file which includes the original illustrations4 ,see #ededf-;h4htm or #ededf-;h4zip3 7https3_/_/www4gutenberg4org_/cache_/epu b_/#ededf_/pg#ededf-;images4html7 or 7https3_/_/www4gutenberg4org_/files_/#ed edf_/ededf-;h4zip7 ,images of the original pages are available through ,internet ,archive4 ,see https3_/_/archive4org_/details_/timecloc ksdescri#jj;cuny ,transcriber's note3 ,text enclosed by underscores is in italics 7italics74 ,however1 to improve readability1 italics notation has been omitted from equations4 ,if the variables are in italics in the surrounding text1 they were in italics in the equations4 ,,time ,,and ,,clocks4 ,illustration3 ,frontispiece4 ,,nuremberg ,,clock4 ,,converted ,,from ,a ,,verge ,,escapement ,,to ,a ,,pendulum ,,movement4 ,,time ,,and ,,clocks3 ,a ,description of ,ancient and ,modern ,methods of ,measuring ,time4 by ,h4 ,h4 ,,cunynghame ,m4,a4 ,c4,b4 ,m4,i4,e4,e4 ,with ,many ,illustrations4 ,london3 ,archibald ,constable ,co4 ,ltd4 #af ,james ,street ,haymarket4 #aijf4 ,bradbury1 ,agnew1 ,co4 ,ld41 ,printers1 ,london and ,tonbridge4 ,,contents4 ,,page ,,introduction #a ,,chapter ,i4 #g ,,chapter ,,ii4 #ej ,,chapter ,,iii4 #ij ,,chapter ,,iv4 #abc ,,appendix ,,on ,,the ,,shape ,,of ,,the ,,teeth ,,of ,,wheels #ahg ,,index #aii ,,time ,,and ,,clocks4 ,,introduction4 ,when we read the works of ,homer1 or ,virgil1 or ,plato1 or turn to the later productions of ,dante1 of ,shakespeare1 of ,milton1 and the host of writers and poets who have done so much to instruct and amuse us1 and to make our lives good and agreeable1 we are apt to look with some disappointment upon present times4 ,and when we turn to the field of art and compare ,greek statues and ,gothic or ,renaissance architecture with our modern efforts1 we must feel bound to admit our inferiority to our ancestors4 ,and this leads us perhaps to question whether our age is the equal of those which have gone before1 or whether the human intellect is not on the decline4 ,this feeling1 however1 proceeds from a failure to remember that each age of the world has its peculiar points of strength1 as well as of weakness4 ,during one period that self-denying patriotism and zeal for the common good will be developing1 which is necessary for the formation of society4 ,during another1 the study of the principles of morality and religion will be in the ascendant4 ,during another the arts will take the lead2 during another1 poetry1 tragedy1 and lyric poetry and prose will be cultivated2 during another1 music will take its turn1 and out of rude peasant songs will evolve the harmony of the opera4 ,to our age is reserved the glory of being easily the foremost in scientific discovery4 ,future ages may despise our literature1 surpass us in poetry1 complain that in philosophy we have done nothing1 and even deride and forget our music2 but they will only be able to look back with admiration on the band of scientific thinkers who in the seventeenth century reduced to a system the laws that govern the motions of worlds no less than those of atoms1 and who in the eighteenth and nineteenth founded the sciences of chemistry1 electricity1 sound1 heat1 light1 and who gave to mankind the steam-engine1 the telegraph1 railways1 the methods of making huge structures of iron1 the dynamo1 the telephone1 and the thousand applications of science to the service of man4 ,and future students of history who shall be familiar with the conditions of our life will1 ,i think1 be also struck with surprise at our estimate of our own peculiar capabilities and faculties4 ,they will note with astonishment that a gentleman of the nineteenth century1 an age mighty in science1 and by no means pre-eminent in art1 literature and philosophy1 should have considered it disgraceful to be ignorant of the accent with which a ,greek or a ,roman thought fit to pronounce a word1 should have been ashamed to be unable to construe a ,latin aphorism1 and yet should have considered it no shame at all not to know how a telephone was made and why it worked4 ,they will smile when they observe that our highest university degrees1 our most lucrative rewards1 were given for the study of dead languages or archological investigations1 and that science1 our glory and that for which we have shown real ability1 should only have occupied a secondary place in our education4 ,they will smile when they learn that we considered that a knowledge of public affairs could only be acquired by a grounding in ,greek particles1 or that it could ever have been thought that men could not command an army without a study of the tactics employed at the battle of ,marathon4 ,but the battle between classical and scientific education is not in reality so much a dispute regarding subjects to be taught1 as between methods of teaching4 ,it is possible to teach classics so that they become a mental training of the highest value4 ,it is possible to teach science so that it becomes a mere enslaving routine4 ,the one great requirement for the education of the future is firmly to grasp the fact that a study of words is not a study of things1 and that a man cannot become a carpenter merely by learning the names of his tools4 ,it was the mistake of the teachers of the ,middle ,ages to believe that the first step in knowledge was to get a correct set of concepts of all things1 and then to deduce or bring out all knowledge from them4 ,admirable plan if you can get your concepts6 ,but unfortunately concepts do not exist ready made--they must be grown2 and as your knowledge increases1 so do your concepts change4 ,a concept of a thing is not a mere definition1 it is a complete history of it4 ,and you must build up your edifice of scientific knowledge from the earth1 brick by brick and stone by stone4 ,there is no magic process by which it can with a word be conjured into existence like a palace in the ,arabian ,nights4 ,for nothing is more fatal than a juggle with words such as force1 weight1 attraction1 mass1 time1 space1 capacity1 or gravity4 ,words are like purses1 they contain only as much money as you put into them4 ,you may jingle your bag of pennies till they sound like sovereigns1 but when you come to pay your bills the difference is soon discovered4 ,this fatal practice of learning words without trying to obtain a clear comprehension of their meaning1 causes many teachers to use mathematical formul not as mere steps in a logical chain1 but like magical chaldrons into which they put the premises as the witches put herbs and babies' thumbs into their pots1 and expect the answers to rise like apparitions by some occult process that they cannot explain4 ,this tendency is encouraged by foolish parents who like to see their infant prodigies appear to understand things too hard for themselves1 and look on at their children's lessons in mathematics like rustics gaping at a fair4 ,they forget that for the practical purposes of life one thing well understood is worth a whole book-full of muddled ill-digested formul4 ,unfortunately it is possible to cram boys up and run them through the examination sieves with the appearance of knowledge without its reality4 ,if it were cricket or golf that were being tested how soon would the fraud be discovered4 ,no humbug would be permitted in those interesting and absorbing subjects4 ,and really1 when one reflects how easy it is to present the appearance of book knowledge without the reality1 one can hardly blame those who select men for service in ,india and ,egypt a good deal for their proficiency in sports and games4 ,better a good cricketer than a silly pedant stuffed full of learning that 8lies like marl upon a barren soil encumbering what is not in its power to fertilize40 ,another kindred error is to expect too much of science4 ,for with all our efforts to obtain a further knowledge of the mysteries of nature1 we are only like travellers in a forest4 ,the deeper we penetrate it1 the darker becomes the shade4 ,for science is 8but an exchange of ignorance for that which is another kind of ignorance0,a and all our analysis of incomprehensible things leads us only to things more incomprehensible still4 ,a ,manfred1 ,act ,,ii41 scene iv4 ,it is1 therefore1 by the firm resolution never to juggle with words or ideas1 or to try and persuade ourselves or others that we understand what we do not understand1 that any scientific advance can be made4 ,,chapter ,i4 ,all students of any subject are at first apt to be perplexed with the number and complication of the new ideas presented to them4 ,the need of comprehending these ideas is felt1 and yet they are difficult to grasp and to define4 ,thus1 for instance1 we are all apt to think we know what is meant when force1 weight1 length1 capacity1 motion1 rest1 size1 are spoken of4 ,and yet when we come to examine these ideas more closely1 we find that we know very little about them4 ,indeed1 the more elementary they are1 the less we are able to understand them4 ,the most primordial of our ideas seem to be those of number and quantity2 we can count things1 and we can measure them1 or compare them with one another4 ,arithmetic is the science which deals with the numbers of things and enables us to multiply and divide them4 ,the estimation of quantities is made by the application of our faculty of comparison to different subjects4 ,the ideas of number and quantity appear to pervade all our conceptions4 ,the study of natural phenomena of the world around us is called the study of physics from the ,greek word or 8inanimate nature10 the term physics is usually confined to such part of nature as is not alive4 ,the study of living things is usually termed biology 7from 1 life74 ,in the study of natural phenomena there are1 however1 three ideas which occupy a peculiar and important position1 because they may be used as the means of measuring or estimating all the rest4 ,in this sense they seem to be the most primitive and fundamental that we possess4 ,we are not entitled to say that all other ideas are formed from and compounded of these ideas1 but we are entitled to say that our correct understanding of physics1 that is of the study of nature1 depends in no slight degree upon our clear understanding of them4 ,the three fundamental ideas are those of space1 time and mass4 ,space appears to be the universal accompaniment of all our impressions of the world around us4 ,try as we may1 we cannot think of material bodies except in space1 and occupying space4 ,though we can imagine space as empty we cannot conceive it as destroyed4 ,and this space has three dimensions1 length1 breadth measured across or at right angles to length1 and thickness measured at right angles to length and breadth4 ,more dimensions than this we cannot have4 ,for some inscrutable reason it has been arranged that space shall present these three dimensions and no more4 ,a fourth dimension is to us unimaginable--,i will not say inconceivable--we can conceive that a world might be with space in four dimensions1 but we cannot imagine it to ourselves or think what things would be like in it4 ,with difficulty we can perhaps imagine a world with space of only two dimensions1 a 8flat land10 where flat beings of different shapes1 like figures cut out of paper1 slide or float about on a flat table4 ,they could not hop over one another1 for they would only have length and breadth2 to hop up you would want to be able to move in a third dimension1 but having two dimensions only you could only slide forward and sideways in a plane4 ,to such beings a ring would be a box4 ,you would have to break the ring to get anything out of it1 for if you tried to slide out you would be met by a wall in every direction4 ,you could not jump out of it like a sheep would jump out of a pen over the hurdles1 for to jump would require a third dimension1 which you have not got4 ,beings in a world with one dimension only would be in a worse plight still4 ,like beads on a string they could slide about in one direction as far as the others would let them4 ,they could not pass one another4 ,to such a being two other beings would be a box one on each side of him1 for if thus imprisoned1 he could not get away4 ,like a waggon on a railway1 he could not walk round another waggon4 ,that would want power of moving in two dimensions1 still less could he jump over them1 that would want three4 ,we have not the smallest idea why our world has been thus limited4 ,some philosophers think that the limitation is in us1 not in the world1 and that perhaps when our minds are free from the limitations imposed by their sojourn in our bodies1 and death has set us free1 we may see not only what is the length and breadth and height1 but a great deal more also of which we can now form no conception4 ,but these speculations lead us out of science into the shadowy land of metaphysics1 of which we long to know something1 but are condemned to know so little4 ,area is got by multiplying length by breadth4 ,cubic content is got by multiplying length by breadth and by height4 ,of all the conceptions respecting space1 that of a line is the simplest4 ,it has direction1 and length4 ,the idea of mass is more difficult to grasp than that of space4 ,it means quantity of matter4 ,but what is matter8 ,that we do not know4 ,it is not weight1 though it is true that all matter has weight4 ,yet matter would still have mass even if its property of weight were taken away4 ,for consider such a thing as a pound packet of tea4 ,it has size1 it occupies space1 it has length1 breadth1 and thickness4 ,it has also weight4 ,but what gives it weight8 ,the attraction of the earth4 ,suppose you double the size of the earth4 ,the earth being bigger would attract the package of tea more strongly4 ,the weight of the tea1 that is1 the attraction of the earth on the package of tea1 would be increased--the tea would weigh more than before4 ,take the package of tea to the planet ,jupiter1 which1 being very large1 has an attraction at the surface #b times that of the earth4 ,its size would be the same1 but it would feel to carry like a package of sand4 ,yet there would be the same 8mass0 of tea4 ,you could make no more cups of tea out of it in ,jupiter than on earth4 ,take it to the moon1 and it would weigh a little over two ounces1 but still it would be a pound of tea4 ,we are in the habit of estimating mass by its weight1 and we do so rightly1 for at any place on the earth1 as ,london1 the weights of masses are always proportioned to the masses1 and if you want to find out what mass of tea you have got1 you weigh it1 and you know for certain4 ,hence in our minds we confuse mass with weight4 ,and even in our ,acts of ,parliament we have done the same thing1 so that it is difficult in the statutes respecting standard weights to know what was meant by those who drew them up1 and whether a pound of tea means the mass of a certain amount of tea or the weight of that mass4 ,for accurate thinking we must1 of course1 always deal with masses1 not with weights4 ,for so far as we can tell mass appears indestructible4 ,a mass is a mass wherever it is1 and for all time1 whereas its weight varies with the attractive force of the planet upon which it happens to be1 and with its distance from that planet's centre4 ,a flea on this earth can skip perhaps eight inches high2 put that flea on the moon1 and with the expenditure of the same energy he could skip four feet high4 ,put him on the planet ,jupiter and he could only skip #c inches high4 ,a man in a street in the moon could jump up into a window on the first floor of a house4 ,one pound of tea taken to the sun would be as heavy as twenty-eight pounds of it at the earth's surface2 and weight varies at different parts of the earth4 ,hence the true measure of quantity of matter is mass1 not weight4 ,the mass of bodies varies according to their size2 if you have the same nature of material1 then for a double size you have a double mass4 ,some bodies are more concentrated than others1 that is to say1 more dense2 it is as though they were more tightly squeezed together4 ,thus a ball of lead of an inch in diameter contains forty-eight times as much mass as a ball of cork an inch in diameter4 ,in order to know the weight of a certain mass of matter1 we should have to multiply the mass by a figure representing the attractive force or pull of the earth4 ,in physics it is usual to employ the letters of the alphabet as a sort of shorthand to represent words4 ,so that the letter m stands for the mass of a body4 ,so again g stands for the attractive pull of the earth at a given place4 w stands for the weight of the body4 ,hence then1 since the weight of a body depends on its mass and also on the attractive pull of the earth1 we express this in short language by saying1 w m g2 or w is equal to m multiplied by g2 the symbol being used for equality1 and the sign of multiplication4 ,in common use is usually omitted1 and when letters are put together they are intended to be understood as multiplied4 ,so that this is written w mg4 ,of course by this equation we do not mean that weight is mass multiplied into the force of gravity1 we only mean that the number of units of weight is to be found by multiplying the number of units of mass into the number of units of the earth's force of gravity4 ,in the same way1 if when estimating the number of waggons1 w1 that would be wanted for an army of men1 n1 which consumed a number of pounds1 p1 of provisions a day1 we might put w np4 ,but this would not mean that we were multiplying soldiers into food to produce waggons1 but only that we were performing a numerical calculation4 ,time is one of the most mysterious of our elementary ideas4 ,it seems to exist or not to exist1 according as we are thinking or not thinking4 ,it seems to run or stand still and to go fast or