valuable for under- water purposes, such as piles, sluices, &c. It is used for bobbins, clogs, pattens, French sabots, basins, plates, herring barrel staves. Dyes are obtained from the bark and shoots. The bark is bitter and astringent. Alder is largely used for making charcoal for gunpowder. It is uniform in texture, soft, and easy to work, but shrinks rather badly. In Britain it is very common, but does not attain a large size, seldom exceeding 40 feet in height. In large quantities it is obtained chiefly from the large alder swamps in Western Russia and Eastern Prussia.

=

Algebraical Signs. The common signs used in algebraical expressions and processes are as follows:- + (plus) denotes that the quantities between which it is placed are to be added together; - (minus) that the quantity before which it is placed is to be subtracted from the one preceding it; the sign signifies signifies that the numbers between which it is placed are equal. Thus a+b+c=d means that the sum of a, b, and c is equal to d. × denotes that one number is to be multiplied by another. This sign is frequently omitted, thus abc has the same meaning as axbx c. The sign ÷ means that the quantity which precedes it is to be divided by the one which follows it. Here again we have an alternative of expressing way division, one number being placed over another

5

The sign placed over any quantity signifies that its root is to be extracted, the particular root being indicated by a small figure placed above this sign. Thus /b, b, /b are read respectively as the third, fourth, and fifth roots of b. In the case of the square root, however, the figure 2 is usually omitted, so that 9 is understood to mean the square root of 9.

When a number is multiplied by itself a number of times, as for instance, bxbxbxb,

this is denoted by b4. So that if we wished to multiply a by itself twice, b by itself three times, and c by itself four times, and to express the product of all these quantities, it would not be stated as aabbbcccc, but as a2 b3 c1, and read as "the product of a squared, b cubed, and c to the fourth power."

Brackets are extensively used in algebra. To prevent confusion, pairs of brackets of different shapes are used, as (), {}, [], while a long stroke,

called a vinculum, sometimes occurs. Two very important rules must be observed in using brackets-(1.) When a bracket is preceded by the sign the bracket may be removed without altering the signs of the terms in it. (2.) When a bracket is preceded by the sign the sign of each term contained within the brackets must be changed.

In cases where several brackets are used it is usual to commence by removing the innermost pair. Thus :

a - [b - {c-d-(e −ƒ')}] =
a-[b-fc-d-e+ƒ}]=
a - [b-c+d+e-ƒ] =
a-b+c-d-e+f

Alignment. Parts of machinery which are in line with each other are in alignment. The head and tail centres of a lathe, for instance, or a length of shafting and its bearings, are in alignment. The term also denotes the act of adjusting to a line.

The methods by which alignment is secured in shop practice vary with the nature of the work, and the degree of accuracy desired. In general, alignment is checked in one of two ways, either by reference to a surface known to be horizontal, or by means of a spirit level. In the first case the surface may be a level one, on which the parts to be aligned rest, or a portion of the work itself is levelled, and used as a base from which to operate. The second depends for its truth on the accuracy of the spirit level, or on the method of its manipulation, as turning it about end for end if not quite true, or else the level is used as a check upon, or in combination with other devices. The common rule alone plays but a small part in aligning work, except by affording rough approximations. In the finest work devices are adopted for multi

The alignment of shafts and of centres affords the most common examples. The preliminary work of marking out for boring holes is done when possible on the marking-off table, using a surface gauge, which ensures the centres so marked at one setting being at the same height. After the holes are bored, and the shafts are in place, the surface gauge is again used, checking the top and bottom of the shafts. The centres of lathes are checked in similar fashion from the surface of the bed; but if very fine precision is required, an indicator is used, by which any error is multiplied a hundredfold. In the case of work for which no level base can be found, as in heavy cheeks, or bedplates that are erected on wood blocking, the main casting or castings are levelled up on wood blocking until some faced or bored part or parts are got true by the level. In the case of holes in frames, set at some distance asunder, and bolted together, a shaft is inserted in the holes, and its top tested with a spirit level. Then when facings or shaft holes are thus levelled, all other shafts, facings, and horizontal faces can be tested either for alignment or parallelism by spirit level.

