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has surpassed it in the economy of coal, and it realizes to the fullest extent Watt's ideal of the expansion of steam from the boiler to the lowest vapor pressure obtainable in the condenser.

Among the minor improvements which in recent years have conduced to a higher efficiency in turbines are the more accurate curvature of the blades to avoid eddy losses in the steam, the raising of the peripheral velocities of the blades to nearly the velocity of the steam impinging upon them, and details of construction to reduce leakages to a minimum. In turbines of 20,00030,000 h. p., 82 per cent. of the available. energy in the steam is now obtainable as break-horse-power; and with a boiler efficiency of 85 per cent. the thermodynamic efficiency from the fuel to the electrical output of the alternator has reached 23 per cent., and shortly may reach 28 per cent., a result rivalling the efficiency of internalcombustion engines worked by producer

gas.

During the twenty years immediately preceding the war turbo-generators had increased in size from 500 kilowatts to 25,000 kilowatts, and the consumption of steam had fallen from 17 pound per kw.-hour to 10.3 pound per kw.-hour. Turbines have. become the recognized means of generating electricity from steam on a large scale, although they have not superseded the Watt engine for pumping mines or the drawing of coal, except in so far as it is a means for generating electricity for these purposes.

In the same period the enginepower in the mercantile marine had risen from 3,900 of the King Edward to 75,000 of the Mauretania.

As regards the Royal Navy, the enginepower of battleships prior to the war had increased from 12,000 i.h.p., to 30,000 s.h.p., while the speed advanced from 17 knots to 23 knots, and during the war, in ships of the Queen Elizabeth class, the power amounted

to 75,000 s.h.p., with a speed of 25 knots. In cruisers similar advances were made. The i.h.p. of the Powerful was 25,000, while the s.h.p. of the Queen Mary was 78,000, with a speed of 28 knots. During the war the power obtained with geared turbines in the Courageous class was 100,000 s.h.p., with a speed of 32 knots, the maximum power transmitted through one gear-wheel being 25,000 h.p., and through one pinion 15,500 h.p.; while in destroyers speeds up to 39 knots have been obtained. The aggregate horse-power of war and mercantile turbined vessels throughout the world is now about 35,000,000.

These advances in power and speed have been made possible mainly by the successive increase in economy and diminution of weight derived from the replacement of reciprocating engines by turbines directcoupled to the propellers, and later by the introduction of reduction gearing between the turbines and the propellers; also by the adoption of water-tube boilers and of oilfuel. With these advances the names of Lord Fisher, Sir William White, and Sir Henry Oram will always be associated.

The Work of Sir William White.-With the great work of the Royal Navy fresh in our minds, we can not but recall the prominent part taken by the late Sir William White in its construction. His sudden death, when president-elect for 1913, lost to the nation and to the association the services of a great naval architect who possessed remarkable powers of prevision and dialectic. He was Chief Constructor to the Admiralty from 1885 to 1901, and largely to him was due the efficiency of our vessels in the great war.

White often referred to the work of Brunel as the designer of the the Great Eastern, and spoke of him as the originator of the cellular construction of the bottoms of ships, since universally adopted, as a means of strengthening the hull and for ob

taining additional safety in case of damage. Scott Russell was the builder of this great pioneer vessel, the forerunner of the Atlantic liners, and the British Association may rightly feel satisfaction in having aided him when a young man by pecuniary grants to develop his researches into the design and construction of ships and the wave-line form of hull which he originated, a form of special importance in paddlewheel vessels.

So much discussion has taken place in the last four years as to the best construction of ship to resist torpedo attacks that it is interesting to recall briefly at the present time what was said by White in his Cantor lectures to the Royal Society of Arts in 1906:

Great attention has been bestowed upon means of defence against underwater torpedo attacks. From the first introduction of torpedoes it was recognized that extreme watertight subdivision in the interior of warships would be the most important means of defence. Experiments have been made with triple watertight skins forming double cellular sides, the compartments nearest the outer bottom being filled, in some cases, with water, coal, cellulose, or other materials. Armor-plating has been used both on the outer bottom and on inner skins.

He also alludes to several Russian ships which were torpedoed by the Japanese, and he concludes by saying:

"Up to date the balance of opinion has favored minute watertight subdivisions and comparatively thin water-tight compartments, rather than the use of internal armor, the use of which, of course, involves large expenditure of weight and cost."'

The present war has most amply confirmed his views and conclusions, then so lucidly and concisely expressed.

While on the subject of steamships, it may perhaps be opportune to say one word as to their further development. The size of ships had been steadily increasing up to the time of the war, resulting in a reduction of power required to propel them per ton of displacement. On the other

hand, thanks to their greater size and more economical machinery, speeds have been increased when the traffic has justified the greater cost. The limiting factor to further increase in size is the depth of water in the harbors. With this restriction removed there is no obstacle to building ships up to 1,000 feet in length or more, provided the volume and character of the traffic are such as to justify the capital outlay.