slowly4 ,how it drags through a wearisome lesson2 how it flies during a game of cricket2 how it seems to stop in sleep4 ,if we measured time by our own thoughts it would be a very uncertain quantity4 ,but other considerations seem to show us that ,nature knows no such uncertainty as regards time1 that she produces her phenomena in a uniform manner in uniform times1 and that time has an existence independent of our thoughts and wills4 ,the idea of a state of things in which time existed no more was quite familiar to medival thinkers1 and was regarded by many of them as the condition that would exist after the ,day of ,judgment4 ,in recent times ,kant propounded the theory that time was only a necessary condition of our thoughts1 and had no existence apart from thinking beings--in fact1 that it was our way of looking at things4 ,scientifically1 however1 we are warranted in treating time as perfectly real and capable of the most exact measurement4 ,for example1 if we arrange a stream of sand to run out of an orifice1 and observe how much will run out while an egg is being boiled hard1 we find as a fact that if the same quantity of sand runs out1 the state of the egg is uniform4 ,if we walk for an hour by a watch1 we find that we can go half the distance that we should if we walked two hours4 ,it is the correspondence of these various experiments that gives us faith in the treatment of time as a thing existing independently of ourselves1 or1 at all events1 independent of our transient moods4 ,the ideas of time acquired by the races of men that first evolved from a state of barbarism were no doubt derived from the observation of day and night1 the month and the year4 ,illustration3 ,,fig4 #a4 ,for1 suppose that a shepherd were on the plains of ,chaldea1 or perhaps on those mountains of ,india known as the roof of the world1 which according to some archologists was the site of the garden of ,eden and the early home of the ,european race1 what would he see8 ,he would see the sun rise in the east1 slowly mount the heavens till it stood over the south at middle day1 then it would sink towards the west and disappear4 ,in summer the rising point of the sun would be more to the northward than in winter1 and so also would be its point of setting ,a4 ,in winter it would rise a little to the south of east1 and set a little to the south of west1 and not rise so high in the heavens at midday1 so that the summer day would be longer than the winter day4 ,if the day were always divided into twelve hours1 whether it were long or short1 then in summer the hours of the day would be long2 in winter they would be short4 ,this mode of dividing the day was that used by the ,greeks4 ,the ,egyptians1 on the other hand1 averaged their day by dividing the whole round of the sun into twenty-four hours1 so that the summer day contained more hours than the winter day4 ,hence1 for the ,egyptians1 sun-rise did not always take place at six o'clock4 ,for in winter it took place after six1 and in summer before six2 and this is the system that has descended to us4 ,the moon also would rise at different places1 varying between ,a and ,b1 and set at places varying between ,a and ,b1 but these would be independent of those at which the sun rose and set4 ,moreover1 the moon each day would appear to get further and further away from the sun in the direction of the arrow1 as shown in the sketch4 ,if the moon rose an hour after the sun on one day1 the next day it would rise more than two hours after the sun1 and so on4 ,this delay in rising of the moon would go on day by day till at last she came right round to the sun again1 as shown at ,m4 ,and in her path she would change her form from a crescent1 as at ,m1 up to a full moon1 when she would be half way round from the sun1 that is1 when she would rise twelve hours after him1 or just be rising as the sun set4 ,this delay and accompanying change of form would go on1 till after three weeks she would have got round to a position ,a1 when she would rise eighteen hours after the sun1 and have become a crescent with her back to the sun2 in fact1 she would always turn her convex side to the sun4 ,at length1 when twenty-eight days had passed1 she would be round again about opposite to the sun1 and consequently her pale light would be extinguished in his beams1 and she would gradually reappear as a new moon on the other side of him4 ,this series of changes of the moon takes place once every twenty-eight days1 and is called a lunar or 8moon0 month1 and was used as a division of time by very early nations4 ,the changes of the seasons recurred with the changes in the times of rising of the sun1 and took a year to bring about4 ,and there were nearly thirteen moon changes in the year4 ,it was also observed that during its cycle of changes1 the sun was slowly moving round backwards among the stars in the same direction as the moon1 only it made its retrograde cycle in a year1 and thus arose the division of time into months and years4 ,the stars turned round in the heavens once in the complete day4 ,the sun1 therefore1 appeared to move back among them1 passing successively through groups of stars1 so as to make the circuit of them all in a year4 ,the stars through which he passed in a year1 and through which the moon travelled in a month1 were divided by the ancients into groups called constellations1 and its yearly path in the heavens was called the zodiac4 ,there were twelve of these constellations in the zodiac called the signs4 ,hence1 then1 the sun passed through a sign in every month1 making the tour of them all in the year4 ,to these signs fanciful names were given1 such as 8the ,ram10 8the ,water-bearer10 8the ,virgin10 8the ,scorpion10 and so on1 and the sun and moon were then said to pass through the signs of the zodiac4 ,hence1 since the path of the sun marked the year1 you could tell the seasons by knowing what sign of the zodiac the sun was in4 ,the age of the moon was easily known by her form4 ,when the winter was over1 then1 just as the sun set the dog star would be rising in the east1 and this would show that the spring was at hand4 ,then the peasants prepared to till the earth and sow the seed and lead the oxen out to pasture1 and celebrated with joyful mirth the glad advent of the spring1 corresponding to our ,easter1 when the sun had run through three constellations of the zodiac4 ,then came the summer heat1 and with many a mystic rite they celebrated ,midsummer's ,day4 ,in autumn1 after three more signs of the zodiac have been traversed by the sun1 the sun again rises exactly in the east and sets in the west1 and the days and nights are equal4 ,this is the autumnal equinox1 and was once celebrated by the feast which we now know as ,michaelmas ,day1 and the goose is the remnant of the ancient festival4 ,illustration3 ,,fig4 #b4 ,and the great winter feast of the ancients is now known to us as ,christmas1 and chosen to celebrate the birth of our ,lord2 for when ,christianity came into the world and the heathens were converted1 the old feast days were deliberately changed into ,christian festivals4 ,to us1 therefore1 the whole heavens1 and the fixed stars with them1 appear to turn from east to west1 or from left to right1 as we look towards the south1 as shown by the big arrow4 ,but the moon and sun1 though apparently placed in the heavens1 move backwards among the fixed stars1 as shown by the small arrows4 ,the sun moves at such a rate that he goes round the circle of the heavens in a year of three hundred and sixty-five days4 ,the moon goes round the circle in twenty-eight and a half days1 or a lunar month4 ,of course1 in reality the sun is at rest1 and it is the earth that moves round the sun and spins on its axis as it moves4 ,but it will presently be shown that the appearance to a person on the earth is the same whether the earth goes round the sun or the sun round the earth4 ,from the works of ,greek writers we know a good deal about the ideas of the world that were entertained by the ancients4 ,the most early notions were1 of course1 connected with the worship of the gods4 ,the sun was considered as a huge light carried in a chariot1 driven by ,apollo1 with four spirited steeds4 ,it descended to the ocean when the day declined1 and then the horses were unyoked by the nymphs of the ocean and led round to the east1 so as to be ready for the journey of the following day4 ,the ,egyptians figured the sun as placed in a boat which sailed over the heavens4 ,at night the sun god descended into the infernal regions1 carrying with him the souls of those who had died during the day4 ,there they passed through different regions of hell1 with portals guarded by hideous monsters4 ,those who had well learned the ritual of the dead knew the words of power wherewith to appease the demons4 ,those unprovided with the watchwords were subjected to terrible dangers4 ,then the soul appeared before ,minos1 and was weighed and dealt with according to its deserts4 ,illustration3 ,,fig4 #c4 ,the earth was considered as a huge island in the midst of a circular sea4 ,gradually1 however1 astronomical ideas became subjected to science4 ,one of the first truths that dawned on astronomers was the fact that the earth was a sphere4 ,for they noticed that as people went further and further to the north1 the elevation of the sun at midday above the horizon became smaller and smaller4 ,this can easily be seen from the diagram4 ,when an observer is at ,a the sun appears at an altitude above the horizon equal to the angle 1 but as he goes along the curved surface of the earth to a point ,b nearer to the north pole1 the sun appears to be lower and only to have an altitude 4 ,from this it was easy for men so skilled in geometry as the ,greeks to calculate how big the earth was4 ,they did so1 and it appeared to have the enormous diameter of #h1jjj miles4 ,they only knew quite a small portion of it4 ,they thought that the rest was ocean4 ,but they had1 of course1 a clear idea of the 8antipodes0 or up-side-down side of it1 and they believed that if men were on the other side of it that their feet must all point towards its centre4 ,from this they got the idea of the centre of the earth as a point of attraction for all things that had an earth-seeking or earthy nature4 ,fire appeared always to desire to go upwards1 so they thought that fire had an earth-repellent1 heaven-seeking character4 ,water they thought partly earth-seeking1 partly heaven-seeking1 for it appeared in the ocean or floated as clouds4 ,air they thought to be indifferent4 ,and out of the four elements fire1 water1 earth1 and air they believed the world was made4 ,the earth they thought must be at rest2 for if it was in motion things would fly off from it4 ,they saw that either the sun must be moving round the earth1 or else the earth must be turning on its axis4 ,they chose the former hypothesis1 because they argued that if the earth were twisting round once in twenty-four hours then such a country as ,greece must be flying round like a spot on the surface of a top1 at the rate of about #ah1jjj miles in twenty-four hours1 that is1 at the rate of about #ahj yards in a second1 or faster than an arrow from a bow4 ,but if that was the case then a bird that flew up from the earth would be left far behind4 ,if a ball were thrown up it would fall hundreds of yards behind the person who threw it4 ,they could not conceive how it was possible for a ball thrown up by someone standing on a moving object not to fall behind the thrower4 ,this decided them in their error4 ,the mistaken astronomy of the ,greeks was also much forwarded by ,aristotle1 the tutor of ,alexander the ,great4 ,this great genius in politics and philosophy was only in the second rank as a man of science1 and1 as ,i think1 hardly equal to ,archimedes or ,hipparchus1 or even to ,ptolemy4 ,aristotle wrote a book concerning the heavens which bristles with the most wantonly erroneous scientific ideas1 such as1 for instance1 that the motion of the heavenly bodies must be circular because the most perfect curve is a circle1 and similar assumptions as to the course of nature4 ,the earth1 then1 being fixed1 they thought that the moon1 the sun1 and the seven planets were carried round it1 fixed each of them in an enormous crystal spherical shell4 ,these spheres1 like coats of an onion1 slid round one upon another1 each carrying his celestial luminary4 ,the moon was the nearest1 then ,mercury1 then ,venus1 then the sun1 then ,mars1 ,jupiter and ,saturn4 ,outside them was the sphere of the stars1 and outside all the 8primum mobile10 or great ,prime ,mover of the universe4 ,when one of the celestial bodies1 such as the moon1 got in front of another1 such as the sun1 there was an eclipse4 ,they soon observed that the moon derived its light from the sun4 ,as they knew the size of the earth1 by comparison they got some vague idea of the huge distances that the heavenly bodies must be from us4 ,in fact1 they measured the distance of the moon with approximate accuracy1 making it #bdj1jjj miles1 or about thirty times the earth's diameter4 ,this1 of course1 gave them the moon's diameter1 for they were easily able to calculate how big an object must be1 that looks as big as the moon and is #bdj1jjj miles away4 ,this large size of the moon gave them some idea of the distance of the sun1 but they failed to realise how big and far away he really is4 ,several ancient nations used weeks as means of measuring time4 ,they made four weeks to the lunar month4 ,the order of the days was rather curiously arranged4 ,for1 assuming that the earth is the centre of the planetary system1 put the planets in a column1 putting the nearest 7the moon7 at the bottom and the furthest off at the top-- ,saturn1 ,jupiter1 ,mars1 ,the ,sun1 ,venus1 ,mercury1 ,the ,moon4 ,then divide the day into three watches of eight hours each1 and let each watch be presided over by one of the planet-gods3 begin with ,saturn4 ,we then have ,saturn as the first god ruling ,saturday1 and ,jupiter and ,mars1 the two other gods1 for that day4 ,the first watch for ,sunday will be the sun2 ,venus and ,mercury will preside over the next two watches of that day4 ,the planet that will preside over the first watch of the next day will be the moon1 and the day will1 therefore1 be called ,monday2 ,saturn and ,jupiter will be the other gods for ,monday4 ,the first watch of the next day will be presided over by ,mars1 and the day will1 therefore1 be called ,mars-day or ,mardi1 or1 in the ,teutonic languages1 ,tuesday1 after ,tuesco1 a ,scandinavian god of war4 ,mercury will give a name to ,mercredi1 or to ,wednesday1 or ,wodin's-day4 ,jupiter to ,jeudi1 or 8,thurs0 day4 ,venus to ,vendredi1 or in the ,scandinavian1 ,friday1 the day of the ,scandinavian goddess ,freya1 the goddess of love and beauty1 who corresponds to ,venus1 and thus the week is completed4 ,illustration3 ,,fig4 #d4 ,this weekly scheme came probably from the ,chaldean astronomers4 ,it appears probable that the great tower of ,babel1 the ruins of which exist to this day1 consisted of seven stages1 one over the other1 the top one painted white1 or perhaps purple1 to represent the ,moon1 the next lower blue for ,mercury1 then green for ,venus1 yellow for the ,sun1 red for ,mars1 orange for ,jupiter1 and black for ,saturn4 ,unfortunately1 of the colours no trace now remains4 ,but nightly on the long terraces the ,babylonian priests observed eclipses and other celestial phenomena4 ,their records were afterwards taken to ,alexandria and kept in the great library that was subsequently burned by the ,turks4 ,in that library they were seen by the astronomer ,ptolemy1 who used them in the writing of his work on astronomy called the 8,great ,syntaxis0 or 8,collection40 ,the original work perished1 but it had been translated into ,arabic by the ,arab astronomers1 who called it 8,al ,magest10 the ,great ,book4 ,it was translated from ,arabic into ,latin1 and remained the textbook for astronomers in ,europe quite down to the time of ,queen ,elizabeth1 when a better system took its place4 ,for the use of men engaged in practical astronomy1 it is very convenient to consider the sun1 moon1 stars1 and planets as going round the earth at rest4 ,for instance1 seamen use the heavenly bodies as in a way hands of a huge clock from which they can know the time and their position on the earth4 8,the ,nautical ,almanac10 which is printed yearly1 gives the true position of these heavenly bodies for every hour1 minute1 and second of the year1 and ,i will presently show how useful this is to sailors4 ,we will deal with the sun first4 ,from the motions of the sun we can observe the time4 ,this is done in every garden by means of sun-dials1 and ,i will now describe how they are constructed4 ,if a light1 such as the light of a candle1 be moved round in a circle at a uniform pace so as to go round once in some given period1 such as twenty-four hours1 it is obvious that it would serve to measure time4 ,thus1 for example1 if a sheet of white paper be placed upon the table1 and a pencil be stuck on to it upright with some sealing wax1 or a pen propped up in an ink-pot1 then a candle held by anyone will cast the shadow of the pen on the paper4 ,illustration3 ,,fig4 #e4 ,if the person holding the candle walk round the table at a uniform speed1 the shadow will go round like the hand of a clock1 and might be made to mark the time4 ,if the candle took twenty-four hours to go round the table1 as the sun takes twenty-four hours to go round the earth1 then marks placed on the paper would serve to measure the hours1 and the paper and pen would serve as a sort of sun-dial4 ,but the sun does not go round the earth as the candle round the table4 ,its path is an inclined one1 like that shown by