It was decided to give the little craft two more coats of shellac varnish before launching her, and the following spring to give her a good coat of marine varnish. Mr. Gregg thought that in another week, say the following Wednesday, the Caroline might be launched with safety, as the varnish would get dry and hard, and the inside paint would also be hard enough. Jessie and the boys were given permission to invite a few friends each to the boat launching, and were promised suitable refreshments to be served on the new grounds, if the weather was favourable. Fred asked his father if he could not build up some temporary picnic tables and seats for the occasion, as there was plenty of material still left unused from the old barn stuff. Permission was granted, and after counting up the number that would probably be present, it was found that three tables, each about fifteen feet long, with necessary seats, would give ample room for the accommodation of the proposed guests, with a good allowance for overflow.

Just then the whistle of a small steam tug, that often plied on the river, gave warning of her approach; and all went down to the river edge to watch her pass and to see what effect her "wash" would have on the new pier and the boat house "skid" or slides. She came up stream rapidly against the tide—which was on the ebb—and there was a considerable "wash" from her wheel, but it struck the bank, the pier, and the "skids" without doing the least harm or giving any evidence that trouble would result from any reasonable wash. The little steamer's exhaust, as she passed, made quite a noise and Jessie was somewhat puzzled at this, as the exhaust from the gas engine of the Caroline only made a plaintive puff in comparison. Her father promised to explain the reason after tea.

Returning to the boat house, George suggested that the name of the boat be painted on both sides of the bow, in large letters, but Mr. Gregg and Fred, thought it better to have "Caroline" placed on the second streaks of sheathing, in gold, the letters to be not more than two inches over all. This was agreed upon, and a young artist, who was a near neighbour, was suggested as the person to do the work.

After tea, Jessie and the boys followed their father into the den, where Mr. Gregg gave the children a brief history of the steam engine, as far back as known, commencing with the Colipyle, the invention of Hero of Alexandria about 130 B.C. An illustration of this is shown in Fig. 30. It was simply a pot or boiler, partly filled with water, the lid or cover being fastened down tightly. On the top of this was attached a hollow bent tube having a tap fitted to it, which supported and communicated with a hollow metal ball hung on another tube or bearing on the other side in such a manner that the ball could revolve easily. Attached to this hollow ball or sphere were four other hollow tubes, so fastened as to project from the surface two or three inches, and these were bent at their outer end, as shown in the illustration. These tubes were of course attached and bent in a direction at right angles to the axis of rotation. The tap leading to the hollow ball, when turned open, allowed the steam from the boiler to rush into the ball and fill it up. If it was closed entirely, the ball would remain still, but the steam exerting an equal pressure on all points of the inner surface, and finding the openings, escaped through with a rush and noise as it condensed in the air, which it pressed against, causing the ball to revolve in an opposite direction to the outflow of steam. This Hero engine or Colipyle, was doubtless the beginning of steam motors, but during the 2,000 or more years since Hero's toy engine was invented, great strides have been made toward bringing the steam engine to its present efficiency.

"But I do not intend," said Mr. Gregg, "to give a history of the growth and development of the machine, at this time. There are numerous works on the subject, obtainable in any fairly-equipped library."

