which is the ordinary position in which the instrument is employed. The telescope, its level, the arc to which it is fixed, the pivot on which it and the arc moves, and the supports on which the pivot rests, may be regarded as forming one part of the entire instrument.

The whole of this part is now fixed upon a horizontal circular plate which turns horizontally upon another plate beneath it. The edges of these two plates meet on a slope, and are also accurately divided; the lower one into degrees and half degrees; the upper or vernier plate, as it is termed, into two opposite verniers. Two spirit-levels are fixed upon the upper plate, at right angles to each other.

This combined arrangement forms the theodolite proper, and is connected with a series of levelling screws below, the whole being attached to a brass cap fitted by well-made hinges to the top of a tripod.

In the field of the telescope are placed exceedingly fino lines, either of gossamer web or platinum wire, at right angles to each other, the point of intersection being in the optical axis; by means of these the axis of the glass can be brought to bear very accurately upon a small distant object.

The vernier plates above alluded to are short scales, differing slightly in the length of the divisions from the length of the divisions on the lower plate, the difference being in the proportion of 11 to 10; and their use is to obtain a greater degree of accuracy in estimating the length of the are through which the upper plate has moved as compared with the lower. The coincidence of a division on the vernier with one on the lower scale indicates what the reading to the third place of decimals is to be. The lines are extremely fine, and the coincidence can only be accurately defined by the use of a magnifying glass, two of which are attached to a theodolite, one to take off hori zontal readings, and one vertical readings.

There are two clamping screws in connection with the horizontal plates-one to bind the two plates together, the other to fix the lower plate to the cap.

From the description we have given, the reader will have but little difficulty in following our description of the manner in which the instrument is used.

The first thing to be done is to adjust the legs of the tripod so as approximately to level the circular plates, without much

inequality in the position of the levelling screws. This being done, the levelling screws can be used to ensure a perfect level. Having brought the bubble of both levels to the centre of the glass tube, loose the lower clamping screw, and move the plates round through 180°; if the bubbles still remain central, the instrument is levelled. Next level the telescope. instrument is now ready for use.

The Carefully bring the arrow of the vernier plate into concidence with 360°, or zero, on the lower plate, and clamp the two plates together. Now turn the whole instrument horizontally until the cross wires in the field of view exactly intersect some small but well-defined distant object-an upright rod, for instance. This done, tighten the lower clamp. Then unclamp the upper plate, and turn the telescope round until the cross wires intersect some other well-defined object, and re-clamp the upper plate. Now bring the microscope to bear upon the vernier plate, and read off the number of degrees, minutes, etc., at which the lines coincide. This number will show the angle through which

the telescope has turned since it rested upon the first object. In other words, you have ascertained what is the angle formed by two straight lines converging from the two distant objects and meeting in the centre of the theodolite.

The reader will remember the uses to which angles were applied in the measurement of lines and surfaces in our Lessons on Mensuration, and it would be superfluous to enlarge upon the immense use of an instrument such as we have described, by which these angles can be correctly measured. Of course considerable practice will be required to render the student proficient in the use of the theodolite, and to ensure perfect accuracy in the readings, it will be found of advantage to double, triple, and even quadruple the angle observed, and to take the

until the second object is intersected by the cross wires. Clamp the arc and observe the reading. This will give the vertical angle required.

Our description of surveying instruments might include several others, as, for instance, the optical square, by which perpendiculars of greater length than those usually set off by the cross-staff can be more accurately arranged; the prismatic compass, an instrument for measuring horizontal angles with great facility, but without that extreme accuracy obtained by the theodolite; the pantagraph, a most useful instrument for reproducing plans upon either the same scale, a larger, or a smaller; the protractor, an instrument for laying down upon paper the angles measured on the field.

We think, however, that in the brief outline we have given of the subject sufficient has been explained to give the student a fair insight into it; indeed, if he has rightly followed our remarks, he will have gained sufficient knowledge of it to render a more minute investigation easy.

Our concluding lesson will contain a more full and comprehensive field-book for practice than we have hitherto given.

KEY TO EXERCISES IN LESSONS IN LAND-SURVEYING.—I. 1. 62 acres, 0 roods, 99 poles. 1 2. 3 acres, 2 roods, 7'6 poles.

LESSONS IN GERMAN.-LX.
§ 68.-VERBS.

(1.) A verb is that part of speech which defines the condition of a subject; that is, shows whether it acts, is acted upon, or merely exists.

(2.) In respect to form, verbs are either regular or irregular, simple or compound.

(3.) In respect to meaning, verbs are active transitive, active intransitive, passive, neuter, reflective, or impersonal. These terms have in German the same general signification which they have in English.