the dotted line4 ,sometimes it is above the level of the table1 sometimes below it4 ,and1 moreover1 its winter path is different from its summer path4 ,whence then it follows that the hour-marks on the paper cannot be put equidistant like the hours on the dial of a clock1 and that some arrangement must be made so that the line as shown by the summer sun shall correspond with the time as shown by the winter sun4 ,illustration3 ,,fig4 #f4 ,let us suppose that ,n ,o ,s is the axis of the heavens1 and the lines ,n ,a ,s1 ,n ,b ,s1 ,n ,c ,s1 are meridian lines drawn from one of the poles ,n of the heavens round on the surface of a celestial sphere whose centre is at ,o4 ,let ,a ,b ,c be a circle also on this sphere1 passing through ,o1 the centre of the sphere1 in a plane at right angles to ,n ,s1 the axis4 ,then ,a ,b ,c is called the equatorial4 ,it is a circle in the heavens corresponding to the equator on the earth4 ,at the vernal and autumnal equinox1 namely on ,march #be and ,september #be1 the sun is in the equatorial4 ,in midsummer and midwinter it is on opposite sides of the equatorial4 ,in midsummer it is nearer to ,n1 as at ,v2 in midwinter it is nearer to ,s1 as at ,w4 ,suppose we were on an island in the midst of a surrounding ocean1 we should only have a limited range of view4 ,if the highest point on the island were #ajj feet1 then from that altitude we should be able to see about thirteen miles to the horizon4 ,more than that could not be seen on account of the rotundity of the earth4 ,let us suppose then such an island surrounded for thirteen miles distant on every side by an ocean1 and let us consider what would be the apparent motions of the sun when seen from such an island4 ,at the vernal and autumnal equinoxes1 when the sun is on the equatorial1 it would appear to rise out of the ocean at a point ,e1 due east2 it traverses half the equatorial and sets in the ocean at a point ,w1 due west4 ,the day is twelve hours long1 from #f a4m4 to #f p4m4 ,illustration3 ,,fig4 #g4 ,in summer the sun is higher1 and nearer to the pole ,n1 say at a point s4 ,it rises at a point a in the ocean more to the north than ,e1 the eastern point1 and sets at a point b1 also more north than ,w1 the western point1 and traverses the path a s b4 ,but to traverse this path it takes longer than twelve hours1 for a s b is more than half the circle a s b4 ,hence then it rises say at #d4cj a4m4 and sets at #g4cj p4m4 ,the night1 during which the sun moves round the path from b to a1 is correspondingly short1 being only nine hours in length1 from #g4cj p4m4 till #d4cj a4m4 ,so you have a long summer day and a short summer night4 ,but in winter1 when the sun gets nearer to the south pole of the heavens1 it rises at a point ,c in the ocean at #g4cj a4m41 and traverses the arc c t d1 and sets at the point d at #d4cj p4m4 ,so that the winter day is only nine hours long4 ,but the winter night lasts from #d4cj p4m4 till #g4cj a4m41 and is therefore fifteen hours long1 the sun going round the path d r c in the interval4 ,it is therefore the obliquity of the poles ,n ,s1 coupled with the fact that the sun's position is nearer to one pole1 ,n1 in summer1 and nearer to the other pole1 ,s1 in winter1 that produces the inequality of days and nights in our latitudes4 ,suppose our island were on the equator4 ,the north pole and the south pole would appear to be on the horizon1 and then whether the sun moved in the circle a s b in the summer1 or ,e ,s ,w at the vernal or autumnal equinoxes1 or c t d in the winter1 in each of these cases1 though the places of rising and setting in the ocean might vary in summer from a and b to c and d in winter1 yet in each of these cases the path from a to b1 ,a to ,b1 and c to d would still always be a half-circle and occupy twelve hours4 ,hence at the equator the days and nights never vary in length1 but the sun always rises at six and sets at six4 ,and1 besides1 it always rises straight up from the ocean and plunges down vertically into it1 so that there is but little twilight and dawn4 ,illustration3 ,,fig4 #h4 ,but now let us suppose we were living at the north pole4 ,in this case the north pole would be directly overhead1 the south pole directly under our feet4 ,at the vernal and autumnal equinoxes the sun would appear with half its disc above the ocean1 and go round the ocean horizon1 always appearing with half its disc above the sea4 ,in summer it would appear at a point s nearer to the pole ,n4 ,it would go round in the heavens1 always appearing above the horizon1 and would never set at all4 ,as the summer waned the sun would become lower and lower1 still1 however1 going round and round without setting till at the autumn equinox it reached the horizon4 ,so that for six months it would never have set4 ,but when it did set1 there would then be six months without a sun at all4 ,illustration3 ,,fig4 #i4 ,thus then all over the world the period of darkness and light is equivalent4 ,at the tropics the days and nights are always equal4 ,at the poles light for six months is followed by darkness for six months4 ,in the intermediate temperate regions nights of varying lengths follow days of varying lengths1 a short night following a long day and vice vers4 ,illustration3 ,,fig4 #aj4 ,it is evident that for a person living on the north pole a sun-dial would be an easy thing to make4 ,all that would be needful would be to put a post vertically in the ground1 and observe its shadow as the sun went round 7,fig4 #aj74 ,illustration3 ,,fig4 #aa4 ,in latitudes such as that of ,england1 where the pole of the earth is inclined at an angle to the horizon1 it is necessary that the rod1 or 8style0 as it is called1 of the sun-dial should be inclined to the horizontal4 ,for if we used an upright 8style10 as ,o ,a1 then when the sun was in the south1 at midday1 the shadow would lie along the same direction1 ,o ,b1 whether the sun were high in summer1 as at ,s1 or low in winter1 as at s4 ,but at other hours1 such as nine o'clock in the morning1 the shadow of the 8style0 ,o ,a would1 when the sun was at its summer position ,t1 lie along ,o ,d1 whereas when the sun was at its winter position t the shadow would lie along ,o ,c4 ,thus the time would appear different in summer and in winter2 and the dial would lead to errors4 ,but if the 8style0 is inclined in the direction of the poles1 then1 however1 the sun moves from or towards the pole4 ,as its position varies in winter and summer1 the shadow still remains unchanged for any particular hour1 and it is only the circular motion of the sun round in its daily path that affects the position of the shadows4 ,illustration3 ,,fig4 #ab4 ,therefore the first condition of making a sun-dial is that the 8style0 which casts the shadow should be parallel to the earth's axis1 that is to say should point to the polar star4 ,this is the case whether the sun-dial is horizontal or is vertical1 and whether it stands on a pillar in the garden or is attached to the wall of a house4 ,to divide the dial1 we have only to imagine it surrounded by a sort of cage formed of twenty-four arcs drawn from the north pole to the south pole1 and equidistant from one another4 ,in its course the sun would cross one of them every hour4 ,hence the points to which the shadows o a1 o b1 o c1 o d1 of the inclined 8style0 ,o ,n would point are the points where these arcs meet the horizontal circle4 ,this consideration leads to a simple method of constructing a sun-dial1 which is given at the end of this chapter in an appendix4 ,sun-dials were largely in use in ancient times4 ,it is thought that the circular rows of stones used by the ,druids were used to mark the sun's path1 and indicate the times and seasons4 ,obelisks are also supposed to have been used to cast sun-shadows4 ,the ,greeks were perfectly acquainted with the method of making sun-dials with inclined 8styles10 or 8gnomons40 ,illustration3 ,,fig4 #ac4 ,small portable sun-dials were once much used before the introduction of watches1 and were provided with compasses by which they could be turned round1 so that the 8style0 pointed to the north4 ,sun-dials were only available during the hours of the day when the sun was shining4 ,the desire to mark the hours of the night led to the adoption of water clocks1 which measured time by the amount of water which escaped from a small hole in a level of water4 ,some care1 however1 is required to secure correct registration4 ,for suppose that we have a vessel with a small pipe leading out near the bottom1 then the amount of water which will run out of the pipe in a given time depends upon the pressure of the water at the pipe1 and this depends in its turn upon ,p ,q1 the head of water in the vessel4 ,whence it follows that the division ,q ,r1 due to say an hour's run of the clock at ,q ,r1 will be more than q r1 the division corresponding to an hour1 at q1 a point lower down between ,p and ,q1 and hence the divisions marked on the vessel to show the hours by means of the level of the water would be uneven1 becoming smaller and smaller as the water fell in the vessel4 ,to avoid the inconvenience of unequal divisions1 the water to be measured was allowed to escape into an empty vessel from a vessel in which its surface was always kept at a constant level4 ,inasmuch as the pressure on the pipe or orifice in the vessel in which the water was always kept at a constant level was always constant1 it followed that equal volumes of water indicated equal times1 and the vessel into which the water fell needed only to be equally divided4 ,as a measure of hours of the day in countries such as ,egypt1 where the hours were always equal1 and thus where the longer days contained more hours1 the water clock was very suitable2 but in ,greece and ,rome1 where the day1 whatever its length1 was always divided into twelve hours1 the simple water clock was as unsuitable as a modern clock would be1 for it always divided the hours equally1 and took no account of the fact that by such a system the hours in summer were longer than in winter4 ,in order1 therefore1 to make the water clock available in ,greece and ,italy1 it became necessary to make the hours unequal1 and to arrange them to correspond with unequal hours of the ,greek day4 ,this plan was accomplished as follows4 ,upon the water which was poured into the vessel that measured the hours was placed a float2 and on the float stood a figure made of thin copper1 with a wand in its hand4 ,this wand pointed to an unequally divided scale4 ,a separate scale was provided for every day in the year1 and these scales were mounted on a drum which revolved so as to turn round once in the year4 ,thus as the figure rose each day by means of a cogwheel it moved the drum round one division1 or one three hundred and sixty-fifth part of a revolution4 ,by this means the scale corresponding to any particular day of winter or summer was brought opposite the wand of the figure1 and thus the scale of hours was kept true4 ,in fact1 the water clock1 which kept true time1 was made by artificial means to keep untrue time1 in order to correspond with the unequal hours of the ,greek days4 ,in the picture ,a is the receiving water vessel1 ,p the pipe through which the water flows2 ,b is the figure1 ,c the rod2 ,d is the drum1 made to revolve by the cogwheel ,e1 containing #cfe teeth1 of which one tooth was driven forward at the close of each day4 ,a syphon ,g was fixed in the vessel ,a1 so that when the figure had risen to the top and pushed forward the lever ,f1 the syphon suddenly emptied the vessel through the pipe ,h1 and the figure fell to the bottom of the vessel ,a and became ready to rise and register another day4 ,the divisions on the drum are1 of course1 uneven4 ,on one side1 corresponding to the summer1 the day hours would reckon about seventy minutes each1 the night hours would be only about fifty minutes each1 so that the day divisions on the scale would be long1 and the night divisions short4 ,the reverse would be the case in winter4 ,and1 therefore1 the lines round the drum would go in an uneven wavy form4 ,illustration3 ,,fig4 #ad4 ,such water clocks as these were used by the ancient ,romans4 ,sand was also used to measure time4 ,as soon as the art of blowing glass had been perfected by the people of ,byzantium1 from whom the art passed to the ,venetians1 sand-glasses were made4 ,these glasses were used for all sorts of purposes1 for speeches and for cooking1 but their most important use was at sea4 ,for it was very important in the early days of navigation to know the speed at which the vessel was proceeding in order that one's place at sea might be calculated4 ,the earliest method was to throw over a heavy piece of wood of a shape that resisted being dragged through the water1 and with a string tied to it4 ,the block of wood was called the log1 and the string had knots in it4 ,the knots were so arranged that when one of them ran through one's fingers in a half-minute measured by a sand-glass it indicated that the vessel was going at the speed of one nautical mile in an hour4 ,the nautical mile was taken so that sixty of them constituted one degree1 that is one three hundred and sixtieth part of a great circle of the earth4 ,each nautical mile has1 therefore1 #f1jhj feet4 ,this is bigger than an ordinary mile on land1 which has only #e1bhj feet4 ,the knots1 therefore1 have to be arranged so that when the ship is going one nautical mile--that is to say1 #f1jhj feet--in an hour1 a knot shall run out during the half-minute run of the minute glass4 ,this is attained by putting the knots #a_/abj #f1jhj #ej feet #g inches apart4 ,as one sailor heaved the log over he gave a stamp on the deck and allowed the cord to run out through his fingers4 ,another sailor then turned the sand-glass4 ,when the sand had all run out1 showing that half a minute had passed1 the man who was letting the cord run through his fingers gripped it fast1 and observed how many knots or parts of knots of string had run out1 and thus was able to tell how many 8knots0 per half-minute the vessel was going1 that is to say1 how many nautical miles an hour4 ,the modern plan of observing the speed of vessels is different4 ,now we use a patent log1 consisting of a miniature screw propeller tied to a string and dragged through the water after the vessel4 ,as it is pulled through the water it revolves1 and the number of revolutions it makes shows how much water it has passed through1 and thus what distance it has gone4 ,the number of revolutions is measured by a counting mechanism1 and can be read off when the log is pulled in4 ,or sometimes the screw is attached to a stiff wire1 and the counting mechanism is kept on board the ship4 ,we use the expression 8knots an hour0 quite incorrectly4 ,it should be 8knots per half-minute10 or 8nautical miles an hour40 ,it is easy to use the flow of sand for all sorts of purposes to measure time4 ,thus1 if sand be allowed to flow from a hopper through a fine hole into a bucket1 the bucket may be arranged so that when a given time has elapsed1 and a given weight of sand has therefore fallen1 the bucket shall tip over1 and release a catch1 which shall then allow a weight to fall and any mechanical operation to be done that is required4 ,thus1 for example1 we might put an egg in a small holder tied to a string and lower it into a saucepan of boiling water4 ,the string might have a counter-weight attached to it1 acting over a pulley and thus always trying to pull it up out of the water4 ,but this might be prevented by a pin passing through a loop in the string and preventing it moving4 ,a hopper or funnel might be filled with sand which was allowed gradually to escape into a small tip-waggon or other similar device1 so that when a given amount of sand had entered the tip-waggon would tip over1 lurch the pin out of the loop1 and thus release the weight1 which in its turn would pull the egg up out of the water in three minutes or any desired time after it had been put in1 or a hole could be made in the saucepan1 furnished with a little tap1 and the water that ran out might be made to fall into a tip-waggon and tip it over1 and thus when it had run out to put an extinguisher on to the spirit lamp that was heating the saucepan1 and at the same time make a contact and ring an electric bell4 ,by this means the egg would be always exactly cooked to the right amount1 would be kept warm after it was cooked1 and a signal given when it was ready4 ,illustration3 ,,fig4 #ae4 ,the sketch shows such an arrangement4 ,the saucepan is about three inches in diameter and two inches high4 ,when filled with water it will hold an egg comfortably4 ,the extinguisher ,e1 mounted on a hinge ,q1 is turned back1 and the spirit lamp ,l is lit4 ,as soon as the water boils1 the tap ,t is turned1 and the water gradually trickles away into the tip-waggon4 ,as soon as it is full it tips over and strikes the arm ,x of the extinguisher1 and turns the lamp out4 ,the little hot water left in the saucepan will keep the egg warm for some time4 ,the waggon ,w must have a weight ,p at one end of it1 and the fulcrum must be nearer to that end1 so that when empty it rests with the end ,p down1 but when full it tips over on the fulcrum1 when the waggon has received the right quantity of water4 ,i leave to the ingenious reader the task of working out the details of such a machine1 which1 if made properly1 will act very well and may be made for a number of eggs and worked with very little trouble4 ,illustration3 ,,fig4 #af4 ,mercury has been used also as an hour-glass4 ,the orifice must be exceedingly fine4 ,or a bubble of mercury may be put into a tube which contains air1 and made gradually as it falls to drive the air out through a minute hole4 ,the difficulty is to get the hole