Steam, as everybody knows, is generated by heat being applied to a closed metal kettle or boiler containing water. This boiler must be strong and properly arranged so as to admit more water—which is usually injected with a force pump—and it must have an outlet for the release of the steam to the cylinder of the engine. Generally, there is a small dome on the top of the boiler, called the "steam dome," and to this the steam outflow pipe is attached. The actual use of this dome is to hold a volume of steam that will remain unmixed with water, as it is placed considerably above water level. On the top of the dome there is an automatic arrangement called a "safety valve," so that when there is too much pressure of steam in the boiler, it will open and allow the over-pressure to escape, and thus prevent the boiler from exploding or being over strained. This valve is controlled by a simple device, somewhat similar to a steelyard. A movable weight is arranged to slide on a long arm which is loosely fixed to the valve flange by a bolt and nut, and extends some distance past the seat of the valve. The arm or lever has an iron pin attached to it directly over the valve seat, which holds down the valve and keeps the steam from escaping. The movable weight on the arm is adjusted so as to regulate the pressure on the valve. When there is too great a pressure, the valve forces up the lever, and at the same time opens a passage for the extra pressure of steam to escape. There are several other contrivances for relieving the boiler of over stress, but the one described, or rather the principle on which it is built, is most in use on this country. There are many kinds of boilers, or steam generators, but the best, and very likely the strongest, are those employed on our first-class railway locomotives. These are frequently under a pressure of 200 or more pounds to the square inch, which seems an enormous load for a hollow shell to carry, yet, so near perfection are they, we rarely hear of a locomotive boiler explosion. As there are many kinds of boilers, so also are there many kinds of steam engines, but all of these latter, with very few exceptions, have a cylinder and piston for converting the force of the steam into useful and effective motion. The manner of using this force and keeping it under proper control is somewhat complex and difficult to describe briefly, without elaborate diagrams, but Mr. Gregg explained, in his own way, how the great force was converted into motion. On the blackboard he drew a rough diagram of a cylinder and valve or steam-chest, with piston and slide-valve, about as shown in Fig. 31, which gives a longitudinal section of the whole arrangement. Here we see near each end, the opening of a double conduit aa, made in the thickness of the side; these are the openings by which the steam comes alternately to work on one end, then on the other, of the piston. These are called the steam-ports. These two open outward on a well-polished surface, and between the two a third opening, E, is seen, which serves to let the steam escape when it has done its work, and is called for that reason the exhaust port. C is the pipe by which the steam gains access to the open air or to the condenser, where it parts with its elastic force.

Here is shown by what contrivance the distribution is effected, consisting, as it does, of two partial operations; the admission of the steam and its escape, which must be repeated twice to obtain a complete phase of the to-and-fro movement of the slide-valve. There are various methods employed according to different engines—but the first described is the one represented by the illustration.

In the valve chest, BB, is seen a prismatic box, open on one side, called the slide-valve, and this is applied by its open face to the well-polished plane on which, as mentioned before, the three ports open. The space BB, is called the valve or steam chest. The steam coming from the boiler by the pipe C spreads out freely in it, but the inside of the slide-valve, on the contrary, is always closed to the entering steam, though constantly in communication with the escape pipe and also with first one then the other of the entrances to the cylinder. Lastly, the movement of the slide-valve is produced by the engine itself, aided by a rod and an eccentric fixed to the shaft of the fly-wheel.

By following the successive and alternating motions of the slide-valve, as represented in Fig. 32, we can easily comprehend the different phases of the distribution of the steam.

This is the machinery for the distribution of steam generally. There are other engines, such as rotary and oscillating, that are supplied by other contrivances, but most of these have fallen, or are fast falling into disuse, as they are not so satisfactory as the ordinary slide-valve. It will be seen upon examination of the sketch, shown in Fig. 32, how the steam enters and leaves the cylinder and the position of the piston under the various positions of the valves. The arrows show the direction of the slide, also the direction of the piston and its position when the slide covers the ports X, or leaves them open, or partly so. The ports for egress or ingress are shown at X, the slide-valve at V, and the cylinder at C. When the piston is near one end of the cylinder, the steam is admitted and forces the piston in the opposite direction, while the valve is so arranged that when the piston starts in that other direction, it begins to open the port at the other end of the cylinder through which the exhausted steam escapes. This makes the noise Jessie asked her father about. There are some engines so devised that the exhaust is made to assist in driving another engine.