(4.) The German, like the English verb, has its moods, tenses, numbers, persons, and participles.

(5.) There are five moods; viz., the indicative, the subjunctive, the conditional, the imperative, and the infinitive. (6.) There are six tenses; viz., the present, the imperfect, the perfect, the pluperfect, the first future, and the second

future.

(7.) Both moods and tenses designate in German just the For same things which the corresponding ones do in English. their general signification, see the paradigms; and for explanation of their uses, see the Syntax.

§ 69.-PARTICIPLES.

minates in ent, and answers in signification to the English par(1.) There are three participles; viz., the present, which terticiple in ing; as, lebent, praising.

(2.) The perfect, which, besides prefixing in most cases the augment ge, ends, in verbs of the Old Form, in en or n; and in those of the New Form, in et or t; and has a meaning corresponding to our participle in ed; as, getragen (ge+trag+en), carried; gelobt (ge+lob+t), praised.

(3.) The future, which is produced by prefixing the particle (to) to the form of the present participle (lobent); thus, zu

Lobend, which means to be praised, that is, praiseworthy.

(4.) The particle ge, mentioned above as being generally prefixed to the perfect participle, was originally designed, it would is altogether omitted are these:seem, to indicate completed action. The instances in which it

First in the case of all verbs compounded with inseparable prefixes (see § 94); as, belehrt (not gebelehrt), informed.

make the infinitive in iren or ieren; as, stutict (from stutiren), Second in the case of verbs from foreign languages, which studied; instead of gestudirt.

* The conditional is made up of the imperfect subjunctive of the

auxiliary verb werden (which see), and the present and perfect infiniby the subjunctive (imperfect and pluperfect), namely, a supposed condition of things, i.e., possibility without actuality. By some it is treated

tive of another verb. It is used to denote what is also often denoted

as a distinct mood; by others, it is made to consist of two tenses: its use is the same in both views,

the Romans, which they played with a ball of leather stuffed with feathers, and the goff-ball is composed of the same materials to this day. During the reign of Edward III. the Latin name cambuca was applied to this pastime, and it derived the denomination, no doubt, from the crooked club or bat with which it was played." Its modern name of golf has the same origin.

Golf is played over a considerable extent of ground, in which small holes to receive the ball are made at distances varying from one to five hundred yards apart. The spots selected for the game are usually commons or heaths covered with short grass, and diversified by various inequalities, which make it more or less difficult to pass the ball on from hole to hole. The Scottish name links, given to the golfing-ground, answers to the English word downs, which suggests the character of the country best fitted for the purpose.

The holes made in the ground are usually not more than four inches in diameter, but about twice that in depth. The spot where each hole is situated is generally distinguished by a coloured flag. The ball is small, and was always made, as Strutt observes, of leather stuffed with feathers in a peculiar way. A piece of hide was soaked in boiling water, and formed into a sphere with a small opening, in which the feathers were inserted and tightly rammed by means of a pointed iron, until as many feathers as would fill a hat were got into the diameter of an inch and a half. As the leather cooled, it contracted upon the feathers. The hole was then sewed up, the mass hammered until it became perfectly round, and a ball possessing great durability, as well as elasticity, was the result. Since the introduction of gutta percha this troublesome process has been dispensed with, golf balls now being usually made of that material. They are painted white, that they may be the more readily discovered when driven to a distance, or among long grass, etc.

The clubs used in driving the balls are of various shapes, according to the character of the blows required in different stages of the game. They vary in length from about 3 to 3 feet, and all consist of a tapering shank or handle, with a head either of wood or iron. The forms of some of the clubs chiefly in use I will be seen in our illustration, although the handles are not shown in the figure.

to hole (entering each) throughout the entire circuit of the links, in the fewest possible number of strokes, and the player or players who can do this in a smaller number of strokes than their opponents achieve the victory. Sometimes the game is reckoned from hole to hole, and the player who counts most holes-that is, who has the largest number scored to him, as having been completed in fewer strokes than those made by his antagonist-is the winner. At other times the number of strokes taken to complete the entire round determines the victory.

If two persons play, it is called a single match, and each, of course, has his ball. If four are engaged, it is termed a "foursome. The players are divided into two sides, each of which has its ball, and they take their strokes alternately.

"

66

In striking or swiping" off, the player places his ball a few yards in front or at the side of the first hole, and he is allowed to make use of any little elevation of sand or earth that may be on the spot to give the ball a better position for a good stroke. This is called teeing the ball, and the starting point is hence termed the teeing-ground. All other strokes must be made from the exact spot which the ball may happen to reach after being struck.