fine enough4 ,all that can be done is to draw out a fine tube in the blow-lamp1 break it off1 and put the broken point in the blow-lamp until it is almost completely closed up4 ,a tube may thus be made about twelve inches long that will take twelve hours for a bubble of mercury to descend in it4 ,but the trouble of making so small a hole is considerable4 ,illustration3 ,,fig4 #ag4 ,king ,alfred is said to have used candles made of wax to mark the time4 ,as they blew about with the draughts1 he put them in lanterns of horn4 ,they had no glass windows in those days1 but only openings closed with heavy wooden shutters4 ,these large shutters were for use in fine weather4 ,smaller shutters were made in them1 so as to let a little light in in rainy weather without letting in too much wind and rain4 ,rooms must then have been very draughty1 so that people required to wear caps and gowns1 and beds had thick curtains drawn round them4 ,when glass was first invented it was only used by kings and princes1 and glass casements were carried about with them to be fixed into the windows of the houses to which they came1 and removed at their departure4 ,oil lamps were also used to mark the time4 ,some of them certainly as early as the fifteenth century were made like bird-bottles2 that is to say1 they consisted of a reservoir closed at the top with a pipe leading out of the bottom4 ,when full1 the pressure of the external atmosphere keeps the oil in the bottle1 and the oil stands in the neck and feeds the wick4 ,as the oil is consumed bubbles of air pass back along the neck and rise up to the top of the oil1 the level of which gradually sinks4 ,of course the time shown by the lamp varies with the rate of burning of the oil1 and hence with the size of the wick1 so that the method of measuring time is a very rough one4 ,,appendix4 ,to make a sun-dial1 procure a circular piece of zinc1 about inch thick1 and say twelve inches in diameter4 ,have a 8style0 or 8gnomon0 cast such that the angle of its edge equals the latitude of the place where the sun-dial is to be set up4 ,this for ,london will be equal to #ea #cj4 ,a pattern may be made for this in wood2 it should then be cast in gun-metal1 which is much better for out-of-door exposure than brass4 ,on a sheet of paper draw a circle ,a ,b ,c with centre ,o4 ,make the angle ,b ,o ,d equal to the latitude of the place for ,london #ea #cj4 ,from ,a draw ,a ,e parallel to ,o ,b to meet ,o ,d in ,e1 and with radius ,o ,e describe another circle about ,o4 ,divide the inner circle ,a ,b ,c into twenty-four parts1 and draw radii through them from ,o to meet the larger circle4 ,through any divisions 7say that corresponding to two o'clock7 draw lines parallel to ,o ,b1 ,o ,c1 respectively to meet in a4 ,then the line ,o a is the shadow line of the gnomon at two o'clock4 ,the lines thus drawn on paper may be transferred to the dial and engraved on it1 or else eaten in with acid in the manner in which etchings are done4 ,illustration3 ,,fig4 #ah4 ,the centre ,o need not be in the centre of the zinc disc1 but may be on one side of it1 so as to give better room for the hours1 etc4 ,a motto may be etched upon the dial1 such as 8,horas non numero nisi serenas10 or 8,qual 'hom senza ,dio1 son senza sol io10 or any suitable inscription1 and the dial is ready for use4 ,it is best put up by turning it till the hour is shown truly as compared with a correctly timed watch4 ,it must be levelled with a spirit level4 ,it must be remembered that the sun does not move quite uniformly in his yearly path among the fixed stars4 ,this is because he moves not in a circle1 but in an ellipse of which the earth is in one of the foci4 ,hence the hours shown on the dial are slightly irregular1 the sun being sometimes in advance of the clock1 sometimes behind it4 ,the difference is never more than a quarter of an hour4 ,there is no difference at midsummer and midwinter4 ,illustration3 ,,fig4 #ai4 ,civil time is solar time averaged1 so as to make the hours and days all equal4 ,the difference between civil time and apparent solar time is called the equation of time1 and is the amount by which the sun-dial is in advance of or in retard of the clock4 ,in setting a dial by means of a watch1 of course allowance must be made for the equation of time4 ,,chapter ,,ii4 ,in the last chapter a short description has been given of the ideas of the ancients as to the nature of the earth and heavens4 ,before we pass to the changes introduced by modern science1 it will be well to devote a short space to an examination of ancient scientific ideas4 ,all science is really based upon a combination of two methods1 called respectively inductive and deductive reasoning4 ,the first of these consists in gathering together the results of observation and experiment1 and1 having put them all together1 in the formulation of universal laws4 ,having1 for example1 long observed that all heavy things tended to go towards the centre of the earth1 we might conclude that1 since the stars remain up in the sky1 they can have no weight4 ,the conclusion would be wrong in this case1 not because the method is wrong1 but because it is wrongly applied4 ,it is true that all heavy things tend to go to the centre of the earth1 but if they are being whirled round like a stone in a sling the centrifugal force will counteract this tendency4 ,the first part of the reasoning would be inductive1 the second deductive4 ,all this reasoning consists1 therefore1 in forming as complete an idea as possible respecting the nature of a thing1 and then concluding from that idea what the thing will do or what its other properties will be4 ,in fact1 you form correct ideas1 or 8concepts10 as they are called1 and reason from them4 ,but the danger arises when you begin to reason before you are sure of the nature of your concepts1 and this has been the great source of error1 and it was this error that all men of science so commonly fell into all through ancient and modern times up to the seventeenth century4 ,of course1 if it were possible by mere observation to derive a complete knowledge of any objects1 it would be the simplest method4 ,all that would be necessary to do would be to reason correctly from this knowledge4 ,unfortunately1 however1 it is not possible to obtain knowledge of this kind in any branch of science4 ,the ancient method resembled the action of one who should contend that by observing and talking to a man you could acquire such a knowledge of his character as would infallibly enable you to understand and predict all his actions1 and to take little trouble to see whether what he did verified your predictions4 ,the only difference between the old methods and the new is that in modern times men have learned to give far more care to the formation of correct ideas to start with1 are much more cautious in arguing from them1 and keep testing them again and again on every possible opportunity4 ,the constant insistence on the formation of clear ideas and the practice of1 as ,lord ,bacon called it1 8putting nature to the torture10 is the main cause of the advance of physical science in modern times1 and the want of application of these principles explains why so little progress is being made in the so-called 8humanitarian0 studies1 such as philosophy1 ethics1 and politics4 ,the works of ,aristotle are full of the fallacious method of the old system4 ,in his work on the heavens he repeatedly argues that the heavenly bodies must move in circles1 because the circle is the most perfect figure4 ,he affects a perplexity as to how a circle can at the same time be convex and also its opposite1 concave1 and repeatedly entangles his readers in similar mere word confusion4 ,regarded as a man of science1 he must be placed1 ,i think1 in spite of his great genius1 below ,archimedes1 ,hipparchus1 and several other ancient astronomers and physicists4 ,his errors lived after him and dominated the thought of the middle ages1 and for a long time delayed the progress of science4 ,the other great writer on astronomy of ancient times was ,ptolemy of ,alexandria4 ,his work was called the 8,great ,collection10 and was what we should now term a compendium of astronomy4 ,although based on a fundamental error1 it is a thoroughly scientific work4 ,there is none of the false philosophy in it that so much disfigures the work of ,aristotle4 ,the reasons for believing that the earth is at rest are interesting4 ,ptolemy argues that if the earth were moving round on its axis once in twenty-four hours a bird that flew up from it would be left behind4 ,at first sight this argument seems very convincing1 for it appears impossible to conceive a body spinning at the rate at which the earth is alleged to move1 and yet not leaving behind any bodies that become detached from it4 ,on the other hand1 the system which taught that the sun and planets moved round the earth1 and which had been adopted largely on account of its supposed simplicity1 proved1 on further examination1 to be exceedingly complicated4 ,each planet1 instead of moving simply and uniformly round the earth in a circle1 had to be supposed to move uniformly in a circle round another point that moved round the earth in a circle4 ,this secondary circle1 in which the planet moved1 was called an epicycle4 ,and even this more complicated view failed to explain the facts4 ,a system which1 like that of ,aristotle and ,ptolemy1 was based on deductions from concepts1 and which consisted rather of drawing conclusions than of examining premises1 was very well adapted to medival thought1 and formed the foundation of astronomy and geography as taught by the schoolmen4 ,illustration3 ,,fig4 #bj4 ,the poem of ,dante accurately represents the best scientific knowledge of his day4 ,according to his views1 the centre of the earth was a fixed point1 such that all things of a heavy nature tended towards it4 ,thus the earth and water collected round it in the form of a ball4 ,he had no idea of the attraction of one particle of matter for another particle4 ,the only conception he had of gravity was of a force drawing all heavy things to a certain point1 which thus became the point round which the world was formed4 ,the habitable part of the earth was an island1 with ,jerusalem in the middle of it ,j4 ,round this island was an ocean ,o4 ,under the island1 in the form of a hollow cone1 was hell1 with its seven circles of torment1 each circle becoming smaller and smaller1 till it got down into the centre ,c4 ,heaven was at the opposite side ,h of the earth to ,jerusalem1 and was beyond the circles of the planets1 in the primum mobile4 ,when ,lucifer was expelled from heaven after his rebellion against ,god1 having become of a nature to be attracted to the centre of the earth1 and no longer drawn heavenwards1 he fell from heaven1 and impinged upon the earth just at the antipodes of ,jerusalem1 with such violence that he plunged right through it to the centre1 throwing up behind him a hill4 ,on the summit of this hill was the ,garden of ,eden1 where our first parents lived1 and down the sides of the hill was a spiral winding way which constituted purgatory4 ,dante1 having descended into hell1 and passed the centre1 found his head immediately turned round so as to point the other way up1 and1 having ascended a tortuous path1 came out upon the hill of ,purgatory4 ,having seen this1 he was conducted to the various spheres of the planets1 and in each sphere he became put into spiritual communion with the spirits of the blessed who were of the character represented by that sphere1 and he supposes that he was thus allowed to proceed from sphere to sphere until he was permitted to come into the presence of the ,almighty1 who in the primum mobile presided over the celestial hosts4 ,the astronomical descriptions given by ,dante of the rising and setting of the sun and moon and planets are quite accurate1 according to the system of the world as conceived by him1 and show not only that he was a competent astronomer1 but that he probably possessed an astrolabe and some tables of the motions of the heavenly bodies4 ,our own poet ,chaucer may also be credited with accurate knowledge of the astronomy of his day4 ,his poems often mention the constellations1 and one of them is devoted to a description of the astrolabe1 an instrument somewhat like the celestial globe which used to be employed in schools4 ,but with the revival of learning in ,europe and the rise of freedom of thought1 the old theories were questioned in more than one quarter4 ,it occurred to ,copernicus1 an ecclesiastic who lived in the sixteenth century1 to re-examine the theory that had been started in ancient times1 and to consider what explanation of the appearance of the heavenly bodies could be given on the hypothesis put forward by ,pythagoras1 that the earth moved round on its own axis1 and also round the sun4 ,it may appear rather curious that two theories so different1 one that the sun goes round the earth and the other that the earth goes round the sun1 should each be capable of explaining the observed appearances of those bodies4 ,but it must be remembered that motion is relative4 ,if in a waltz the gentleman goes round the lady1 the lady also goes round the gentleman4 ,if you take away the room in which they are turning1 and consider them as spinning round like two insects in space1 who is to say which of them is at rest and which in motion8 ,for motion is relative4 ,i can consider motion in a train from ,london to ,york4 ,as ,i leave ,london ,i get nearer to ,york1 and ,i move with respect to ,london and ,york4 ,but if both ,london and ,york were annihilated how should ,i know that ,i was in motion at all8 ,or1 again1 if1 while ,i was at rest in the train at a station on the way1 instead of the train moving the whole earth began to move in a southward direction1 and the train in some way were left stationary1 then1 though the earth was moving1 and the train was at rest1 yet1 so far as ,i was concerned1 the train would appear to have started again on its journey to ,york1 at which place it would appear to arrive in due time4 ,the trees and hedges would fly by at the proper rate1 and who was to say whether the train was in motion or the earth8 ,the theory of ,copernicus1 however1 remained but a theory4 ,it was opposed to the evidence of the senses1 which certainly leads us to think that the earth is at rest1 and it was opposed also to the ideas of some among the theologians who thought that the ,bible taught us that the earth was so fast that it could not be moved4 ,therefore the theory found but little favour4 ,it was in fact necessary before the question could be properly considered on its merits that more should be known about the laws of motion1 and this was the principal work of ,galileo4 ,the merit of ,galileo is not only to have placed on a firm basis the study of mechanics1 but to have set himself definitely and consciously to reverse the ancient methods of learning4 ,he discarded authority1 basing all knowledge upon reason1 and protested against the theory that the study of words could be any substitute for the study of things4 ,alluding to the mathematicians of his day1 8,this sort of men10 says ,galileo in a letter to the astronomer ,kepler1 8fancied that philosophy was to be studied like the #8neid' or #8,odyssey1' and that the true reading of nature was to be detected by the collating of texts40 ,and most of his life was spent in fighting against preconceived ideas4 ,it was maintained that there could only be seven planets1 because ,god had ordered all things in nature by sevens 78,dianoia ,astronomica10 #afaj72 and even the discoveries of the spots on the sun and the mountains in the moon were discredited on the ground that celestial bodies could have no blemishes4 8,how great and common an error10 writes ,galileo1 8appears to me the mistake of those who persist in making their knowledge and apprehension the measure of the knowledge and apprehension of ,god1 as if that alone were perfect which they understand to be so4 ,but 444 nature has other scales of perfection1 which we1 being unable to comprehend1 class among imperfections4 8,if one of our most celebrated architects had had to distribute the vast multitude of fixed stars over the great vault of heaven1 ,i believe he would have disposed them with beautiful arrangements of squares1 hexagons1 and octagons2 he would have dispersed the larger ones among the middle-sized or lesser1 so as to correspond exactly with each other2 and then he would think he had contrived admirable proportions2 but ,god1 on the contrary1 has shaken them out from ,his hand as if by chance1 and we1 forsooth1 must think that ,he has scattered them up yonder without any regularity1 symmetry1 or elegance40 ,in one of ,galileo's 8,dialogues0 ,simplicio says1 8,that the cause that the parts of the earth move downwards is notorious1 and everyone knows that it is gravity40 ,salviati replies1 8,you are out1 ,master ,simplicio3 you should say that everyone knows that it is called gravity2 ,i do not ask you for the name1 but for the nature1 of the thing of which nature neither you nor ,i know anything40 ,too often are we still inclined to put the name for the thing1 and to think when we use big words such as art1 empire1 liberty1 and the rights of man1 that we explain matters instead of obscuring them4 ,not one man in a thousand who uses them knows what he means2 no two men agree as to their signification4 ,the relativity of motion mentioned above was very elegantly illustrated by ,galileo4 ,he called attention to the fact that if an artist were making a drawing with a pen while in a ship that was in rapid passage through the water1 the true line drawn by the pen with regard to the surface of the earth would be a