Of course, there are many kinds of steam engines, but all are run on the same principle, or nearly so. As you know, steam is generated in boilers by fire being applied to the outside and the water made hot enough to raise steam. A steam engine is said to be externally heated, while gas, oil, and other similar engines are internally heated, because instead of the steam driving the piston, the gas, oil, or other explosive matter is admitted into the clearance or space between the piston and the end of the cylinder, where it is exploded by an electric spark from a battery provided for the purpose, and this is called the "ignition." The explosion causes the gas and air in the cylinder to expand, bringing a great pressure on the piston, forcing it to move toward the other end of the cylinder, and making the whole machine move. One great advantage of employing a gas engine is that no boiler is required, a very important matter, as boilers take up a great deal of space. The coal or wood necessary to keep up steam also takes space that could be used for other purposes, all of which make the use of steam objectionable when it is possible to employ suitable gas engines. Besides, the make-up of a steam engine is of such a character that it is very expensive, while the first cost of gas engines is much lower.

All gas, oil, or other explosive engines are internal heaters, because the heat is generated in the cylinder at each explosion, and this is one of the main features that distinguishes the gas from the steam engine. Of course, there are many attachments and connections to steam and gas engines that would take too long to describe, and in a great measure be unnecessary. A few items may prove both useful and profitable and it is well to know firstly: How to estimate the horse-power of an engine.

When steam engines were first introduced they were largely used to take the place of the horses previously employed for raising water from mines. Naturally people inquired, when buying an engine, what amount of work it would perform as compared with horses. The earliest engine builders found themselves very much at a loss to answer this question so they had to ascertain how much a horse could do.

The most powerful draught horses and the best of any then known were the London brewers' horses. These, it was ascertained, were able to travel at the rate of two and a half miles per hour and work eight hours per day. The duty, in this case, was hoisting a load of 150 pounds out of a mine shaft by means of a cable. When a horse moves two and a half miles per hour, he travels 220 feet in a minute, and, of course, at the speed named, the 150-pound load would be raised vertically that distance. That is equal to 300 pounds lifted 110 feet per minute, or, 3,000 pounds lifted 11 feet or 33,000 pounds lifted one foot high in one minute. That is the standard of horse-power, as we all know. It is much more, however, than the average horse can do, and therefore the builders were confident that the engines would take the place of fully as many horses as the horse-power would indicate that they should.

Of course, 33,000 pounds lifted 1 foot per minute is much more convenient for calculation than 150 pounds lifted 220 feet, and therefore the former rate has been adopted. The amount of work, or number of "foot-pounds," is the same in either case. A foot-pound represents the amount of power required to lift one pound one foot high. To find the number of horse-power in any engine, we multiply the area of the piston by the average pressure per square inch upon it; multiply this result by the distance which the piston travels per minute in feet and the result is the number of foot-pounds per minute which the engine can raise. Divide by 33,000 and the result will be the number of horse-power. The number of feet per minute travelled by the piston is twice the number of strokes per minute multiplied by the length of the stroke. This gives the amount of horse-power sufficiently accurate for all practical purposes.

It necessarily takes time to do work, but the amount of work done has nothing whatever to do with the time taken to do it.

If a man, weighing 150 pounds, walks up the 900 steps leading to the highest attainable level in the Washington Monument, 500 feet high, he does work against gravity equal to 75,000 foot-pounds, irrespective of the time taken in the ascent. Then the work done in a given time, divided by the time, is called the power of activity.

Power is the time rate of doing work. In the English gravitational system, the unit of power is the horse-power (H.P.); it is the rate of doing work equal to 33,000 foot-pounds a minute, or 550 foot-pounds a second.

In the centimetre-gramme-second (C.G.S.) system (in which the unit is 1 gramme moving at the rate of 1 cm. a second), the unit of power is the watt. It equals work done at the rate of one joule (10,000,000 ergs) a second.

One horse-power is equivalent to 746 watts.

A kilowatt (K.W.) is 1,000 watts.

It is therefore nearly 1¹⁄₃ horse-power.

To convert kilowatts into horse-power add one-third; to convert horse-power into kilowatts, subtract one-fourth.

For example, 60 K.W. equals 80 H.P. and 100 H.P. equals 75 K.W.

The expression foot-pound is in general use among English-speaking engineers, and as explained it is the unit of work done by a force of one pound working through a distance of one foot. It is not a fixed standard of measurement, since the weight of a pound is not the same in all heights above sea level, and on this ground it is open to objection. It is the nearest constant, however, we have yet discovered, hence its general adoption.