The case of shafting stands apart, and will be more suitably treated in extenso under the head of Shafting, because there are several methods by which shaft bearings are aligned.

Alignment of large erections is done by means of straining a fine wire or cord between parts. The "set" of beams under strain is often tested in this manner. A more correct method is that of the theodolite, which alone is suitable for checking objects that are at a considerable distance apart. Alignment in a perpendicular direction is done by plumb lines, or plumb rules, and spirit level in combination.

Aliquot Part.-One number is said to be an aliquot part of another when it divides evenly into that number without leaving a remainder. Thus, 5 is an aliquot part of 100 because it is contained exactly 20 times in 100. Similarly 6d. is an aliquot part of 1s.; 4 stones is an aliquot part of a hundredweight; 9 inches an aliquot part of a yard; and 12 hours an aliquot part of a day. The arithmetical rule of

number of articles by means of aliquot parts.

All-gear Head.-A term applied to the fast headstock of those lathes in which stepped cones are abandoned for a single belt pulley, and toothed gears for changing speeds. See High-Speed Lathes.

Alligator Shears.-See Shears, Shearing Machines.

Allotropy. The property possessed by some elements and compounds of existing in more than one form so far as their physical properties are concerned. The diamond, the graphite in a lead pencil, and a lump of charcoal are widely different in their appearance and physical properties, yet chemically they are perfectly identical with each other, each one consisting of carbon. Hence we speak of these three varieties of carbon as allotropic modifications of the element.

Sulphur too occurs in several allotropic modifications differing in crystalline form, in colour, and solubility in carbon bisulphide. It is found in octahedral crystals readily soluble in CS,; in crystals of prismatic form from fusions; and in the peculiar plastic form, obtained by heating sulphur to about 230° Cent., and pouring it into cold water, where it settles as a soft tenacious mass readily drawn out into long threads. In the latter form it is insoluble in CS. Unlike the allotropic modifications of carbon, these forms of sulphur change more or less rapidly into ordinary sulphur.

Phosphorus again occurs in various allotropic forms. First we have ordinary phosphorus, kept under water on account of its great inflammability when exposed to the air. If ordinary phosphorus is heated to a temperature not exceeding 240° Cent. in an atmosphere incapable of acting chemically upon it, it becomes changed into a red amorphous condition. This form is non-poisonous, and need not be kept under water. It may even be heated up to 250° without igniting. Above that temperature it is changed into ordinary yellow phosphorus, inflames, and is transformed into the pentoxide. The paper on the side of a box of safety matches is coated with a mixture of amorphous phosphorus and powdered glass. In the atmosphere there exists a very

interesting example of allotropy, for oxygen and ozone are allotropic forms of the same gas. Ozone is really condensed oxygen possessing 1 times the density of the latter. Ozone is formed, among other ways, during electrical discharges in oxygen; by the slow oxidation of phosphorus in moist air; by oxidising ether vapour with a hot glass rod; and is found in the neighbourhood of the flame of hydrogen burning in air. As with sulphur, ozone (03) has a very strong tendency to throw off its third atom and exist as an ordinary molecule of oxygen (O2). Because of this it is a very active oxidising agent.

The chief present interest in allotropy to the engineer lies in the fact that it was for a period a working hypothesis of the different characteristics of a metal existing under different conditions. The different phenomena of hard, and soft, and mottled iron, for example, seemed to afford an excellent example of allotropy in metals, as did also the remarkable facts published by the late Sir W. C. Roberts-Austen in his classical Cantor lectures relating to gold and copper. In these and other cases the addition of elements almost infinitesimally minute in quantity, produced most radical differences in the resulting compound, or mixture, for it was uncertain what was really happening. The very small particles of antimony, bismuth, lead, or other elements added to gold seemed utterly incapable either of diffusing themselves through the mass, or of entering into chemical union with the immensely larger body. The remarkable differences produced by the sudden or slow cooling of iron containing carbon, though known well enough in everyday practice, seemed inexplicable, excepting on the allotropic hypothesis, which, however, did not afford any real explanation of the modus operandi of the processes going on. At the present time the Allotropists seem to have been driven off the battle-ground by the microscope, an instrument which few thought of much value in metallurgy, except as a dilettanti pursuit. What the microscope has shown is this;-that the masses of the principal metal are unchanged in themselves by the entrance of the alloy into their midst. But the alloy insinuates itself between the masses, separating, segregating, laminating, and gener

ally weakening the whole lump. It is not that the iron or gold or copper are changed, but that they are weakened by the presence of a parasitic element which is often undesirable. See Microstructure of Metals.