long straight line with some small dents or variations in it4 ,yet the very same line traced by the pen upon a paper carried along in the ship made up a drawing4 ,whether you saw a long uneven line or a drawing in the path that the pen had traced depended altogether on the point of view with which you regarded its motion4 ,illustration3 ,,fig4 #ba4 ,but the first great step in science which ,galileo made when quite a young professor at ,pisa was the refutation of ,aristotle's opinion that heavy bodies fell to the earth faster than light ones4 ,in the presence of a number of professors he dropped two balls1 a large and a small one1 from the parapet of the leaning tower of ,pisa4 ,they fell to the ground almost exactly in the same time4 ,this experiment is quite an easy one to try4 ,one of the simplest ways is as follows3 ,into any beam 7the lintel of a door will do71 and about four inches apart1 drive three smooth pins so as to project each about a quarter of an inch2 they must not have any heads4 ,take two unequal weights1 say of #a lb4 and #c lbs4 ,anything will do1 say a boot for one and pocket-knife for the other2 fasten loops of fine string to them1 put the loops over the centre peg of the three1 and pass the strings one over each of the side pegs4 ,now of course if you hitch the loops off the centre peg ,p the objects will be released together4 ,this can be done by making a loop at the end of another piece of string1 ,a1 and putting it on to the centre peg behind the other loops4 ,if the string be pulled of course the loop on it pulls the other two loops off the central peg1 and allows the boot and the knife to drop4 ,the boot and the knife should be hung so as to be at the same height4 ,they will then fall to the ground together4 ,the same experiment can be tried by dropping two objects from an upper window1 holding one in each hand1 and taking care to let them go together4 ,illustration3 ,,fig4 #bb4 ,this result is very puzzling2 one does not understand it4 ,it appears as though two unequal forces produced the same effect4 ,it is as though a strong horse could run no faster than a weaker one4 ,the professors were so irritated at the result of this experiment1 and indeed at the general character of young ,professor ,galileo's attacks on the time-honoured ideas of ,aristotle1 that they never rested till they worried him out of his very poorly paid chair at ,pisa4 ,he then took a professorship at ,padua4 ,let us now examine this result and see why it is that the ideas we should at first naturally form are wrong1 and that the heavy body will fall in exactly the same time as the light one4 ,we may reason the matter in this way4 ,the heavy body has more force pulling on it2 that is true1 but then1 on the other hand there is more matter which has got to be moved4 ,if a crowd of persons are rushing out of a building1 the total force of the crowd will be greater than the force of one man1 but the speed at which they can get out will not be greater than the speed of one man2 in fact1 each man in the crowd has only force enough to move his own mass4 ,and so it is with the weights3 each part of the body is occupied in moving itself4 ,if you add more to the body you only add another part which has itself to move4 ,a hundred men by taking hands cannot run faster than one man4 ,but1 you will say1 cannot a man run faster than a child8 ,yes1 because his impelling power is greater in proportion to his weight than that of a child4 ,if it were the fact that the attraction of gravity due to the earth acted on some bodies with forces greater in proportion to their masses than the forces that acted on other bodies1 then it is true that those different bodies would fall in unequal time4 ,but it is an experimental fact that the attractive force of gravity is always exactly proportional to the mass of a body1 and the resistance to motion is also proportional to mass1 hence the force with which a body is moved by the earth's attraction is always proportional to the difficulty of moving the body4 ,this would not be the case with other methods of setting a body in motion4 ,if ,i kick a small ball with all my might1 ,i shall send it further than a kick of equal strength would send a heavier ball4 ,why8 ,because the impulse is the same in each case1 but the masses are different4 ,but if those balls are pulled by gravity1 then1 by the very nature of the earth's attraction 7the reason of which we cannot explain71 the small ball receives a little pull1 and the big ball receives a big pull1 the earth exactly apportioning its pull in each case to the mass of the body on which it has to act4 ,it is to this fact1 that the earth pulls bodies with a strength always in each case exactly proportional to their masses1 that is due the result that they fall in equal times1 each body having a pull given to it proportional to its needs4 ,the error of the view of ,aristotle was not only demonstrated by ,galileo by experiment1 but was also demonstrated by argument4 ,in this argument ,galileo imitated the abstract methods of the ,aristotelians1 and turned those methods against themselves4 ,for he said1 8,you0 7the ,aristotelians7 8say that a lighter body will fall more slowly than a heavy one4 ,well1 then1 if you bind a light body on to a heavy one by means of a string1 and let them fall together1 the light body ought to hang behind1 and impede the heavy body1 and thus the two bodies together ought to fall more slowly than the heavy body alone2 this follows from your view3 but see the contradiction4 ,for the two bodies tied together constitute a heavier body than the heavy body alone1 and thus1 on your own theory1 ought to fall more quickly than the heavy body alone4 ,your theory1 therefore1 contradicts itself40 ,the truth is that each body is occupied in moving itself without troubling about moving its neighbour1 so that if you put any number of marbles into a bag and let them drop they all go down individually1 as it were1 and all in the time which a single marble would take to fall4 ,for any other result would be a contradiction4 ,if you cut a piece of bread in two1 and put the two halves together1 and tie them together with a thread1 will the mere fact that they are two pieces make each of them fall more slowly than if they were one8 ,yet that is what you would be bound to assert on the ,aristotelian theory4 ,hold an egg in your open hand and jump down from a chair4 ,the egg is not left behind2 it falls with you4 ,yet you are the heavier of the two1 and on ,aristotelian principles you ought to leave the egg behind you4 ,it is true that when you jump down a bank your straw hat will often come off1 but that is because the air offers more resistance to it than the air offers to your body4 ,it is the downward rush through the air that causes your hat to be left behind1 just as wind will blow your hat off without blowing you away4 ,for since motion is relative1 it is all one whether you jump down through the air1 or the air rushes past you1 as in a wind4 ,if there were no air1 the hat would fall as fast as your body4 ,this is easy to see if we have an airpump and are thus enabled to pump out almost all the air from a glass vessel4 ,in that vessel so exhausted1 a feather and a coin will fall in equal times4 ,if we have not an airpump1 we can try the experiment in a more simple way4 ,for let us put a feather into a metal egg-cup and drop them together4 ,the cup will keep the air from the feather1 and the feather will not come out of the cup4 ,both will fall to the ground together4 ,but if the lighter body fall more slowly1 the feather ought to be left behind4 ,if1 however1 you tie some strings across a napkin ring so as to make a sort of rough sieve1 and put a feather in it1 and then drop the ring1 then as the ring falls the air can get through the bottom of the ring and act on the feather1 which will be left floating as the ring falls4 ,let us now go on to examine the second fallacy that was derived from the ,aristotelians1 and that so long impeded the advance of science1 namely1 that the earth must be at rest4 ,the principal reason given for this was that if bodies were thrown up from the earth they ought1 if the earth were in motion1 to remain behind4 ,now1 if this were so1 then it would follow that if a person in a train which was moving rapidly threw a ball vertically1 that is perpendicularly1 up into the air1 the ball1 instead of coming back into his hand1 ought to hit the side of the carriage behind him4 ,the next time any of my readers travel by train he can easily satisfy himself that this is not so4 ,but there are other ways of proving it4 ,for instance1 if a little waggon running on rails has a spring gun fixed in it in a perpendicular position1 so arranged that when the waggon comes to a particular point on the rails a catch releases the trigger and shoots a ball perpendicularly upwards1 it will be found that the ball1 instead of going upwards in a vertical line1 is carried along over the waggon1 and the ball as it ascends and descends keeps always above the waggon1 just as a hawk might hover over a running mouse1 and finally falls not behind the waggon1 but into it4 ,so1 again1 if an article is dropped out of the window of a train1 it will not simply be left behind as it falls1 but while it falls it will also partake of the motion of the train1 and touch the ground1 not behind the point from which it was dropped1 but just underneath it4 ,the reason is1 that when the ball is dropped or thrown it acquires not only the motion given to it by the throw1 or by gravity1 but it takes also the motion of the train from which it is thrown4 ,if a ball is thrown from the hand1 it derives its motion from the motion of the hand1 and if at the time of throwing the person who does so is moving rapidly along in a train1 his hand has not only the outward motion of the throw1 but also the onward motion of the train1 and the ball therefore acquires both motions simultaneously4 ,hence then it is not correct reasoning to say1 because a ball thrown up vertically falls vertically back to the spot from which it was thrown1 that therefore the earth must be at rest2 the same result will happen whether the earth is at rest or in motion4 ,you can no more tell whether the earth is at rest or in motion from the behaviour of falling bodies than you can tell whether a ship on the ocean is at rest or in motion from the behaviour of bodies on it4 ,but you will say4 ,then why do we feel sea-sick on a ship8 ,the answer is1 that that is because the motion of the ship is not uniform4 ,if the earth1 instead of turning round uniformly1 were to rock to and fro1 everything on it would be flung about in the wildest fashion4 ,for as soon as the earth had communicated its motion to a body which then moved with the earth1 if the earth's motion were reversed1 the body would go on like a passenger in a train on which the break is quickly applied1 and he would be shot up against the side of the room4 ,nay1 more1 the houses would be shaken off their foundations4 ,changes of motion are perceptible so long as the change is going on4 ,we are therefore justified in inferring from the behaviour of bodies on the earth1 not that the earth is at rest1 but that it is either at rest1 or else1 if it is in motion1 that its motion is uniform and not in jerks or variable4 ,illustration3 ,,fig4 #bc4 ,for if it were not so1 consider what would be happening around us4 ,the earth is about #h1jjj miles in diameter1 and a parallel of latitude through ,london is therefore about #ai1jjj miles long1 and this space is travelled in twenty-four hours4 ,so that ,london is spinning through space at the rate of over #a1jjj feet a second1 due to the earth's rotary motion alone1 not to speak of the motion due to the earth's path round the sun4 ,if a boy jumped up two and a half feet into the air1 he would take about half a second to go up and come down1 but if in jumping he did not partake of the earth's motion1 he would land more than #ejj feet to the westward of the point from which he jumped up1 and if he did it in a room1 he would be dashed against the wall with a force greater than he would experience from a drop down from the top of ,mont ,blanc4 ,he would be not only killed1 but dashed into an indistinguishable mass4 ,if the earth suddenly stood still1 everything on it would be shaken to pieces4 ,it is bad enough to have the concussion of a train going thirty miles an hour when dashed against some obstacle4 ,but the concussion due to the earth's stoppage would be as of a train going about #hjj miles an hour1 which would smash up everything and everybody4 ,thus1 then1 the first effect of the new ideas formulated by ,galileo was to show that the ,copernican theory that the earth moved round on its axis1 and round the sun1 was in agreement with the laws of motion4 ,in fact1 he introduced quite new ideas of force1 and these ideas ,i must now endeavour to explain4 ,let us consider what is meant by the word 8force40 ,if ,i press my hand against the table1 ,i exert force4 ,the harder ,i press1 the more force there is4 ,if ,i put a weight on a stand1 the weight presses the stand down with a force4 ,if ,i squeeze a spring1 the spring tries to recover itself and exerts a certain force4 ,in all these cases force is considered as a pressure4 ,and ,i can measure the force by seeing how much it will press things4 ,if ,i take a spring1 and press it in an inch1 it takes perhaps a force of #a lb4 ,it will take a force of #b lbs4 to press it in another inch4 ,or again1 if ,i pull it out an inch1 it takes a force of #a lb4 ,if ,i pull it out another inch1 it takes a force of #b lbs4 ,we thus always get into the habit of conceiving forces as producing pressures and being measured by pressures4 ,illustration3 ,,fig4 #bd4 ,this is a perfectly legitimate way of looking at the matter1 just as the cook's method of employing a spring balance to weigh masses of meat is a perfectly legitimate way of estimating the forces acting upon bodies at rest4 ,but when you come to consider the laws of the pendulums of clocks1 to which all that ,i am saying is a preparation1 then you have to deal with bodies in motion4 ,and for this purpose a new idea of force altogether is requisite4 ,we shall no longer speak of forces as producing pressures4 ,we shall treat them quite independently of their pressing power4 ,the sun exerts a force of attraction on the earth1 but it does not press upon it4 ,it exerts its force at a distance4 ,hence then we want a new idea of 8force40 ,this idea is to be the following4 ,we will consider that when a force acts upon a body it endeavours to cause it to move2 in fact1 it tries to impart motion to the body4 ,we may treat this motion as a sort of thing or property4 ,the longer the force acts on the body1 the more motion it imparts to it1 provided the body is free to receive that motion4 ,so that we may say that the test of the strength of the force is how much motion it can give to a body of a given mass in a given time4 ,it does not matter how the force acts4 ,it may act by means of a string and pull it2 it may act by means of a stick and push it2 it may act by attraction and draw it2 it may act by repulsion and repel it2 it may act as a sort of little spirit and fly away with it4 ,in all these cases it acts4 ,the more it acts1 the more effect it has4 ,in double the time it produces double the motion4 ,if the mass is big1 it takes more force to make the mass move2 if the mass of the body is small1 it is moved more easily4 ,therefore when we want to measure a force in this way we do not press it against springs to see how much it will press them in4 ,what we do is to cause it to act on bodies that are free to move and see what motions it will produce in them4 ,of course we can only do this with things that are free to move4 ,you cannot treat force in this way if you have only a pair of scales2 in that case you would have to be content with simply measuring pressures4 ,it is important clearly to grasp this idea4 ,if a body has a certain mass1 then the force acting on it is measured by the amount of motion that will in a given time be imparted to that mass1 provided that the mass is free to move4 ,this is to be our definition of force4 ,therefore1 by the action of an attraction or any other force on a body free to move2 motion is continually being imparted to the body4 ,motion is1 as it were1 poured into it1 and therefore the body continually moves faster and faster4 ,here is a ball flying through the air4 ,let us suppose that forces are acting on it4 ,how can we measure them8 ,we cannot feel what pressures are being exerted on it4 ,the only thing we can do is to watch its motions1 and see how it flies4 ,if it goes more and more quickly1 we say1 8,there is propelling force acting on it02 if it begins to stop1 we say again1 8,there is retarding force acting on it40 ,so long as it does not change its speed or direction1 we say1 8,there is no force acting on it40 ,by this method1 therefore1 we tell whether a body is being acted on by force1 simply by observing its speed or its change of speed4 ,merely to say a body is moving does not tell us that force is acting on it4 ,all we know is that1 if it is moving1 force has acted on it4 ,it is only when we see it changing its speed or direction1 that is changing its motion1 that we say force is acting4 ,every change of motion1 either in direction or speed1 must be the result of force1 and must be proportional to that force4 ,this is what we mean when we say motion is the test and measure of force4 ,this most interesting way of looking at the matter lies at the root of the whole theory of mechanics4 ,it is the foundation of the system which the stupendous genius of ,newton conceived in order to explain the motion