"Dry steam" is the steam in which no condensation is visible, and it may generally be obtained at a 10-pound pressure per inch, but no exact dividing line of pressure can be defined between dry steam and wet. If care is taken in covering pipes and cylinders, to prevent condensation, a pressure of 10 pounds should make steam as dry as gas, and if the steam pipe is carried through a good, hot fire at some point, the fire will superheat the steam and render it more dry. Wet steam, of course, is steam that can be seen, through having been more or less condensed by contact with air or cold. There can be no steam without heat, but steam does not require as much heat as is generally supposed. Suppose we take one pound of water at 32 degrees Fahrenheit and apply a fixed and known quantity of heat until it boils; we will assume that it takes 20 minutes, and we have supplied the water 180 heat units, which, added to the 32 contained in the water at the start, makes 212 degrees Fahrenheit or heat units, and is the sensible heat of steam at atmospheric pressure. Now let us continue the same quantity of heat per minute until all the water has evaporated into steam, and we will then find that it has taken five and one-third times as long, or 107 minutes to do this work. Consequently we have used five and one-third times 180 or 960 heat units; or, to be exact, 966 heat units. Now the temperature of the steam is the same as the water from which it has evaporated, or 212 degrees Fahrenheit, and this 966 heat units is the latent heat of steam at atmospheric pressure. All steam has a sensible heat corresponding with the temperature of the water it has evaporated from. If you boil water under a pressure of five atmospheres, or 75 pounds pressure, the sensible heat is 306 degrees Fahrenheit, the boiling point at that pressure, but the latent heat has decreased by the same number of heat units that the boiling point increased, so the total is the same in all cases. In the first instance we have 212 degrees minus 32, plus 966, or 1,146; and in the second 306 degrees minus 32, plus 872 or 1,146 heat units. This may be considered a fair description of latent heat.

The most useful quality of steam yet discovered is its power of expansion. It follows what is known as Marriott's Law of Expanding Gases, which means one-half the pressure double the volume. So if we let steam into an engine cylinder, at 80 pounds' pressure, and cut it off at one-fourth stroke, it is at 80 pounds up to the point of cut-off. At one-half stroke, because it has doubled its volume, it is reduced to one-half pressure, or 40 pounds; while at three-fourths stroke the volume has trebled and the pressure has dropped to nearly 27 pounds, and this is why it is economical to run engines that use steam expansively. Steam at 27 pounds' pressure is very much cooler than steam at 80 pounds, and this difference in temperature has been converted into mechanical work by our steam (heat) engine.

There are many other peculiarities about steam and steam engines that a young boy should know, and the information can readily be obtained from books in any good library.

The steam turbine, of which so much has been heard lately, is not constructed like an ordinary steam engine with cylinder, slide-valve and other attachments; but more like the Hero engine, with this difference that the steam jet or jets act on a wheel having vanes or blades, the expansion producing a velocity which rotates the wheel containing the vanes. A modern turbine, of the Parsons type, such as are employed on the great Atlantic steamers, is a tremendously high speed engine. It does not derive its power from the static force of steam expanding behind a piston, as in a reciprocating engine. In this case the expanding steam produces kinetic energy of the steam particles, which receive a high velocity by virtue of the expansion, and, acting upon the vanes of a wheel, force it around at a high speed of rotation in the same manner as a stream of water rotates a water-wheel. The expansion produces velocity in a jet of steam, and this is the main difference between the ordinary engine and the modern steam turbine.

Among gas and internal explosion engines there exist some differences, both in construction and in the manner of supplying fuel. The gas-producing engine may be considered the better class, though it has not as yet gained the popularity of the gasolene one. The gas by which this style of engine is operated is produced by a special process, namely, by passing air and steam through a fire of hot coals. After generation the gas passes over a flash-boiler and a portion of its great heat is withdrawn, thus permitting it to enter a scrubber—a cylinder filled with coke and sawdust—while fairly cool. In passing over the flash-boiler the great heat raises all the steam necessary for the production of gas required in the operation of the engine and plant. In passing through the scrubber the gas is not only cooled, but is freed from particles of suspended matter, the coke removing the heavier particles, and the sawdust, the tar, or any other volatile matter that may be left.