Tungsten Steel.-Among other important pre-war developments that have had a direct bearing upon the war, mention should be made of the discovery and extensive use of alloys of steel. The wonderful properties conferred upon steel by the addition of tungsten were discovered by Muschet in 1868, who has not been sufficiently credited with his share in making the Bessemer process a practical success, and later this alloy was investigated and improved by Maunsel White and Taylor, of Philadelphia. The later showed that the addition of tungsten to steel has the following effect: That after the steel has been quenched at a very high temperature near its melting point, it can be raised to a much higher temperature than is possible with ordinary carbon tool-steel without losing its hardness and power of cutting metal. In other words, it holds the carbon more tenaciously in the hardened state, and hence tungsten-steel tools, even when redhot, can cut ordinary mild steel. It has revolutionized the design of machine tools, and has increased the output on heavy munition work by 100 per cent., and in ordinary engineering by 50 per cent.

The alloys of steel and manganese with which Sir Robert Hadfield's name is associated have proved of utility in immensely increasing the durability of railway and tramway points and crossings, and for the hard teeth of machinery for the crushing of stone and other materials, and, in fact, for

any purposes where great hardness and strength are essential.

A QUESTION CONCERNING THE
NATURE OF VELOCITY

TOLMAN'S remarkable success in deriving by means of his principle of similitude1 a large number of physical laws, laws which have also been otherwise derived by the more natural and usual method of experimentation and measurement, ought to indicate that there is

Investigation of Gaseous Explosions.Brief reference must also be made and it will be gratifying to do so-to the important work of one of the committees of the British Association appointed in 1908, under the chairmanship of the late Sir William Preece, for the investigation of probably something fundamentally right about

gaseous explosions, with special reference to temperature. The investigations of the committee are contained in seven yearly reports up to 1914. Of the very important work of the committee I wish to refer to one investigation in particular, which has proved to be a guiding star to the designers and manufacturers of internal-combustion engines in this country. The members of the committee more directly associated with this particular investigation were Sir Dugald Clerk, Professor Callendar, and the late Professor Bertram Hopkinson.

The investigation showed that the intensity of the heat radiated by the incandescent gases to the walls of the cylinder of a gas-engine increases with the size of the cylinder, the actual rate of this increase being approximately proportional to the square root of the depth of the radiating incandescent gas; the intensity was also shown to increase rapidly with the richness of the gas. It suffices now to say that the heat in a large cylinder with a rich explosive mixture is so intense that the metal eventually cracks. The investigation shows why this occurs, and by doing so has saved enormous sums to the makers of gas- and oil-engines in this country, and has led them to avoid the large cylinder, so common in Germany before the war, in favor of a multiplicity of smaller cylinders.

CHARLES A. PARSONS (To be continued)

his method of procedure. His argument involves two universes, while physics knows only one-and the bearing of his conclusions upon the single universe that we know is not altogether apparent. When he further asks it to be assumed that the velocity of light and the charge of the electron shall be the same in both universes, his argument seems far removed from the facts of the laboratory and its relevance to the usual physics may be, and indeed has been, brought into serious question.

But his argument may be developed without any appeal to two universes. So developed it has an important bearing upon the theories of the nature of electricity and of the manner of the propagation of light. Consider any two observers in our present universe, each of whom with a different set of standards of measurement makes experiments and determines laws. The laws determined by the two observers will have the same algebraic form and will differ only in the value of the constants which they involve. Since all of the measureable quantities of physics are defined in terms of three fundamental and ultimately undefined quantities, each observer will need only three standards2 in order that he may

1 Tolman, Phys. Rev., 3, 244, 1914; 4, 145, 1914; 6, 219, 1915; 8, 8, 1916; 9, 237, 1917. Buckingham, ibid., 4, 345, 1914. Nordstrom, Finska Vetenskaps Soc. Forh., 57, 1914-15; Afd. A. No. 22. Ishiwara, Science Report of Tohoku Imp. Univ., 5, 33, 1916. Ehrenfest-Afanassjewa, Phys. Rev., 8, 1, 1916. Bridgman, ibid., 8, 423, 1916. Karrer, ibid., 9, 290, 1917.

2 All seem agreed that length and time are fundamental and undefinable. About the third quantity, force or mass, or energy, as the case may be, there seems to be considerable debate. The argument of the present paper is valid, whichever one of them is favored. I have chosen force be

:

measure all quantities which come within his observation. The standards of the two observers, O and O', may be connected by algebraic equations, for length, l'x l, for time t'=yt, and for force, f'=zf, where x, y and z are constants which may have any value and which express the ratio between the magnitudes of the corresponding standards of the two observers. From these three equations corresponding "transformation equations," involving x, y and z, for all of the measureable quantities of physics may be calculated. Suppose now that the two observers got together and O says to O':

Surely it is the privilege of each of us to work with whatever standards he prefers, you prefer foot-seconds while I prefer gram-centimeters; yet let us, for such and such reasons and for our mutual convenience, each still keeping his standards different from those of the other, so alter our standards that we can both report all electrical charges and all velocities by precisely the same numerical value.

