such valuable information about the depths of the sea.Of course, it is not with the intention of giving to such scientific authorities a lesson that I address the Society, but if you represent scientists, I represent the seamen, and it is useful from time to time to have a talk between these two classes of men. Every scientific study should be started by the scientist, but the sooner they can associate ordinary practical men with the work the better it will be. We practical seamen are more numerous than scientists; we constantly navigate the sea, and we have more opportunities of making contributions to science than they have. Certainly, they can make their observations in a more exact way than we can, but the laws of nature—particularly those concerning Oceanography—are so imperfectly known, that there is very much to be done even by the rough hands of the ordinary seamen.
On the Survey by the S.S. ‘Britannia’ of the Cable Route between Bermuda, Turk's Islands, and Jamaica
Authors: Peake R. E. , Murray Sir John 
Published: June 2019

The following is a brief account of the principal points of interest resulting from the survey lately made to find a suitable route for a cable to be laid from Bermuda to Turk's Islands and from thence to Jamaica.As engineers to the Direct West India Cable Co., my firm, Messrs Clark, Forde, & Taylor, strongly advised that a more than usually complete set of soundings should be taken along the route over which it was proposed that the cable should be laid, our principal reason being that, as the Bermuda group has been raised almost vertically from the bed of the Atlantic by volcanic action, it was impossible, with the limited information available, to say whether similar action might not have taken place elsewhere on the proposed route for the new cable.The task of carrying out this survey was undertaken by the Telegraph Construction and Maintenance Co. with their s.s. ‘Britannia,’ which was fitted up with all necessary apparatus, and was also well adapted for the work.Sounding operations were commenced off Grand Turk Island on the 4th November 1897, and completed on the 2nd December following at Bermuda, during which time 182 soundings were taken, apart from the profile soundings taken off Grand Turk. The laying of the cable was commenced at Bermuda on the 5th January 1898, and completed on the 18th of the same month.As a result of this work the following suggest themselves as points worthy of notice:—(1) The even slope of the ground from the neighbourhood of Bermuda to the deepest water found in Lat. 24° 50′ N., no indication being discovered of any upheaval similar to that which has produced the Bermudas with their adjoining shoals.
The Energy of the Röntgen Rays
Authors: Moffat Alexander 
Published: June 2019

The number of experiments that have been made on the Röntgen rays is already very large, and much has been learned from them regarding the properties of these rays. There has been, however, as yet, but little done to determine their energy. Indeed, the only accurate work which has been carried out in this direction is that of E. Dorn (Wied. Ann., Bd. 63, p. 160), who measured the heat produced by Röntgen rays falling on a metal plate. This investigation is, however, not complete, as Dorn did not determine the number per second or the duration of the discharges of the Röntgen rays.On the suggestion of Professor E. Wiedemann (Erlangen), in whose laboratory I have been working, I have tried to investigate this subject; and, although I have not had time to complete my experiments, as I now find I have to return to India much earlier than I expected, I shall describe the methods adopted and the results obtained, in the hope that they may not be without interest.I first sought to determine in absolute measure the quantity of light produced on a screen of barium platino-cyanide by Röntgen rays. For this purpose I used an optical bank with the barium platino-cyanide screen and the Röntgen lamp at one end, the source of light which I used as a standard of comparison at the other end, and between them a movable photometer. The arrangement of the apparatus is shown in the following diagram.
On the Development and Morphology of the Marsupial Shoulder-Girdle
Authors: Broom R. 
Published: June 2019

AbstractAn examination is made of a series of early stages in the development of the shoulder-girdle in the common Phalanger (Trichosurus vulpecula), and of early stages in the development of that of the Ring-tailed Phalanger (Pseudochirus peregrinus), and of the Rock-wallaby (Petrogale penicillata). Though in their main features there is much similarity between the girdles of the different genera, there are certain peculiar features in each.In a Trichosurus fœtus of 8·5 mm., though the main part of the scapula is chondrified, together with the glenoid portion of the coracoid and a portion of the acromion, the rest of the arch, the sternum, and the greater part of the clavicle, are still mesenchymatous. The coracoid can be traced downwards as a fan-like expansion, which meets the first rib and the sternum. Between the coracoid and the clavicle a feebly-developed thin sheet apparently represents the precoracoid (epicoracoid). The clavicle is partly ossified at its upper part, and it is very manifest that there is no cartilaginous basis.In the Trichosurus fœtus, at birth (14 mm.), the scapula is well developed. The acromion is a large process which springs from the anterior border of the blade. The spine is not yet formed, though its basis can be distinctly traced as a membranous structure stretching from the acromion upwards along the outer side of the scapula in its anterior third. There is no cartilaginous basis for this part of the spine. The coracoid is of large size, and its lower part, which is somewhat bulbous, articulates with the sternum and with the first rib.
Application of Sellmeier's Dynamical Theory to the Dark Lines D1, D2 produced by Sodium-Vapour
Authors: Kelvin Lord 
Published: June 2019