One of the most important requirements in a gas-producer is that it shall be adapted to the work it has to do. Its construction should be compact and simple, so as to permit the easy removal of worn out parts. The feeding device should be such as to secure a uniform distribution of fuel.

The blast should be so introduced as to burn out all the carbon in the ash zone, and yet not produce localized combustion along the walls. The construction should permit the easy removal of ashes, and render the machine safe, while the entire process of gasification should be clean. The radiation loss should be low, and the producer must be made efficient to insure satisfaction.

It should be borne in mind that because of the presence of carbon monoxide, producer gas will always be more or less poisonous. The carbon monoxide has a specific toxic effect on the human system, and when inhaled enters into direct combination with the blood, and brings about very dangerous effects.

As water is always required for cooling purposes when running a gasolene engine, it is well to know about how much will be required. One authority says: "The quantity of water required at the ordinary temperature of 60 degrees F. inlet and 150 degrees outlet, to keep the cylinder of gas engines cool is 4.5 to 5 gallons per indicated horse-power-hour. The jacket pipe should be from 1 to 2 inches diameter for engines up to 20 horse-power, while for larger engines the sizes are generally 2 to 3 inches for the inlet and 2.5 to 3.5 inches for the outlet. Tanks for circulating the water are generally made with a capacity for furnishing 20 to 30 gallons per indicated horse-power. This rule may be taken as about correct, but, if anything, it is rather an over-estimation of quantity necessary."

All the foregoing was made as clear as possible to the listeners by Mr. Gregg before the children went to bed.

Next morning Fred called up his artist friend, and got him to come down to gild the name "Caroline" on the boat before the next coat of varnish should be applied. The artist made an outline of the name while George and Jessie stood by and watched the process with considerable interest. They saw him measure off each letter, outline it with a pencil lightly, and then paint inside the lines with a substance known as "gold size," obtained from any store dealing in painters' supplies. While the size was still sticky the artist applied "gold leaf," which he had brought in a little book along with him. Jessie was surprised to see him cut the gold with a thin pallette knife, having a blunt but smooth edge. She watched him pick up the small pieces of gold with a camel's hair brush, which he rubbed in his own hair now and again whenever it would not pick up the gold. The metal was applied bit by bit over and beyond the lines of the letters, and a light puff of breath forced it down to the size. When one side of the boat was finished, so far as laying on the coat of gold was concerned, Jessie was very much disappointed, as the name seemed merely a smudge. She could not make out the letters, but the artist told her to wait until to-morrow and he would show her how well they could be seen. Next day with a flat camel's hair brush he dusted away the surplus gold, and the letters showed up in good style, much to the gratification of Jessie and George. This part of the work being done, the boys took down their varnish pots, and gave the little craft another coat, to make her quite spruce and gay.

Fred, and Nick, who was still in the employ of Mr. Gregg, laid off a space on the ground for tables and seats to accommodate the young folks who were coming to the launch on the following Wednesday. Nick found a number of old cedar posts, and with a saw cut off 18 pieces about two feet long and as many more twice that length. The first were intended to place the seats on; the second lot were to sustain the tables. The spots for the tables were chosen, measured off, and small stakes driven into the ground to show where the posts were to be placed. Five posts were intended for each table—two at each end, two feet apart, and nine feet apart in the length of the table. The single post was placed in the centre of the table both ways. When the stakes were all in place, Nick made holes deep enough to take in the posts so that their tops measured just two feet and two inches above the level of the ground. The tables were to be two feet and six inches high when finished, as that is the regulation height. It was attained, in this case, as follows—First by the height of the posts from the ground, two feet two inches; then by a plank two inches thick laid across the two posts, making the height two feet four inches, and the table top, two inches thick, laid on these cross planks, which brought it up to the required height. A piece of plank the same thickness was nailed on the centre post across, so that it would support the table top. Planks that had been used in the loft of the old barn did service for the table tops, bearing pieces, and the bench seats. The last were constructed in the same manner as the tables, the short posts being let into the ground—three under each seat—and fourteen inches above ground so that when the plank seat was nailed on top of them, the seats were just sixteen inches, the regulation height of stools, benches, and chairs, though it is sometimes varied to suit conditions. The benches were placed about four inches out from the edge of the table and were found to be "just the thing."