After the player has hit his ball off in the direction of the second hole, the antagonist follows. Provided the latter does

3

The usual number of the set of clubs with which each player is furnished is six, but sometimes as many as ten are used, this being at the player's option. They are carried for the player by an attendant, called his caddie, who hands him from time to time that which the occasion requires. A brief explanation of their various uses will be requisite.

The ordinary or play-club (Fig. 1) is used for striking off, and throughout the game, when the ball has to be driven to a considerable distance. Resembling this in shape, but not so long in the handle, is the "putter," which is employed when the ball is near the hole, and it requires great nicety in the play to make it just reach the spot and fall in. "Putting" is the great art in golf. There are many other features in the game in which particular players possess special dexterity, but without being a good "putter" a player can rarely, if ever, excel in the long run. The " spoon" (Fig. 2) is a member of a somewhat numerous family, called respectively "long spoon," ""short spoon,' ","mid spoon," and "baffing spoon." They are all, as the name implies, spooned or scooped out in the face, this shape being useful in striking a ball out of sunken ground, etc. The different kinds of spoon are adapted to the different degrees of force necessary to drive a ball the required distance to its hole. "Cleeks" (Fig. 3) and "sand-irons" have an iron head, and are used in driving balls out of "bunkers" (sand pits), "whins" (gorse bushes), and some of the other "hazards" or awkward and unfavourable positions in which a ball gets placed in the course of a game. The iron-headed "niblick" (Fig. 4) is for tipping or lifting a ball out of a cart-rut or similar impediment to its progress.

The whole object of the game is to drive the ball from hole

not hit his ball as far as his predecessor, he plays again; and so on all through the game, the ball that is farthest from the hole always being the next in order to be struck.

Various technical terms are used in relation to the strokes. If the first player, we will say, goes nearer to the hole in two strokes than his opponent, the second player must follow his last stroke with a third, and this is called playing one more, or the odds. If player No. 2 is still behind, he must strike the ball again, or play two more, and so on. When the next stroke will make the number equal on both sides, it is termed playing the like. If the player has made two strokes less than his opponent, his next is called one off two; if there is a difference of three strokes between them, it is one off three, etc. When the ball is holed by each in the same number of strokes, that hole is said to be halved.

The rules of the game vary somewhat in different clubs and localities, but among the laws generally accepted, in addition to those we have touched upon in our description, are the following:

1. The ball must be teed or struck off at a distance of not less than two, or more than four, club-lengths in front or at the side of the hole.

2. The side gaining one hole is entitled to strike off first for the next.

3. The ball must not be changed during the play, nor touched with the hand, unless it is driven into water, when it may be lifted, but the player loses a stroke.

4. All loose impediments, such as stones, etc., may be removed, if within a club's length from the ball.

5. If a ball is completely hidden by whins or gorse, etc., the latter may be thrust aside sufficiently to give a sight of it. 6. A ball stuck fast in mud or sand may be loosened, but it must be placed lightly on the same spot.

7. If one ball lies within a distance of six inches before another, it must be lifted until the latter is played.

8. A split ball may be replaced by another, but a stroke is lost.

9. Loss of a ball is loss of the hole to the player.

10. Any one striking his adversary's ball, or impeding it in its progress, loses a stroke, and a stroke is also lost by the player who touches his own ball with his foot.

In conclusion, we may remark that it is not necessary for young people, who may desire to have a little golfing practice, that they should be furnished with the implements used in the regular game. They may make shift at first with hockey sticks and balls, and make their links upon any open heath or common, placing the holes as the nature and extent of the ground may suggest, and being guided as to their number by the same circumstances.

HEAT.-II.

EFFECTS OF HEAT-EXPANSION-MODES OF MEASURING IT-TREVELYAN INSTRUMENT-CHANGE OF STATE.

WE have now to notice the principal effects which heat produces on different bodies submitted to its influence. Take a rod, A (Fig. 5), of brass or copper, about half an inch in diameter, and cut a gauge of metal of the shape shown at B, so that the rod may just fit lengthways between the ends of the gauge, and also fit tightly in the hole, C. If now the rod be dipped in boiling water, or held over a source of heat so that its temperature may be raised, we shall find that it will no longer enter the gauge nor pass through the hole. It is clear, then, that the dimensions of the rod have been increased by its elevation of temperature, and we thus learn that one of the effects of heat is to produce expansion.