It is difficult to state the case for both theories without going deeply into the history of the researches on the changes which are produced in iron containing carbon. These will be treated with reasonable fulness under iron, so that here we will assume a knowledge of that subject.

The differences between the Allotropists and the Carbonists may be tersely put in this way. The Allotropists hold that iron (around which the controversy has chiefly taken place), which exists in different forms, hard, soft, and in a stage between the two, exists thus by value of modification in the iron, produced by carbon. The Carbonists hold that these changes in the state of iron are produced by changes in the condition of the carbon. The three states of iron are ever present to the foundryman, who has always been unconsciously a Carbonist, because it has always been held that the hard or white, soft or grey, and the mottled or medium soft iron, were states caused mainly by the relative proportions in which the combined, or the graphitic forms of carbon were present. Carbon is an allotropic element, and it seems therefore unnecessary to attempt to explain obvious facts by the assumption of an allotropic condition in the iron itself.

Alloys. In no department of metallurgy has greater advance been made during recent years than in the study of alloys. And this term is employed in a vastly more comprehensive sense than it was only a few years since. It now includes all the irons and steels as well as the copper alloys, or those of tin, zinc, lead, &c., or those of the precious metals. The subject has been attacked from the mechanical and the chemical side, and the microscope has proved a most valuable aid in these researches. A new literature has been created dealing with this subject, and the names of a few workers in the field have become almost as familiar as household words. The Institution of Mechanical Engineers has fostered a long series of original investigations in charge of an

Alloys Research Committee, whose labours go back to 1890, and who have issued several valuable Reports, published in the Proceedings of the Institution. The late Professor W. C. Roberts-Austen, F.R.S., was the leading spirit of this Committee.

Outside work has been done by Osmund, Gautier, Stead, Turner, Sorby, and others, to whose labours frequent reference must be made in these volumes. The subject of alloys, using the term in its latest modern sense, is not only most fascinating, but one which promises to effect changes in the older methods of those who have to produce and work in metals, in the irons, the steels, copper, and the other commercial metallic elements.

It has always been known in a practical way how a very small proportion of an alloying element is able to effect a most extensive change in the physical characteristics of the alloy produced. The question was long disputed whether an alloy was a simple mixture, or a true chemical compound. For the first it was argued that some metallic elements would not mix properly with others, as lead for example with copper or brass, liquation taking place, or tin with copper, appearing as white spots in the castings, hence the reason for making a preliminary mixture or a "temper" in some of the copper alloys. For the second, the fact that a practically new metal is produced by alloying in different proportions, such for example as soft brass at one extreme, and bell, or speculum metals at the other, favoured the belief in chemical combination. right in certain cases; with suitable mixing the fact of chemical combination is undoubted. Along this line of research many of the most interesting results of recent years have been achieved.

Both are

Much of the research of Sir W. C. RobertsAusten was undertaken to investigate the properties of metals based on the law enunciated by Newlands and Mendeléef, expressed thus: "The properties of the elements are a periodic function of their atomic weights." It was known that the effect of impurities added to gold was nearly proportional to their atomic volume, but it was not known whether this held good for other metals. The researches of

The effect of these elements on iron will be found under Iron. Just here we remark that iron is an exceedingly complicated substance even as an element. For pure iron exists in two varieties, the a, or soft, and the ẞ, or hard quality, and impure irons are affected greatly by the presence of the foreign elements, which while detracting from the purity of the metal, add to its value physically and commercially, and an intimate knowledge of which lies at the basis of a scientific treatment of iron and steel in the shops.