When Nick had planted the first post for the tables and got it the right height, he took that one for his guide and by the aid of a long parallel straight edge which he laid on the guide post and the one he was setting, and also a spirit-level on the straight edge, he managed to get all the posts alike in height and this made the tops of the three tables nice and level. It was quite an achievement to have three large tables and six long seats placed in "picnic style" at so small a cost and with so little effort.

In order to have the tables and seats neat and clean, George turned on the garden hose and gave them a good wash off, and when they were dry again the place was as inviting as a country hotel dining-room. When Mrs. Gregg, Jessie, and Grace Scott had the tables set and garnished for the launch, the lay out was charming, none the less so because it was a little rustic.

Another coat of varnish, the third, was given the boat the day before she was to be launched, and Fred had a strong rope attached to the winch, with a heavy iron hook fastened to the end of it. A stout iron ring was bolted to the stern of the boat and made secure. Mr. Gregg had purchased a number of small flags and "burgees" and had one made with the name "Caroline" in large letters wrought on it, ready to be unfurled when the launch was made, and Walter Scott, his mother and sister Grace, and others had been invited to attend.

A number of temporary swings were fixed up by Nick and Fred to the trees, some for the large folks, others for the smaller ones, and everything was at last ready for the great event, which was to take place the next day at two o'clock.

VI

PROPELLER AND OTHER SCREWS

Nick had the grounds nicely raked off; the decayed branches and shrubs he moved, and made everything about the place as clean and as neat as possible. Flags and other decorations were hung or placed about the grounds, on the trees and buildings, but particularly about the tables and the boat house. Newspapers were spread over the tables, linen covers above them, and the whole surroundings took on a most festive appearance.

It was just 11 o'clock when The Mocking-Bird arrived and tied up to the new dock. On board were Mrs. Scott, Grace, and the maid, who came to help, besides several of the invited guests whom Walter had brought down with him. All were welcomed by Fred, Jessie, and George and then the women visitors went to the house to assist Mrs. Gregg.

Mr. Gregg came home from his office earlier than usual and took a half holiday in honour of the occasion. The guests, in little groups, arrived on time, and before the clock struck two Nick had everything prepared for the launch. He and Fred and George had the Caroline nicely placed on the skid, ready to "let go" the winch, and a flag pole was fixed up on the bow of the boat. To this the flag with the name on it was lightly tied, in such a manner that when a string was pulled it would unfurl, and show the name. The string looping up the flag was left long enough to enable Mr. Gregg, standing on the dock, to hold the end in his hand, and by pulling it to loosen the flag as soon as the boat touched the water.

Everything being ready, Walter Scott invited as many of the young people to get into the Mocking-Bird as could crowd on board with comfort, and each was provided with a whistle or a horn, as he ran his boat half way across the river. The children on shore were also given horns and whistles, and all were told to blow as loud as they pleased when the boat touched the water. Mr. Gregg, having Mrs. Gregg and Mrs. Scott standing beside him, gave the word, "Ready!" Nick and Fred answered, "Aye, aye, sir!" and the master of ceremonies called out in a loud voice: "Let her go!"

Nick freed the winch, Fred and George gave a little push, and the Caroline slid down the skids, into the water, without the least hitch. The horns and whistles made a great din, and when the flag was let free to open up and show the name "Caroline" there was another blast of noise by horns and whistles, mingled with voices of the younger people, who cried out with all their might, "Hurrah for the Caroline!"