§ 1. For a perfectly definite mechanical representation of Sellmeier's theory, imagine for each molecule of sodium-vapour a spherical hollow in ether, lined with a thin rigid spherical shell, of mass equal to the mass of homogeneous ether which would fill the hollow. This rigid lining of the hollow we shall call the sheath of the molecule, or briefly the sheath. Within this put two rigid spherical shells, one inside the other, each movable and each repelled from the sheath with forces, or distribution of force, such that the centre of each is attracted towards the centre of the hollow with a force varying directly as the distance. These suppositions merely put two of Sellmeier's single-atom vibrators into one sheath.§ 2. Imagine now a vast number of these diatomic molecules, equal and similar in every respect, to be distributed homogeneously through all the ether which we have to consider as containing sodium-vapour. In the first place, let the density of the vapour be so small that the distance between nearest centres is great in comparison with the diameter of each molecule. And in the first place also, let us consider light whose wave-length, is very large in comparison with the distance from centre to centre of nearest molecules. Subject to these conditions we have (Sellmeier's formula)where m, m denote the ratios of the sums of the masses of one and the other of the movable shells of the diatomic molecules in any large volume of ether, to the mass of undisturbed ether filling the same volume; k, k the periods of vibration of one and the other of the two movable shells of one molecule, on the supposition that the sheath is held fixed; ve the velocity of light in pure undis turbed ether; vs the velocity of light of period τ in the sodium-vapour.
Decorated and Sculptured Skulls from New Guinea
Authors: Turner Sir Wm. 
Published: June 2019

The ten skulls to which I would direct attention this evening were collected in the island of New Guinea. The first to come into my possession was given to me in 1895 by one of my pupils, Mr F. N. Johnston, the nine others have been recently purchased from dealers. I am not able to name the tribe or tribes by whom the skulls had been sculptured, neither can I state the precise locality at which they were obtained; but the dealer from whom I bought eight specimens told me that they came from the Purari River district. This river rises in the range of the Albert Victor Mountains, and after a known course of 130 miles, it discharges its waters by several mouths into the head of the great gulf of Papua. It is said to be the largest river in the British territory, next to the Fly River.In a valuable memoir by Messrs Dorsey and Holmes, on a collection of sixteen decorated skulls from New Guinea, published in 1897, the authors state that although they cannot give the locality from which the specimens came, it is probable that they were collected on the northern shore of the Papuan Gulf, in the British Protectorate. Mantegazza and Regalia have figured a skull from Canoe Island in the Fly River, where the frontal bone was sculptured with four concentric circles. Professor Haddon, in his elaborate memoir on the Decorative Art of New Guinea, says that in the museum at Florence are seven skulls, collected by D'Albertis in the Fly River district, which have designs carved on the frontal bone.
Note on Mr Joseph O. Thompson's Results regarding Vibrating Wires
Authors: Peddie Dr W. 
Published: June 2019

In 1865 Lord Kelvin published the results of experiments which first made evident “a very remarkable fatigue of elasticity, according to which a wire which has been kept vibrating for several hours or days through a certain range came to rest much quicker when left to itself than when set in vibration after it has been at rest for several days and then immediately left to itself.” On the strength of Lord Kelvin's statement this elastic fatigue of metals has been regarded as a definitely ascertained fact. But, quite recently (Physical Review, March 1899), Mr Joseph O. Thompson has published a paper “On the period and logarithmic decrement of a continuously vibrating wire,” in which he states that it seems probable that “for constant temperature and constant amplitude the logarithmic decrement is constant.” This conclusion is based upon his observation that the logarithmic decrement, in the case of a copper wire, when the amplitude of vibration varied from about 185° to 175°, had the same value after it had been continuously vibrated through the average arc of 180° for fifty consecutive hours as it had at the commencement of that period. Observations upon other metals seemed to support the conclusion.Lord Kelvin also stated that fatigue caused an increase of the period of vibration. Mr Thompson finds that “no matter what metal was used, no matter whether the arc of vibration was as small as 20° or as high as 200°, no matter whether the wire was long or short, thick or thin (provided of course the breaking strength of the wire was at least twice the weight of the disc), the result was uniformly the same, namely, that when temperature and amplitude of vibration remained constant, the period of vibration was a constant quantity.”