Numerous experiments have been carried out, which have had for their object the determination of certain matters connected with the effects of alloying elements on the rate of, and method of cooling, and temperature of the alloys at the "freezing point," or the point when solidification commences. Light has been sought on the behaviour of the alloys employed by engineers, by noting that of alloys of the precious metals, particularly silver and gold. It is proved that alloys are not homogeneous, except in certain proportions which vary in the case of different metals. Levol concluded that the only homogeneous alloy of silver and copper was that containing 71.893 per cent. of silver, and 28.107 per cent. of copper, and that this is a definite combination of the two metals, having the formula AgCu. Sir W. C. Roberts-Austen found that a cubical mass of silver alloy measuring 45 mm. or 13 inches on the side gave different analyses at different planes. The alloy contained 92.5 per cent. of

silver, and 75 per cent. of copper, and it was cooled rapidly. Then it was found that the silver was richer by 1.28 per cent. at the centre of the cube than at the external corners. This partial separation of the alloying elements, known as liquation, is a phenomenon familiar to brassfounders and plumbers as occurring in alloys of copper, lead, tin, and zinc.

The term "eutectic alloy," generally accepted, and employed by metallurgists, was first given by Guthrie to the residual alloy which is left finally as being the last portion of a mass to cool. The first portions of an alloy thrown off in cooling have definite atomic proportions, but the final or residual alloy does not contain its constituents in due atomic proportions. This eutectic alloy is the most fusible.

For many years observers have followed a course of experimenting in which alloys have been regarded as resembling saline solutions in their method of crystallisation. The analogy lies in this, that saline solutions in freezing, liquate, or reject a portion of the fluid part of the mass, the "mother liquor," after the bulk of the salt has crystallised out. This corresponds with the eutectic alloy. But the common alloys have several such liquations; there are four at least in the copper-zinc series, and six in the copper-tin series; meaning by "series," the range of all the possible unions which can take place in these metals.

The cooling of an alloy is represented graphically by a curve passing through vertical ordinates which represent temperature, and horizontal abscissæ which represent time. As the mass cools, the course of the cooling curve runs obliquely downwards, until the metal begins to "freeze," or solidify. There is then a pause in that course, represented by a horizontal line, during which period solidification is going on. This may occur quickly, but generally it is delayed. When the solidification is complete, the curve continues its oblique downward course until it reaches atmospheric temperature.

Photographic records of the cooling of silvercopper alloys have shown that more than one freezing point occurs, which is considered to be due to the falling out of differently constituted alloys from the mass. Heat also is evolved at

these points. The term critical point, or points, is applied to those at which freezing, or solidification occurs.

Gold, which has been freely employed by Sir W. C. Roberts-Austen in experiments on the behaviour of alloys, offers many advantages over iron in researches of this character. It can be prepared in a very high degree of purity, and it is not liable to oxidation. Experiments on it were conducted when alloyed with bismuth, platinum, silicon, manganese, aluminium, silver, and other elements. A study of the effects of aluminium proved the most interesting to engineers, because of the connection of the latter with iron. The gold combined with it most readily, and showed a marked granular structure. The physical properties of the gold were completely disorganised, the point of initial freezing was lowered, the metal only partly solidified during a long range of temperatures, and it could easily be poured at several hundred degrees below its initial freezing point.

The fact that there is a direct connection between the melting point of an alloy and its mechanical properties has a practical bearing in the case of those alloys which have to be subjected to heat treatment in manufactures.

A

Weakness is a result of the alloying of a strong metal, having a high melting point, with a minute quantity of one that is weak, with the concomitant of a low melting point. great distinction must, however, be made between such minute quantities, and large proportions. A trace of a metal with a low melting point and large atomic volume renders the metal with high melting point weak. But a large quantity of the first named will often produce an alloy stronger than either one of its constituents possesses.

Some of these facts have long been known by workers in metals, but not understood. They appear now to be related intimately to the fact that the majority of alloys have more than one freezing point, or point at which solidification takes place. Experiments have indicated that when alloys have in addition to a main freezing point, subsidiary ones, the last named is usually associated with low tenacity of the alloy.

In experiments on copper-bismuth, and silverleads, it has been found that the upper