The launch being over, and everything having gone all right, the young people were called to lunch. They all sat at the tables which were nicely garnished and well supplied, and there was plenty of small talk, and much laughter and jollity. After lunch, Fred, Walter and George boarded the Caroline, supplied her with gasolene, and tried to run her. They found a little difficulty in starting, but after the engine was warmed up a little, she went off beautifully, and answered her tiller in fine style. The boys ran her up and down the river for a while, then tied her to the dock, and Walter and Fred invited all the girls to "Come and have a sail." The boys were promised one when the two boats returned, which they did in the course of half an hour. The swings were put in use, dancing and romping began, and the afternoon was passed in fun and frolic.

In the evening, Mr. Gregg, Jessie, and the boys took a trip, and Mr. Gregg was well pleased with the boat's performance, particularly with the working of the screw. In mentioning this, he awakened the curiosity of George, who reminded his father that he had not yet explained to them about the screw as a mechanical power.

That evening George was told to bring his blackboard and equipment into the den, and the father at once began explaining the mechanical qualities of the screw. He told of its great usefulness in the industrial arts. As one of the mechanical powers, it may be considered an inclined plane, wrapped spirally round a solid cylinder. The advantage gained by it depends on the slowness of its forward or backward progress, that is, on the number of turns or threads, as they are called, in a given distance. It is always used in combination with a lever of some sort. When employed as a lifting machine it has great power, and is used to produce compression or to raise or move heavy weights. If a screw is formed on the inside surface of a hollow cylinder, it is called a nut, and used to overcome a resistance; either the screw or the nut may be fixed and the other movable. The acting force is generally applied at the end of a lever or wrench or rim of a wheel. Fig. 33 represents a screw and nut operated by a lever or length of radius r; p is the pitch of the screw or height of the inclined plane for one revolution of the screw. W is the resistance at the nut and P is the force at the end of the lever r. Remembering that, while the resistance W is raised the distance p the force P revolves around a complete circle and moves a distance 2πν. Let us now apply the condition
Σwork = 0
and we have

P2πν - Wp = 0 or — = P2πν/p    (6).

The worm gear (Fig. 34) is a special case of screw and nut, where the latter is replaced by a toothed wheel called a worm wheel. The teeth work in with the thread of the screw or worm, and thus, as the worm revolves, the worm wheel revolves about its axis. P is the force acting on the worm at a radius r. r´ is the pitch radius of the teeth in the worm wheel and r´´ is the radius of the drum on which W acts. Let K, corresponding to W in equation W P (6), be the force at the pitch circle and worm threads due to the force P; then
K = P2W/p    (7).

Now apply Σm = 0 to the worm wheel and we have
Kr´´ = Wr´´ or K = wr´´    (8).

Substituting the value of K in (7) in equation (8) we have
P2πν = Wr´´ or P2πν = Wr´´p    (9).

Now it is evident that the distance p´ moved by W while K moves through the distance p is to p as r´´ is to r´ or p´ : p :: r´´ : r´ or
p´ = pr´´/r´    (10).

Substituting this value of pr´´/r´ in equation (9) we have P2πν = Wp´ or the condition Σwork = 0, since 2πν is the distance moved by (P) while W moves the distance p´.

No provision for friction has been made in any of the examples given, so that allowance must be made for this propensity whenever any of the foregoing rules are applied to practice. The amount of allowance required will vary and must be made to suit conditions.

An endless screw is sometimes used as a component part of graduating machines, counting machines, etc. It is also employed in conjunction with a wheel and axle to raise heavy weights. The distance between the threads of the screw is called the pitch or step. These threads are sometimes square, sometimes acutely pointed or edged, sometimes rounded off on the edges. Power is often applied by means of a lever or other contrivance attached to the end of the screw, or by a long handled wrench (a monkey wrench for instance), which, when turned, moves forward in the direction of its axis, overcoming resistance. In the case of the screw-jack, it may be used to raise a heavy weight. The relation between the force applied and the resistance to be overcome is important to note, for every time the screw performs one revolution it moves forward through a distance equal to the space between one thread and the next.