of the sun1 moon1 and stars4 ,forces were treated by him as proportional to the motions1 and the motions proportional to the forces1 and with this idea he solved a part of the riddle of the universe4 ,galileo had partly seen the same thing1 but he never saw it so clearly as ,newton4 ,great discoveries are only made by seeing things clearly4 ,what required the force of a genius in one age to see in the next may be understood by a child4 ,hence then we say a force is that which in a given time produces a given motion in a given mass which is free to move4 ,you must have time for a force to act in2 for however great the force1 in no time there can be no motion4 ,you must have mass for a force to act on2 no mass1 no effect4 ,you must have free space for the mass to move in2 no freedom to move1 no movement4 ,but what is this 8mass08 ,we do not know2 it is a mystery4 ,we call it 8quantity of matter40 ,in uniform substances it varies with size4 ,double the volume1 double the mass4 ,cut a cake in half1 each half has the same 8mass40 ,but then is mass 8weight08 ,no1 it is not4 ,weight is the action of the earth's attraction on matter4 ,no earth to attract1 and you would have no weight1 but you would still have 8mass40 ,what then is matter8 ,of that we have no idea4 ,the greatest minds are now at work upon it4 ,but mass is quantity of matter4 ,knock a brick against your head1 and you will know what mass is4 ,it is not the weight of the brick that gives you a bump2 it is the mass4 ,try to throw a ball of lead1 and you will know what mass is4 ,try to push a heavy waggon1 and you will know what mass is4 ,weights1 that is earth attractions on masses1 are proportional to the masses at the same place4 ,this1 as we have seen1 is known by experiment4 ,therefore1 when a force acts for a certain time on a mass that is free to move1 however small the force and however small the time1 that body will move4 ,when a baby in a temper stamps upon the earth it makes the earth move--not much1 it is true1 but still it moves2 nay1 more1 in theory1 not a fly can jump into the air without moving the earth and the whole solar system4 ,only1 as you may imagine they do not show it appreciably4 ,still1 in theory the motion is there4 ,hence then there are two different ways of considering and estimating forces1 one suitable for observations on bodies at rest1 the other suitable for observations of bodies that are free to move4 ,the force of course always tends to produce motion4 ,if1 however1 motion is impossible1 then it develops pressures which we can measure1 and calculate1 and observe4 ,if the body is free to move1 then the force produces motions which we can also measure1 calculate1 and observe4 ,and we can compare these two sets of effects4 ,we can say1 8,a force which1 acting on a ball of a mass of one pound1 would produce such and such motions1 would if it acted on a certain spring produce so much compression40 ,the attraction of the earth on masses of matter that are not free to move gives rise to forces which are called weights4 ,thus the attraction of gravitation on a mass of one pound produces a pressure equal to a weight of one pound4 ,unfortunately the same word 8pound0 is used to express both the mass and the weight1 and has come down to us from days when the nature of mass was not very well appreciated4 ,but great care must be taken not to confuse these two meanings4 ,but the earth's attractions and all other forces acting upon matter which is free to move give rise to changes of motion4 ,the word used for a change of motion is 8acceleration0 or a quickening4 8,he accelerated his pace10 we say4 ,that is1 he quickened it2 he added to his motion4 ,so that force1 acting on mass during a time1 produces acceleration4 ,from this1 then1 it follows that if a force continues to act on a body the body keeps moving quicker and quicker4 ,when the force stops acting1 the motion already acquired goes on1 but the acceleration stops4 ,that is to say1 the body goes on moving in a straight line uniformly at the pace it had when the force stopped4 ,if1 then1 a body is exposed to the action of a force1 and held tight1 what will happen8 ,it will1 of course1 remain fixed4 ,now let it go--it will then1 being a free body1 begin to move4 ,as long as the force acts1 the force keeps putting more and more motion into the body1 like pouring water into a jug1 the longer you pour the faster the motion becomes4 ,the body keeps all the motion it had1 and keeps adding all the motion it gains4 ,it is like a boy saving up his weekly pocket-money3 he has what he had1 and he keeps adding to that4 ,so if in one second a motion is imparted of one foot a second1 then in another second a motion of one foot a second more will be added1 making together a motion of two feet a second2 in another second of force action the motion will have been increased or 8accelerated0 by another foot per second1 and so on4 ,the speed will thus be always proportional to the force and the time4 ,if we write the letter ,v to represent the motion1 or speed1 or velocity2 ,f to represent the acceleration or gain of motion2 and ,t to represent the time1 then ,v ,,ft4 ,here ,v is the velocity the body will have acquired at the end of the time ,t1 if free to move and submitted to a force capable of producing an acceleration of ,f feet per second in a unit of time4 ,v is the final velocity4 ,the average velocity will be #a_/b ,v1 for it began with no velocity and increased uniformly4 ,how far will the body have fallen in the interval8 ,manifestly we get that by multiplying the time by the average velocity1 that is ,s #a_/b ,,vt1 where ,v1 as ,i said1 is the final velocity1 but we found that ,v ,,ft4 ,hence by substitution ,s #a_/b ,,ft ,t #a_/b ,,ft4 ,it is to be carefully borne in mind that these letters ,v1 ,s1 and ,t do not represent velocities1 spaces1 and times1 but merely represent arithmetical numbers of units of velocities1 spaces1 and times4 ,thus ,v represents ,v feet per second1 ,s represents ,s feet1 and ,t represents ,t seconds4 ,and when we use the equation ,v ,,ft we do not mean that by multiplying a force by a time you can produce a velocity4 ,if1 for instance1 it be true that you can obtain the number of inhabitants 7,h7 in ,london by multiplying the average number of persons 7,p7 who live in a house by the number of houses 7,n71 this may be expressed by the equation ,h ,,pn4 ,but this does not mean that by multiplying people into houses you can produce inhabitants4 ,h1 ,p1 and ,n are numbers of units1 and they are numbers only4 ,therefore when a body is being acted on by an accelerating force it tends to go faster and faster as it proceeds1 and therefore its velocity increases with the time4 ,but the space passed through increases faster still1 for as the time runs on not only does the space passed through increase1 but the rate of passing also gets bigger4 ,it goes on increasing at an increasing rate4 ,it is like a man who has an increasing income and always goes on saving it4 ,his total mounts up not merely in proportion to the time1 but the very rate of increase also increases with the time1 so that the total increase is in proportion to the time multiplied into the time1 in other words to the square of the time4 ,so then1 if ,i let a body drop from rest under the action of any force capable of producing an acceleration1 the space passed through will be as the square of the time4 ,now let us see what the speed will be if the force is gravity1 that is the attraction of the earth4 ,turning back to what was said about ,galileo1 it will be remembered that he showed that all bodies1 big and small1 light and heavy1 fell to the earth at the same speeds4 ,what is that speed8 ,let us denominate by ,g the number of feet per second of increase of motion produced in a body by the earth's action during one second4 ,then the velocity at the end of that second will be ,v ,,gt4 ,the space fallen through will be ,s #a_/b ,,gt4 ,what ,i want to know then is this3 how far will a body under the action of gravity fall in a second of time8 ,this1 of course1 is a matter for measurement4 ,if we can get a machine to measure seconds1 we shall be able to do it2 but inasmuch as falling bodies begin by falling sixteen feet in the first second and afterwards go on falling quicker and quicker1 the measurements are difficult4 ,galileo wanted to see if he could make it easier to observe4 ,he said to himself1 8,if ,i can only water down the force of gravity and make it weaker1 so that the body will move very slowly under its action1 then the time of falling will be easier to observe40 ,but how to do it8 ,this is one of those things the discovery of which at once marks the inventor4 ,illustration3 ,,fig4 #be4 ,the idea of ,galileo was1 instead of letting the body drop vertically1 to make it roll slowly down an incline1 for a body put upon an incline is not urged down the incline with the same force which tends to make it fall vertically4 ,can any law be discovered tending to show what the force is with which gravity tends to drag a mass down an incline8 ,there is a simple one1 and before ,galileo's time it had been discovered by ,stevinus1 an engineer4 ,stevinus' solution was as follows4 ,suppose that ,a ,b ,c is a wedge-shaped block of wood4 ,let a loop of heavy chain be hung over it1 and suppose that there is a little pulley at ,c and no friction anywhere4 ,then the chain will hang at rest4 ,but the lower part1 from ,a to ,b1 is symmetrical2 that is to say1 it is even in shape on both sides4 ,hence1 so far as any pull it exerts is concerned1 the half from ,a to ,d will balance the other half from ,b to ,d4 ,therefore1 like weights in a scale1 you may remove both1 and then the force of gravity acting down the plane on the part ,a ,c will balance the force of gravity acting vertically on the part ,c ,b4 ,now the weight of any part of the chain1 since it is uniform1 is proportional to its length4 ,hence1 then1 the gravitational force down the plane of a piece whose weight equals ,c ,a is equal to the gravitational force vertically of a piece whose weight equals ,c ,b4 ,in other words1 the force of gravity acting down a plane is diminished in the ratio of ,c ,b to ,c ,a4 ,but when a body falls vertically1 then1 as we have seen1 ,s #a_/b ,,gt1 where ,s is the space it will fall through1 ,g the number of feet per second of velocity that gravity1 acting vertically on a body1 will produce in it in a second1 and ,t the number of seconds of time4 ,if then1 instead of falling vertically1 the body is to fall obliquely down a plane1 instead of ,g we must put as the accelerating force ,g 7vertical height of the end of the plane7_/7length of the plane74 ,to try the experiment1 he took a beam of wood thirty-six feet long with a groove in it4 ,he inclined it so that one end was one foot higher than the other4 ,hence the acceleration down the plane was #a_/cf ,g1 where ,g is the vertical acceleration due to gravity which he wanted to discover4 ,then he measured the time a brass ball took to run down the plane thirty-six feet long1 and found it to be nine seconds4 ,whence from the equation given above #cf feet #a_/b acceleration of gravity down the plane 7#i seconds74 ,whence it follows that the acceleration of gravity down the plane is 7#cf #b7_/7i7 feet per second4 ,but the slope of the plane is one thirty-sixth to the vertical4 ,therefore the vertical acceleration of gravity1 i4e41 the velocity which gravity would induce in a vertical direction in a second1 is equal to thirty-six times that which it exercises down the plane1 i4e41 #cf 7#cf #b7_/7i72 and this equals #cb feet per second4 ,though this method is ingenious1 it possesses two defects4 ,one is the error produced by friction1 the other from failure to observe that the force of gravity on the ball is not only exerted in getting it down the plane1 but also in rotating it1 and for this no allowance has been made4 ,the allowance to be made for rotation is complicated1 and involves more knowledge than ,galileo possessed4 ,still the result is approximately true4 ,illustration3 ,,fig4 #bf4 ,the next attempt to measure ,g1 that is the velocity that gravity will produce on a body in a second of time1 was made by ,attwood1 a ,cambridge professor4 ,his idea was to weaken the force of gravity and thus make the action slow1 not by making it act obliquely1 but by allowing it to act1 not on the whole1 but only on a portion of the mass to be moved4 ,for this purpose he hung two equal weights over a very delicately constructed pulley4 ,gravity1 of course1 could not act on these1 for any effect it produced on one would be negatived by its effect on the other4 ,the weights would therefore remain at rest4 ,if1 however1 a small weight ,w1 equal say to a hundredth of the combined weight of the weights ,a and ,b and ,w1 were suddenly put on ,a1 then it would descend under an accelerating force equal to a hundredth part of ordinary gravity4 ,we should then have ,s 7the space moved through by the weights7 #a_/b ,g_/#ajj t4 ,with such a system1 he found that in #g seconds the weights moved through #i feet4 ,whence he got #i #a_/b ,g_/#ajj 7#g74 ,from which ,g 7#b #i #ajj7_/7g7 #cb feet per second nearly4 ,thus by letting gravity only act on a hundredth part of the total weight moved1 namely ,a1 ,b1 and ,w1 he weakened its action #ajj times1 and thus made the time of falling and the space fallen through sufficiently large to be capable of measurement4 ,to sum up1 when a body free to move is acted upon by the force of gravity1 its speed will increase in proportion to the time it has been acted upon1 and the space it will pass through from rest is proportional to the square of the time during which the accelerating force has acted on it4 ,gravity is1 of course1 not the only accelerating force with which we are acquainted4 ,if a spring be suddenly allowed to act on a body and pull it1 the body begins to move1 and its action is gradually accelerated1 just as though it were attracted1 and the acceleration of its motion will be proportional to the time during which the accelerating force acts4 ,similarly1 if gunpowder be exploded in a gun-barrel1 and the force thus produced be allowed to act on a bullet1 the motion of the bullet is accelerated so long as it is in the barrel4 ,when the bullet leaves the barrel it goes on with a uniform pace in a straight line1 which1 however1 by the earth's attraction is at once deflected into a curve1 and altered by the resistance of the air4 ,illustration3 ,,fig4 #bg4 ,it has been already stated that motions may be considered independently one of another1 so that if a body be exposed to two different forces the action of these forces can be considered and calculated each independently of the other4 ,let us take an example of this law4 ,we have seen if a body is propelled forwards1 and then the force acting on it ceases1 that it proceeds on with uniform unchanging velocity1 and if nothing impeded it1 or influenced it1 it would go on in a straight line at a uniform speed4 ,we have also seen that if a body is exposed to the action of an accelerating force such as gravity it constantly keeps being accelerated1 it constantly keeps gaining motion1 and its speed becomes quicker and quicker4 ,illustration3 ,,fig4 #bh4 ,let us suppose a body exposed to both of these forces at the same time4 ,shoot it out of a cannon1 and let an accelerating force act on it1 not in the direction it is going1 but in some other direction1 say at right angles4 ,what will happen8 ,in the direction in which it is going1 its speed will remain uniform4 ,in the direction in which the accelerating force is acting1 it will move faster and faster4 ,thus along ,a ,b it will proceed uniformly4 ,if it proceeded uniformly also along ,a ,c 7as it would do if a simple force acted on it and then ceased to act71 then as a result it would go in the oblique line ,a ,d1 the obliquity being determined by the relative magnitude of the forces acting on it4 ,but how if it went uniformly along ,a ,b1 but at an accelerated pace along ,a ,c8 ,then while in equal times the distances along ,a ,b would be uniform the distances in the same times along ,a ,c would be getting bigger and bigger4 ,it would not describe a straight line2 it would go in a curve4 ,this is very interesting4 ,let us take an example of it4 ,suppose we give a ball a blow horizontally2 as soon as it quits the bat it would of course go on horizontally in a straight line at a uniform speed2 but now if ,i at the same instant expose it to the accelerating force of gravity1 then1 of course1 while its horizontal movement will go on uniformly1 its downward drop will keep increasing at a speed varying as the time4 ,and while the total distances horizontally will be uniform in equal times1 the total downward drop from ,a ,b will be as the squares of the times4 ,here1 then1 you have a point moving uniformly in a horizontal direction1 but as the squares of the times in a vertical direction4 ,it describes a curve4 ,what curve8 ,why1 one whose distances go uniformly one way1 but increase as the squares the other way4 ,illustration3 ,,fig4 #bi4 ,this interesting curve is called a parabola4 ,with a ball simply hit by a bat1 the motion is so very fast that we cannot see it well4 ,cannot we make it go slowly8 ,let us remember what ,galileo did4 ,he used an inclined plane to water down his force of gravity4 ,let us do the same4 ,let us take an inclined plane and throw on it a ball horizontally4 ,it will go in a curve4 ,its speed is uniform horizontally1 but is accelerated downwards4 ,if we desire to trace the curve it is easy to do4 ,we coat the ball with cloth and then dip it in the inkpot4 ,it will then describe a visible parabola4 ,if ,i tilt up the plane and make the force of gravity big1 