O' may be conceived to reply:

We know indeed that electrical charges are made up of a number of ultimate charges or electrons and that each of these little charges has the same magnitude. If we report all charges by the same number, that is virtually the same as each of us reporting the same count. I see that in favor of cause it seems to me to be primary in the course of experience, not because it makes any difference in the general argument. Many physicists, perhaps most, are disposed to believe that there are two additional fundamental and ultimately undefined quantities necessary to complete the structure of modern physics, namely, (1) temperature or entropy (for thermodynamics) and (2) quantity of electricity or magnetic permeability (for electromagnetics). But temperature is defined by the gas-law, and charge is defined by Coulomb's law. These laws, discovered by the experimentation of workers in whose minds temperatures and charges (respectively) were regarded as equal if in similar situations they produced equal effects, have gradually come in the history of science to assume the sacred functions reserved for definitions. It can not be asserted too strongly that they are not "laws." This, however, is methodology, not theoretical physics, and not the central argument of the present paper.

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Transformation equations involving only one unknown quantity, x, may now be written connecting all of the measurable quantities of O with the corresponding quantities of O'. These equations are identical with those of Tolman; and O and O', working with the perfectly legitimate mathematical reasoning that Tolman uses, may derive, by virtue of their simple agreement, all of the conclusions which he derives from his principle of similitude.

So long as O and O' have no agreement between themselves, the transformation equations connecting their various quantities will involve three unknown quantities, x y and z.

3 To illustrate the method of reasoning-The transformation equation for energy density is

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Only when the number of these unknown quantities is reduced to one, does it become possible for them to make use of the mathematical reasoning, involving the solution of functional equations, which has led in the hands of Tolman to such a wide variety of useful results. Since x is the ratio between their standards of length-measurement, and y that between their standards of time-measurement, they can express y in terms of x if they agree to make the same numerical report about any one kind of quantity which involves both length and time for its definition, that is, if they agree to make the same reports either about velocities or about accelerations. By making a corresponding second agreement about some quantity which involves for its definition force and time or length or both, such for instance as charge or mass or energy, they will be able to express z in terms of x— and to derive an entire set of transformation equations which involve only one unknown quantity. With this new set of equations at hand, they may undertake to set up functional expressions and to derive laws as Tolman has done.

Evidently the number of the different possible sets of transformation equations is quite considerable, for there are many measurable quantities in physics which involve for their definition more than one of the three fundamental undefined quantities. I have calculated nine such different sets. Several of them lead to some of the conclusions which may be deduced from the equations of O and O' above (based upon agreements concerning velocities and charges); several of them lead, in cases where the set of O and O' has proved fertile, to insoluble or absurd functional equations which point to no solution. Some of them lead to laws which are contrary to those whose validity has been established by experiment. None of the sets is as fertile or leads to as many well established laws as the set which is based upon the agreement of O and O' to report all charges and all velocities by the same numerical value. But this agreement is the only thing in the way of an assumption which is involved in the simpli

fied form of Tolman's principle of similitude that is developed by O and O' of this paper. The noteworthy success of Tolman in deriving from his principle a large number of experimentally valid laws is evidence that an agreement between observers working with different standards of measurement to report the same charges and velocities by the same number is somehow more intimately in harmony with the order of nature than any other similar agreement relative to some other of the quantities of physics.

Electrical charges may be regarded as if they are made up of a countable number of small units. This has been adequately demonstrated by the researches of Millikan and others in which electrons have actually been isolated and counted. But it could also have been predicted-for, as an assumption, it leads in the hands of 0 and O' to many conclusions which are otherwise verified by experimental fact. In the same way the assumption that velocities are of such sort that there is only one right way to report their magnitude, is one which leads, vastly better than any similar assumption, to the deduction of laws which are established in fact. Hence the assumption is probably true.

Professor Tolman has kindly read the first draft of this paper. He suggests that the conclusion that velocity is of such nature that there is only one right way to report its magnitude, a conclusion which has here been reached by abstract reasoning, may be interpreted concretely to mean that "any given velocity is most sensibly regarded as a given fraction of the maximum possible velocity, namely that of light."

TENNEY L. DAVIS

DEPARTMENT OF CHEMISTRY,
MASSACHUSETTS INSTITUTE OF TECHNOLOGY,
CAMBRIDGE, MASS.

JACQUES DANNE

WITH the outbreak of the world conflict in 1914 Le Radium at once ceased publication, all of its editors being called into service. The decision for service was no less definite than the assurance that publication would be

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