The Archimedian screw we have read and heard so much about is simply a hollow pipe wound around a cylinder. It was often used in olden times for raising water, but is now only occasionally applied. The lower end of the spiral pipe is, of course, left open and immersed in water, as shown in the illustration (Fig. 35), a device for raising water, the supply stream being the motive power. The oblique shaft of the wheel has extending through it a spiral passage, the lower end of which is immersed in water; and the stream, acting upon the wheel at its lower end, produces its revolution, by which the water is conveyed upward continuously through the spiral passage and discharged at the top. An arrangement like this could easily be constructed at the edge of most rivers to raise water to irrigate the grounds, if so desired, and the little flutter wheel at the bottom of the inclined shaft would be powerful enough to lift all the water required. Fred thought that would be a great scheme, and determined to try his hand at it one of these days, but he was told that a wheel of that kind could only work at intervals, as the river's flow was often running in opposite directions owing to the inflow of the tidal water.

These Archimedian water raisers are often fitted with a crank handle on top, and a man, standing on a platform, turns the crank and thus lifts up all the water the machine will carry. The Archimedian screw is used for many other purposes than raising water. With wide, thin wings, similar to the construction shown at Fig. 36, and enclosed in a case or jacket, it is employed by millers to convey grain and other mill requirements, and it is also good for moving coal, ore, gravel, and like material, but when used for these coarser purposes the propelling blades are made of steel, riveted or bolted to a strong iron shaft. The case or jacket containing the revolving blades, if horizontal, need not be covered on top, as the blades will propel the material without jamming or clogging, if the jacket is smooth inside, and fits fairly close to the blades.

This style of a screw may be used as a sort of turbine water wheel, if cased in a cylindrical penstock or tube, and a body of water allowed to fall into the upper end of the tube. The force of the water will give a rotary motion to the blades and shaft, and, the latter having a geared wheel or pulley attached to its top, motion is imparted to other shafts and wheels.

Another application of the screw is shown at Fig. 37, where one is arranged on a shaft or axle to give a rotary motion. This device is called a "worm and wheel," and is frequently used in the make-up of machine engines and mathematical instruments. The illustration shows how the power or force of a screw may be conceived. For instance, suppose the wheel C has a screw on its axis working in the teeth of the wheel D, having 48 teeth. It is plain that for every time the wheel C and screw are turned round by the handle or crank A, the wheel D will be turned once round. Then, as the circumference of a circle, described by the crank A, is equal to the circumference of a groove round the wheel D, the velocity of the crank will be 48 times as great as the velocity of any given point in the groove. Consequently, if a line C goes round the groove, and has a weight of 48 pounds hung to it, a power equal to one pound at the handle will balance and support the weight. To prove this by experiment, let the circumference on the grooves of the wheels C and D be equal to one another; and then if a weight H, of one pound, is suspended by a line going round the groove of the wheel C, it will balance a weight of 48 pounds hanging by the line G; and a small addition to the weight H will cause it to descend, and to raise the other weight.

If a line C, instead of going round the groove of the wheel D, goes round its axle I, the power of the machine will be as much increased as the circumference of the groove exceeds the circumference of the axle, supposing which to be six times 8, then one pound at H will balance 288 pounds, hung to the line on the axle; thus showing the advantage of this machine as being 288 to 1. A man who can lift by his natural strength alone, 100 pounds, by making use of this combination, will be able to raise 28,800 pounds alone, and if a system of pulleys were applied to the cord H, the power would be further increased to an amazing degree.

When a screw and wheel are attached, as shown, the screw is sometimes called a "worm" and sometimes an "endless screw."

The propeller wheel (Fig. 38) is a screw having a large helical dimension. The example shown has four blades, each of which, when rotated, may be said to make one quarter of a revolution and when at work in the water has the same effect as the working of a nut, producing motion in direction of the axis and so propelling the boat or vessel. The action of the wheel pressing backward against the water tends to push the craft forward.