the parabola is long and thin2 if ,i weaken down the force of gravity by making the plane nearly horizontal1 then it is wide and flat4 ,one can also show this by a stream of peas or shot4 ,the little bullets go each with a uniform velocity horizontally1 and an accelerated force downwards4 ,instead of peas we can use water4 ,a stream of it rushing horizontally out of an orifice will soon bend down into a parabola4 ,thus then ,i have tried to show what force is and how it is measured4 ,i repeat again1 when a body is free to move1 then1 if no further force acts on it1 it will go on in a straight line at a uniform speed1 but if a force continues to act on it in any direction1 then that force produces in each unit of time a unit of acceleration in the direction in which the force acts1 and the result is that the body goes on moving towards the direction of acceleration at a constantly increasing speed1 and hence passing over spaces that are greater and greater as the speed increases4 ,this is the notion of a 8force40 ,in all that has been said above it has been assumed that the attraction of gravity on a body does not increase as that body gets nearer to the earth4 ,this is not strictly true2 in reality the attractive force of gravity increases as the earth's centre is approached4 ,but small distances through which the weights in ,attwood's machine fall make no appreciable difference1 being as nothing compared to the radius of earth4 ,for practical purposes1 therefore1 the force may be considered uniform on bodies that are being moved within a few feet of the earth's surface4 ,it is only when we have to consider the motions of the planets that considerations of the change of attractive force due to distance have to be considered4 ,i am glad to say that the most tiresome1 or rather the most difficult1 part of our inquiry is now over4 ,with the help of the notions already acquired1 we are now ready to get to the pendulum1 and to show how it came about that a boy who once in church amused himself by watching the swinging of the great lamps instead of attending to the service laid the foundation of our modern methods of measuring time4 ,,chapter ,,iii4 ,we have examined the action of a body under the accelerating or speed-quickening force due to gravity1 the attractive force of which on any body is always proportional to the mass of that body4 ,let us now consider another form of acceleration4 ,illustration3 ,,fig4 #cj4 ,take the case of a strip of indiarubber4 ,if pulled it resists and tends to spring back4 ,the more ,i pull it out the harder is the pull ,i have to exert4 ,this is true of all springs4 ,it is true of spiral springs1 whether they are pulled out or pushed in1 and in each case the amount by which the spring is pulled out or pushed in is proportional to the pressure4 ,this law is called ,hooke's law4 ,it was expressed by him in ,latin1 8,ut tensio1 sic vis03 8,as the extension1 so the force40 ,it is true of all elastic bodies1 and it is true whether they are pulled out or pushed in or bent aside4 ,the common spring balance is devised on this principle4 ,the body to be weighed is hung on a hook suspended from a spring4 ,the amount by which the spring is pulled out is a measure of the weight of the body4 ,if you take a fishing rod and put the butt end of it on a table and secure it by putting something heavy on the end1 then the tip will bend down on account of its own weight4 ,mark the point to which it goes4 ,now1 if you hang a weight on the tip1 the tip will bend down a little further4 ,if you put double the weight the tip will go down double the distance1 and so on until the fishing rod is considerably bent1 so that its form is altered and a new law of flexure comes into play4 ,suppose ,i use a spring as an accelerating force4 ,for example1 suppose ,i suspend a heavy ball by a string and then attach a spiral spring to it and pull the spring aside4 ,the ball will be drawn after the spring4 ,if then ,i let the ball go1 it will begin to move4 ,the force of the spring will act upon it as an accelerating force1 and the ball will go on moving quicker and quicker4 ,but the acceleration will not be like that of gravity4 ,there will be two differences4 ,the pull of the spring will in no way depend on the mass of the ball1 and the pull of the spring1 instead of being constant1 like the pull of gravity1 will become weaker and weaker as the ball yields to it4 ,consequently the equations above given which determine the relations between this space passed through1 the velocity1 and the time which were determined in the case of gravity are no longer true1 and a different set of relations has to be determined4 ,this can be easily done by mathematics4 ,but ,i do not propose to go into it4 ,i prefer to offer a rough and ready explanation1 which1 though it does not amount to a proof1 yet enables us to accept the truth that can be established both by experiment and by calculation4 ,illustration3 ,,fig4 #ca4 ,let a heavy ball 7,a7 be suspended by a long string1 so that the action of gravity sideways on the ball is very small and may be neglected1 and to each side attach an indiarubber thread fastened at ,b and ,c4 ,then when the ball is pulled aside a little1 say to a position ,d1 it will tend to fly back to ,a with a force proportioned to the distance ,a ,d4 ,what will be the time it will take to do this8 ,if the distance ,a ,d is small1 the ball has only a small distance to go1 but then1 on the other hand1 it has only small forces acting on it4 ,if the distance ,a ,d is bigger1 then it has a longer distance to go1 but larger forces to urge it4 ,these counteract one another1 so that the time in each case will be the same4 ,illustration3 ,,fig4 #cb4 ,the question is this3--,will you go a long distance with a powerful horse1 or a small distance with a weak horse8 ,if the distance in each case is proportioned to the power of the horse1 then the amount of the distance does not matter4 ,the powerful horse goes the long distance in the same time that the weak horse goes the short distance4 ,and so it is here4 ,however far you pull out the spring1 the accelerative pull on the ball is proportioned to the distance4 ,but the time of pulling the ball in depends on the distance4 ,so that each neutralises the other4 ,whence then we have this most important fact1 that springs are all isochronous2 that is to say1 any body attached to any spring whatever1 whether it is big or small1 straight or curly1 long or short1 has a time of vibration quite independent of the bigness of the vibration4 ,the experiment is easy to try with a ball mounted on a long arm that can swing horizontally4 ,it is attached on each side to an elastic thread4 ,if pulled aside1 it vibrates1 but observe1 the vibration is exactly the same whether the bigness of the vibration is great or small4 ,if the pull aside is big1 the force of restitution is big2 if the pull is small1 the force of restitution is small4 ,in one case the ball has a longer distance to go1 but then at all points of its path it has a proportionally stronger force to pull it2 if the ball has a smaller distance to go1 then at all the corresponding points of its path it has a proportionally weaker force to pull it4 ,thus the time remains the same whether you have the powerful horse for the long journey or the weaker horse for the smaller journey4 ,illustration3 ,,fig4 #cc4 ,next take a short1 stiff spring of steel4 ,one of the kind known as tuning forks may be employed4 ,the reader is probably aware that sounds are produced by very rapid pulsations of the air4 ,any series of taps becomes a continuous sound if it is only rapid enough4 ,for example1 if ,i tap a card at the rate of #bfd times in a second1 ,i should get a continuous sound such as that given by the middle ,c note of the piano4 ,that1 in fact1 is the rate at which the piano string is vibrating when ,c is struck1 and that vibration it is that gives the taps to the air by which the note is produced4 ,this can be very easily proved4 ,for if you lift up the end of a bicycle and cause the driving wheel to spin pretty rapidly by turning the pedal with the hand1 then the wheel will rotate perhaps about three times in a second4 ,if a visiting card be held so as to be flipped by the spokes as they fly by1 since there are about thirty-six of them1 we should get a series of taps at the rate of about #ajh a second4 ,this on trial will be found to nearly correspond to the note ,a1 the lowest space on the bass clef of music4 ,as the speed of rotation is lowered1 the tone of the note becomes lower2 if the speed is made greater1 the pitch of the note becomes higher1 and the note more shrill4 ,however far or near the card is held from the centre of the wheel makes no difference1 for the number of taps per second remains the same4 ,so1 again1 if a bit of watch-spring be rapidly drawn over a file1 you hear a musical note4 ,the finer the file1 and the more rapid the action1 the higher the note4 ,the action of a tuning fork and of a vibrating string in producing a note depends simply on the beating of the air4 ,the hum of insects is also similarly produced by the rapid flapping of their wings4 ,it is an experimental fact that when a piano note is struck1 as the vibration gradually ceases the sound dies away1 but the pitch of the note remains unchanged4 ,a tune played softly1 so that the strings vibrate but little1 remains the same tune still1 and with the same pitch for the notes4 ,a 8siren0 is an ingenious apparatus for producing a series of very rapid puffs of air4 ,it consists of a small wheel with oblique holes in it1 mounted so as to revolve in close proximity to a fixed wheel with similar holes in it4 ,if air be forced through the wheels1 by reason of the obliquity of the orifices in the movable wheel it is caused to rotate4 ,as it does so1 the air is alternately interrupted and allowed to pass1 so that a series of very rapid puffs is produced4 ,as the air is forced in1 the wheel turns faster and faster4 ,the rapidity of succession of the puffs increases so that the note produced by them gradually increases in pitch till it rises to a sort of scream4 ,for steamers these 8sirens0 are worked by steam1 and make a very loud noise4 ,it is1 however1 impossible to make a tuning fork or a stretched piano spring alter the pitch of its note without altering the elastic force of the spring by altering its tension1 or without putting weights on the arms of the tuning fork to make it go more slowly4 ,and this is because the tuning fork and the piano spring1 being elastic1 obey ,hooke's law1 8,as the deflection1 so the force02 and therefore the time of back spring is in each case invariable1 and the pitch of the note produced therefore remains invariable1 whatever the amplitude of the vibration may be4 ,upon this law depends the correct going of both clocks and watches4 ,wonderful nature1 that causes the uniformity of sounds of a piano1 or a violin1 to depend on the same laws that govern the uniform going of a watch6 ,nay1 more1 all creation is vibrating4 ,the surge of the sea upon the coast that swishes in at regular intervals1 the colours of light1 which consist of ripples made in an elastic ether1 which springs back with a restitutional force proportioned to its displacement1 all depend upon the same law4 ,this grand law by which so many phenomena of nature are governed has a very beautiful name1 which ,i hope you will remember4 ,it is called 8harmonic motion10 by which is meant that when the atoms of nature vibrate they vibrate1 like piano strings1 according to the laws of harmony4 ,the ancient ,pythagorean philosophers thought that all nature moved to music1 and that dying souls could begin to hear the tones to which the stars moved in their orbits4 ,they called it1 as you know1 the music of the spheres4 ,but could they have seen what science has revealed to man's patient efforts1 they would have seen a vision of harmony in which not a ray of light1 not a string of a musical instrument1 not a pipe of an organ1 not an undulation of all-pervading electricity1 not a wing of a fly1 but vibrates according to the law of harmony1 the simple easy law of which a boy's catapult is the type1 and which1 as we have seen1 teaches us that when an elastic body is displaced the force of restitution1 in other words1 the force tending to restore it to its old position1 is proportional to the displacement1 and the time of vibration is uniform4 ,the last is the important thing for us2 we seem to get a gleam of a notion of how the clock and watch problem is going to be solved4 ,but before we get to that we have yet to go back a little4 ,about the year #aehj an inattentive youth 7it was our friend ,galileo again7 watched the swing of one of the great chandeliers in the cathedral church at ,pisa4 ,the chandeliers have been renewed since his day1 it was one of the old lamps that he watched4 ,it had been lit1 and allowed to swing through a considerable space4 ,he expected that as it gradually came to rest it would swing in a quicker and quicker time1 but it seemed to be uniform4 ,this was curious4 ,he wanted to measure the time of its swing4 ,for this purpose he counted his pulse-beats4 ,so far as he could judge1 there were exactly the same number in each pendulum swing4 ,this greatly interested him1 and at home he began to try some experiments4 ,as he got older his attention was repeatedly turned to that subject1 and he finally established in a satisfactory way the law that1 if a weight is hung to the end of a string and caused to vibrate1 it is isochronous1 or equal-timed1 no matter what the extent of the arc of vibration4 ,the first use of this that he made was to make a little machine with a string of which you could vary the length1 for use by doctors4 ,for the doctors of that day had no gold watch to pull out while with solemn face they watched the ticks4 ,they were delighted with the new invention1 and for years doctors used to take out the little string and weight1 and put one hand on the patient's pulse while they adjusted the string till the pendulum beat in unison with the pulse4 ,by observing the length of the string1 they were then able to tell how many beats the pulse made in a minute4 ,but ,galileo did not stop there4 ,he proceeded to examine the laws which govern the pendulum4 ,we will follow these investigations1 which will largely depend on what we have already learned4 ,before1 however1 it is possible to understand the laws which govern the pendulum1 there are one or two simple matters connected with the balance and operation of forces which have to be grasped4 ,suppose that we have a flat piece of wood of any shape like ,fig4 #cd1 and that we put a screw through any spot ,a in it1 no matter where1 and screw it to a wall1 so that it can turn round the screw as round a pivot4 ,illustration3 ,,fig4 #cd4 ,illustration3 ,,fig4 #ce4 ,next we will knock a tintack into any point ,b1 and tie a string on to ,b4 ,then if ,i pull at the string in any direction ,b ,c the board tends to twist round the screw at ,a4 ,what will the strength of the twisting force be8 ,it will depend on the strength of the pull1 and on the 8leverage10 or distance of the line ,c ,b from ,a4 ,we might imagine the string1 instead of being attached at ,b1 to be attached at ,d2 then1 if ,i put ,p as the strength of the pull1 the twisting power would be represented by ,p ,a ,d4 ,this is called the 8moment0 of the force ,p round the centre ,a4 ,it would be the same as if ,i had simply an arm ,a ,d1 and pulled upon it with the force ,p4 ,it is an experimental truth1 known to the old ,greek philosophers1 that moments1 or twisting powers1 are equal when in each case the result of multiplying the arm by the power acting at right angles to it is equal4 ,now suppose ,a ,b is a pendulum1 with a bob ,b of #aj lbs4 weight1 and suppose it has been drawn aside out of the vertical so that the bob is in the position ,b4 ,then the weight of the bob will act vertically downwards along the line ,b ,c4 ,the moment1 or twisting power1 of the weight will be equal to #aj lbs4 multiplied by ,a ,d1 ,a ,d being a line perpendicular to ,b ,c4 ,illustration3 ,,fig4 #cf4 ,now suppose that another string were tied to the bob ,b1 and pulled in a direction at right angles to ,a ,b1 with a force ,p just enough to hold the bob back in the position ,b4 ,the pull along ,d ,b ,a ,b would be the moment of that pull round the point ,a4 ,but1 because this moment just holds the pendulum up1 it follows that the moment of the weight of the pendulum round ,a is equal to the moment of the pull of the string ,b ,d round ,a4 ,whence ,p ,a ,b #aj lbs4 ,a ,d4 ,whence ,p #aj lbs4 7,a ,d7_/7,a ,b74 ,but ,a ,b is always the same1 whatever the side deflection or displacement of the pendulum may be4 ,whence then we see that when a pendulum is pulled aside a distance ,e ,b 7which is always equal to ,a ,d71 then the force tending to bring it back to ,e is always proportional to ,e ,b4 ,but if the pendulum be fairly long1 say #ci-a_/g inches1 and the displacement ,e ,b be small1--in other words1 if we do not drag it much out of the vertical1--then we may say that the force tending to bring it back to ,f1 its position of rest1 is not very different from the force tending to bring it back to ,e4 ,but ,f ,b is the 8displacement0 of the pendulum1 and1 therefore1 we find that when a pendulum is displaced1 or deflected1 or pulled aside a little1 the amount of the deflection is always very nearly proportional to the force which was used to produce the deflection4 ,this important law can be verified by experiment4 ,if ,c is a small pulley1 and ,b ,c a string attached to a pendulum ,a ,b whose bob is ,b4 ,then if a weight ,d be tied to the string and passed over a pulley ,c1 the amount ,f ,b by