If we take a flask (Fig. 6) with a long narrow neck, and fill it with water so that the liquid may stand a little way in the neck, we shall find, on exposing the bulb to the flame of a lamp, that the column of liquid will rise. The experiment may easily be shown in a large room, by placing the flask in the course of the rays from the electric or some other powerful lamp, and placing a lens so that an enlarged image of the tube may be thrown on a screen. It will then be seen that on the application of the source of heat to the flask, the column of liquid falls slightly before it begins to rise. This at first seems strange, but it arises from the fact that the heat reaches the glass first, and expands that before it has had time to expand the water. The flask accordingly becomes slightly larger, and hence the column of water sinks in it. The expansion of metals is so great that in large engineering worksas, for instance, long iron bridges-allowance has to be made for it, as otherwise the structure would be distorted and weakened. It is very important, therefore,

b

Fig. 8.

a

rod of glass is placed between the supports at one end of the trough, so that the bar may press against it. On the top of the other two is a rod turning in bearings, and carrying at one end a telescope. Fixed to this rod is another at right angles to it, which presses against the other end of the bar under examination. An accurately-divided scale is placed on the wall of the room opposite to the telescope, which has cross wires placed in it, so as to mark the centre of its field of view. It will easily be seen that when the rod elongates it will turn the axle which car

to ascertain the exact amount of expansion which different substances undergo when their temperature is raised. The simplest means of doing this is to take a rod of the metal, and having placed it so that one end presses against an adjusting screw and the other against the short end of a lever, heat it by means of a spirit-lamp. The longer limb of the lever then serves as an index, and shows the amount of elongation. Sufficient accuracy cannot, however, be obtained in this way, as the exact temperature of the bar cannot be determined. The method devised by Lavoisier and Laplace, and represented in Fig. 7, is therefore frequently adopted. A metal trough is placed over a furnace between four stone supports, and the bar to be tested is placed in this. A

VOL. V.

B

A

B

It must be remembered that this table merely indicates the linear increase-that is, the increase in one direction. Most substances, however, expand equally in each direction, and then the cubical expansion may be taken at three times the above fractions.

The enlargement of bodies by heat is easily accounted for by the dynamical theory, for, when the particles vibrate more widely, they naturally endeavour to get further apart, so as to have more space. We may regard the particles of any body as being held together by two opposing forces-cohesion, which tends to draw them more closely together, and heat, which tends to drive them further apart. If the heat be increased the body 126

expands a little by its influence, and then, as the particles get farther separated, it assumes the liquid state; and finally, in the case of many substances, the heat altogether overcomes the cohesion, and the particles fly apart in the form of vapour. When the source of heat is removed, and that already acquired by the substance has been imparted to surrounding objects, cohesion again comes into play, and the substance resumes the liquid or solid state.

Advantage is frequently taken of this property which the metals possess of expanding and again contracting. Some years ago the walls of a large building in Paris had bulged outwards considerably so as to endanger the structure. A number of iron rods were accordingly taken and passed through the building from side to side, the ends passing outside through large face-plates, and being secured by nuts screwed on to them. When these were screwed up as far as possible, the alternate rods were expanded by being heated, and then the nuts could be screwed up further on them. As they cooled the walls were drawn together to a slight extent, and the same process was then repeated with the other rods; and in this way the walls were gradually brought to the perpendicular. For a similar reason the tire is always made hot before being put on a wheel, and then as it cools it forces the different pieces more closely together, and renders the wheel much stronger. So, too, in the manufacture of Armstrong guns, the different coils are shrunk on; and in making boilers the plates are riveted together with hot rivets. The contraction of the metal while cooling renders the joint in each case much more close and tight than it would otherwise be.

In large iron bridges, like that over the Menai Straits, or some of those across the Thames, the heat of the sun's rays is sufficient to curve and raise the bridge in the middle, producing often a greater deflection than the heaviest load does.

By reference to the table of expansions given above, it will be seen that some metals expand more than others for a similar increase of temperature. Hence, if thin bars of two different metals-as, for example, copper and iron-be taken, and riveted firmly together, and then exposed to an elevated temperature, the copper will expand more than the iron, and the bar will become curved, the iron being on the inner side. If, on the other hand, it be exposed to a lower temperature, the copper bar will become the shorter, and thus that will be the inner one in the curve. This fact is sometimes turned to account in the manufacture of compensating pendulums. As has been explained, any increase in the length of a pendulum makes it vibrate more slowly; hence in hot weather a chronometer would lose a little. To guard against this, different forms of compensating pendulum have been tried. The most usual plan is that known as the gridiron pendulum, which was explained in our Lessons in Mechanics. Another plan is represented in Fig. 8, a, b, c. A compound bar of copper and iron, with balls at each end, is fixed to the pendulum rod, the copper side of the bar being underneath, as that metal is the more expansible. When the temperature falls the pendulum rod contracts and raises the bob; the strip, however, curves downwards, as shown in the middle figure, and thus the centre of gravity remains stationary. If the temperature rises, the strip curves upwards, and thus the balls at the end of it rise and compensate for the increase in the length of the rod. A similar plan is adopted in the balancewheels of the best watches.

Another application of the same principle is made in Breguet's metallic thermometer (Fig. 9). A compound ribbon is here twisted into a spiral, which is fixed to the stand at its upper end, and carries a needle below. This spiral coils or uncoils as the temperature changes, and the needle shows the readings on the graduated disc.

There is one more experiment which must be described here, as it is a good illustration of expansion, and at the same time illustrates the conversion of heat into motion. The apparatus employed is known as the "rocker," or Trevelyan instrument, from the name of the gentleman who first constructed it. He had one day laid a hot soldering iron on a block of lead to cool, and was surprised soon after by hearing a distinct sound given off by the iron. On investigation he found that it was thrown into rapid vibration, which caused the sound. The best form of rocker for trying the experiment is represented in Fig. 10. A piece of brass, A, is taken, about five inches long and an inch and a half wide. Its section is almost triangular, but a small

groove is made along the apex, c, and a piece of wire terminating in a knob, B, is fixed in one end. Let the rocker now be raised to a high temperature, and then placed so that the knob, B, may rest upon a table, while the grooved edge of brass lies upon a block of lead. A succession of quick taps will be heard, and the rocker will be found to be in rapid vibration. By increasing the width of the groove the vibrations may be rendered more and more rapid until a distinct musical note is obtained.

The explanation of this is easily given." When the rocker is laid on the block a portion of one edge of it comes in actual contact with the lead. This metal, being very expansible, immediately throws out a small protuberance, and thus tilts the rocker, which therefore rests upon a fresh portion. This immediately expands in like manner, and in this way it is kept in rapid vibration, and produces the sound which is heard. The heat which the rocker possessed becomes slowly lost, being employed in imparting motion to the brass, and this motion becomes in turn communicated to the air, manifesting itself in the form of sound. Thus far we have been concerned with the expansion of solids. We have now to see how liquids expand under the influence of heat, and in their case it is evidently the cubical and not the linear expansion with which we have to deal. As, however, the liquid must be contained in some vessel, and that vessel expands as well as the liquid, we must distinguish between the apparent and the real expansion of the liquid, the latter being the larger of the two by just the amount that the vessel is increased in capacity. Thus, let the liquid in the flask (Fig. 6) stand at the level A, and when it is immersed in a jar of hot water let it rise to the level B; the apparent expansion is the quantity contained in the tube between A and B. If, however, the flask had retained exactly its original capacity, the liquid would have risen higher in the stem, showing that the real expansion is greater.

Liquids generally do not expand uniformly: the amount of expansion between 50° and 60°, for example, would not be the same as that between 190° and 200°. Mercury, however, is an exception to this rule, as between 32° and 212° it expands uniformly, and hence it is specially fitted for use in the construction of thermometers. The following table shows the apparent expansion in glass of several liquids when raised from 32° to 212°:

-

The way in which the real expansion of mercury is ascertained is by filling two vertical tubes with it, and making them communicate by a small tube opening into their lower ends (Fig. 11). One tube is now surrounded by a jacket containing boiling water, while the other is surrounded by melting ice. The mercury in the hot one will stand at a higher level than that in the other. This difference is measured by a telescope properly adjusted, and shows the real expansion.

There is an interesting experiment in connection with the expansion of water which shows a departure from the usual rule. Let a tall glass vessel be filled with water, with a small thermometer at the bottom of it, and a second near the top. Now put the whole in a place where the temperature is below the freezing point; both thermometers will fall, the lower one, however, more rapidly than the other till it reaches about 40°, when it will become stationary. The upper one will continue to fall down to 32°, and then the water will begin to freeze, and the vessel will probably be cracked.

The explanation of this is found in the fact that at first the cooler water from the top and sides, being more dense, sinks to the bottom. When, however, water attains the temperature of 39.4°, it has attained its maximum density, and then, instead of continuing to contract, it expands slightly till it reaches the freezing point, when it suddenly expands still further. Thus, in the above experiment, the water at 39-4° was at its greatest density, and hence remained at the bottom. This provision is of great importance to us, as, were it not for it, the coldest water would sink to the bottoms of our seas and rivers till all attained a temperature of 32°, and they would then be slowly converted into masses of solid ice, whereas now the colder water and ice on the top protects that below.

The great expansion of water on becoming converted into ice is often so painfully manifested in the bursting of our waterpipes and plugs during a frost, that it need not be illustrated further. It is well, however, to guard against the common error