which the weight ,d will deflect the bob ,b is almost exactly proportional to ,d1 so long as we only make the deflection ,e ,b small1 that is two or three inches1 where say #ci-a_/g inches is the length ,a ,b of the pendulum4 ,if ,f ,b is made too big1 then the line ,b ,f can no longer be considered nearly equal to the arc of deflection ,e ,b1 and the proposition is no longer true4 ,hence then1 both by experiment and on theory1 we find that for small distances the displacement of a pendulum bob is approximately equal to the force by which that displacement is produced4 ,but if so1 then from what has gone before1 we have an example of harmonic motion4 ,the weight of the bob1 tending to pull the bob back to ,e1 acts just as an elastic band would act1 that is to say pulls more strongly in proportion as the distance ,f ,b is bigger4 ,in fact1 if we could remove the force of gravity still leaving the mass ,b of the pendulum bob1 the force of an elastic band acting so as to tend to pull the bob back to rest might be used to replace it4 ,it would be all one whether the bob were brought back to rest by the downward force of its own gravity1 or by the horizontal force of a properly arranged elastic band of suitable length4 ,illustration3 ,,fig4 #cg4 ,but the motion of the bob1 under the influence of the pull of an elastic band where the strain was always proportional to the displacement1 would1 as we have seen1 be harmonic motion1 and performed in equal times whatever the extent of the swing4 ,whence then we conclude that if the swings of a pendulum are not too big1 say not exceeding two and a half inches each way1 the motion may be considered harmonic motion1 and the swings will be made in equal times whether they are large or small ones4 ,in other words1 a clock with a #ci-a_/g inch pendulum and side swing on each side if not over two inches will keep time1 whatever the arc of swing may be4 ,this may be verified experimentally4 ,take a pendulum of wood #ci-a_/g inches long1 and affix to its end a bob of #aj lbs4 weight4 ,the pendulum will swing once in each second4 ,to pull it aside two inches we should want a weight such that its moment about the point of support was equal to the moment of the force of gravity acting on the bob1 about the point of support4 ,in other words1 the weight required #ci-a_/g inches #aj lbs4 #b inches4 ,whence the weight required #a_/b lb4 7nearly74 ,now fix a similar pendulum ,a ,b #ci-a_/g inches long1 horizontally1 with a weight ,b of #aj lbs4 on it4 ,fasten it to a vertical shaft ,c ,d1 with a tie rod of wire or string ,a ,b so as to keep it up1 and attach to each side of the rod ,a ,b elastic threads ,e ,f and ,e ,g4 ,let these threads be tied on at such a point that when ,b is pulled aside two inches the force tending to bring it back to rest is half a pound4 ,then if set vibrating the rod will swing backwards and forwards in equal times1 no matter how big1 the arc of vibration 7provided the arc is kept small71 and the time of oscillation will be that of a pendulum1 namely1 one swing in a second4 ,in fact1 whether you put ,a ,b vertically and let it swing on the pivots ,c and ,d by the force of gravity1 or put it horizontally1 and thus prevent gravity acting on it1 but make it swing under the accelerating influence of a pair of elastic bands so arranged as to be equivalent to gravity1 in each case it will swing in seconds4 ,illustration3 ,,fig4 #ch4 ,it is this curious property of the circle that makes the vertical force of gravity on a pendulum pull it as though it were a horizontally acting elastic band2 that is the reason why a pendulum is equal-time-swinging1 or1 as it is called1 isochronous1 from two ,greek words that mean 8the same0 and 8time40 ,but it must be remembered that this equal swinging is only approximate1 and only true when the arc of vibration is small4 ,here then we have a proof which shows us that the pendulum of a clock and the balance wheel of a watch depend on exactly the same principles4 ,they are each an example of harmonic motion4 ,the next question that arises is whether the weight of the pendulum has any influence upon the time of its vibration4 ,a little reflection will soon convince us that it has none4 ,for we know that the time that bodies take to fall to the ground under the action of gravity is independent of the weight4 ,a falling #b lb4 weight is only equivalent to two pound-weights falling side by side4 ,in the same way and by the same reasoning we might take two pendulums of equal length1 and each with a bob weighing #a lb4 ,they would1 if put side by side close together swing in equal times4 ,but the time would be the same if they were fastened together1 and made into one pendulum4 ,for inasmuch as the fall of a pendulum is due to gravity1 and the action of gravity upon a body is proportional to its mass1 it follows that in a pendulum the part of the gravitational force that acts upon each part of the mass is occupied in moving that mass1 and the whole pendulum may be considered as a bundle of pendulums tied together and vibrating together4 ,the same would be the case with a pendulum vibrating under the influence of a spring4 ,if you have two bobs and two springs1 they will vibrate in the same time as one bob accelerated by one spring4 ,in this case1 however1 the force of the one spring must be equal to the combined force of the two springs4 ,in other words1 the springs must be made proportional in strength to the masses4 ,hence1 then1 you cannot increase the speed of the vibration of a pendulum by adding weight to the bob4 ,on the other hand1 if you have a bob vibrating under the influence of a spring1 like the balance wheel of a watch1 then if you increase the bob without increasing the spring1 since the mass to be moved has increased without a corresponding increase in the accelerating force acting on it1 the time of swing will alter accordingly4 ,but in the case of gravity1 by altering the mass1 you thereby proportionally alter the attraction on it1 and therefore the time of swing is unaltered4 ,illustration3 ,,fig4 #ci4 ,the explanation which has been given above of the reasons why a pendulum swings backwards and forwards in a given time independently of the length of the arc through which it swings1 that is to say of the amount by which it sways from side to side1 is only approximate1 because in the proof we assumed that the arc of swing and the line ,f ,b were equal1 which is not really and exactly true4 ,galileo never got at the real solution1 though he tried hard4 ,it was reserved for another than he to find the true path of an isochronous pendulum and completely to determine its laws4 ,huygens1 a ,dutch mathematician1 found that the true path in which a pendulum ought to swing if it is to be really isochronous is a curve called a cycloid1 that is to say the curve which is traced out by a pencil fixed on the rim of a hoop when the hoop is rolled along a straight ruler4 ,it is the curve which a nail sticking out of the rim of a waggon wheel would scratch upon a wall4 ,i will not go into the mathematical proof of this4 ,clocks are not made with cycloidal pendulums1 because when the arc of a pendulum is small the swing is so very near a cycloid as to make no appreciable difference in time-keeping4 ,i am now glad to be able to say that ,i have dealt with all the mathematics that is necessary to enable the mechanism of a clock to be understood4 ,it all leads up to this3-- 7#a7 ,a harmonic motion is one in which the accelerating force increases with the distance of the body from some fixed point4 7#b7 ,bodies moving harmonically make their swings about this point in equal times4 7#c7 ,a spring of any sort or shape always has a restitutional force proportional to the displacement4 7#d7 ,and therefore masses attached to springs vibrate in equal times however large the vibration may be4 7#e7 ,the bob of a pendulum1 oscillating backwards and forwards1 acts like a weight under the influence of a spring1 and is therefore isochronous4 7#f7 ,the time of vibration of a pendulum is uninfluenced by changes in the weight of the bob1 but is influenced by changes in the length of the pendulum rod4 ,the time of vibration of a mass attached to a spring is influenced by changes in the mass4 ,we have now to deal with the application of these principles to clocks and watches4 ,clocks had been known before the time of ,galileo1 and before the invention of the pendulum4 ,they had what is known as balance1 or verge escapements4 ,strictly in order of time ,i ought to explain them here4 ,but ,i will not do so4 ,i will go on to describe the pendulum clock1 and then ,i will go back and explain the verge escapement1 which1 we shall see1 is really a sort of huge watch of a very imperfect character4 ,as soon as ,galileo had discovered that pendulums were isochronous1 that is1 equi-time-swinging1 he set to work to see whether he could not contrive to make a timepiece by means of them4 ,this would be easy if only he could keep a pendulum swinging4 ,when a pendulum is set swinging1 it soon comes to rest4 ,what brings it to rest8 ,the resistance of the air and the friction of the pivots4 ,therefore what is obviously wanted is something to give it a kick now and then1 but the thing must kick with discretion4 ,if it kicked at the wrong time1 it might actually stop the pendulum instead of keeping it going4 ,you want something that1 just as the pendulum is at one end and has begun to move1 will give it a further push4 ,suppose that ,i have a swing and that ,i put a boy in it1 and ,i swing him to and fro4 ,i time my pushes4 ,as he comes back against my hand ,i let him push it back1 and then just as the swing turns ,i give it a further push4 ,but ,i cannot stand doing that all day4 ,i must make a machine to do it4 ,now what sort of a machine8 ,first1 the machine must have a reservoir of force4 ,i can't get a machine to do work unless ,i wind it up1 nor a man to do work unless ,i feed him1 which is his way of being wound up4 ,but then what do ,i want him to do8 ,i want him1 when ,i give him a push1 to push me back harder4 ,i want a reservoir of force such that when a pendulum comes back and touches it1 the touch1 like the pressure of the trigger of a gun1 shall allow some pent-up power to escape and to drive the pendulum forward4 ,this is the case in a swing4 ,each time that the swing returns to my hands ,i give it a push1 which serves to sustain the motion that would otherwise be destroyed by friction and the resistance of the air4 ,such an arrangement1 if it can be contrived mechanically1 is called an 8escapement40 ,an arrangement of this kind was contrived by ,galileo4 ,he provided a wheel1 as is here shown1 with a number of pins round it4 ,the pendulum ,a ,b has an arm ,a ,h attached to it1 and there is a ratchet ,c ,d which engages with the pins4 ,the ratchet has a projecting arm ,e ,f4 ,illustration3 ,,fig4 #dj4 ,when the pendulum comes back towards the end of its beat1 the arm ,a ,h strikes the arm ,e ,f1 and raises the ratchet ,c ,d4 ,this releases the wheel1 which has a weight wound up upon it1 and therefore at once tries to go round4 ,the consequence is1 that the pin ,g strikes upon the arm ,a ,h1 and thus on its return stroke gives an impetus to the pendulum4 ,as the pin ,g moves forward it slides on the arm ,a ,h till it slips over the point ,h4 ,the wheel now being free1 would fly round were it not that when the pendulum returned1 and the arm ,a ,h was lowered1 the ratchet had got into position again and its point ,d was ready to meet and stop the next pin that was coming on against it4 ,at each blow of the pins against the pendulum a 8tick0 is made1 at each blow of a pin against the ratchet a 8tock0 is sounded1 so that as it moves the pendulum makes the 8tick-tock0 sound with which we are all familiar4 ,hence then a clock consists of a wheel1 or train of wheels1 urged by a weight or spring1 which strives continually to spin round1 but its rotation is controlled by an escapement and pendulum1 so contrived as only to allow it to go a step forward at regular equal intervals of time4 ,but this would make only a poor sort of escapement4 ,for the mode of driving the pendulum adds a complication to the swing of the pendulum4 ,instead of the pendulum being simply under the accelerative force of gravity1 it is also subjected to the acceleration of the pin ,g4 ,this acceleration is not of the 8harmonic0 order4 ,hence so far as it goes it does not tend to assist in giving a harmonic motion to the pendulum1 but1 on the contrary1 disturbs that harmonic motion4 ,besides this1 the impulse of the pin is in practice not always uniform4 ,for if the wheel is at the end of a train of wheels driven by a weight1 though the force acting on it is constant1 yet1 as that force is transmitted through a train of wheels1 it is much affected by the friction of the oil4 ,and on colder days the oil becomes more coagulated1 and offers greater resistance4 ,moreover1 as will be explained more in detail afterwards1 the fact that the impulse is administered by ,g at the end of the stroke of the pendulum is disadvantageous1 as it interferes with the free play of the pendulum4 ,from all these causes the above escapement is imperfect in character1 and would not do where precision was required4 ,illustration3 ,,fig4 #da4 ,it is now time to return to the old-fashioned escapements which were in use before the time of ,galileo4 ,these consisted of a wheel called a crown wheel1 with triangular teeth4 ,on one side of this wheel a vertical axis was fitted1 with projecting 8pallets0 e f4 ,across the axis a verge or rod e f was placed1 fitted with a ball at each end4 ,when the crown wheel attempted to move on1 one of its teeth came in contact with a pallet4 ,this urged the pallet forward1 and thereby caused an impulse to be given to the axis1 on which was mounted the verge1 carrying the balls4 ,these of course began to move under the acceleration of the force thus impressed upon the pallet4 ,meantime1 however1 the other pallet was moving in the opposite direction1 and by the time the first pallet had been pushed so far that it escaped or slid past the tooth of the crown wheel1 which was pressing upon it1 the other pallet had come into contact with the tooth on the other side of the crown wheel4 ,this tended to arrest the motion of the verge1 to bring the balls to a standstill1 and ultimately to impart a motion in a contrary direction to them4 ,thus then the arrangement was that of a pendulum not acted on by gravity1 for the balls neutralised one another4 ,the pendulum was1 however1 not subjected to a harmonic acceleration1 but alternately to a nearly uniform acceleration from ,a to ,b and ,b to ,a4 ,as a result1 therefore1 the time of oscillation was not independent of the arc of swing1 but varied according to it1 as also according to the driving power of the crown wheel4 ,at each stroke there was a considerable 8recoil40 ,for as each tooth of the wheel came into play it was unable at first to overcome and drive back the pallet against which it was pressing1 but1 on the contrary1 was for a time itself driven back by the pallet4 ,illustration3 ,,fig4 #db4 ,of course1 so long as the motions of the wheel and verge were exactly uniform1 fair time was kept4 ,but the least inequality of manufacture produced differences4 ,nevertheless it was on this principle that clocks were made during the thirteenth1 fourteenth and fifteenth centuries4 ,they were mostly made for cathedrals and monasteries4 ,one was put up at ,westminster1 erected out of money paid as a fine upon one of the few ,english judges who have been convicted of taking bribes4 ,the time of swing of these clocks depended entirely upon the ratio of the mass of the balls at the end of the verge as compared with the strength of the driving force by which the acceleration on the pallets was produced4 ,they were very commonly driven by a spring instead of a weight4 ,the spring consisted of a long strip of rather poor quality steel coiled up on a drum4 ,as it unwound it became weaker1 and thus the acceleration on the verge became weaker1 and the clock went slower4 ,in order1 therefore1 to keep the time true1 it became necessary to devise some arrangement by which the driving force on the crown wheel should be kept more constant4 ,this gave rise to the invention of the fusee4 ,the spring was put inside a drum or cylindrical box4 ,one end of the spring was fastened to an axis1 which was kept fixed while the clock was going2 the other was fastened to the inside of the drum4 ,round the drum a cord was wound1 which1 as the drum was moved by the spring1 tended to be wound up on the surface of the drum4 ,owing to the unequal pull of the spring1 this cord was pulled by the drum strongly at first1 and afterwards more feebly4 ,to compensate its action a conical wheel was provided1 with a spiral path cut in it in such a way and of such a size and proportion that as the wheel was turned round by the pull of the drum the cord was on different parts of it1 so that the leverage or turning power on it varied1 becoming greater as the pull of the cord became weaker1 and in such a ratio that one just compensated the other1 and the turning power of the axle was kept uniform4 ,in this manner small table clocks were made which kept very tolerable time4 ,illustration3 ,,fig4 #dc4 ,huygens converted these clocks into pendulum clocks in a very simple manner4 ,he removed one of the balls1 lengthened the verge1 and slightly increased the weight of the other ball4 ,by this means1 while the crown wheel still continued to drive the verge and remaining ball1 the acceleration on that ball now no longer depended entirely on the force of the crown wheel4 ,the acceleration and retardation were now almost entirely governed by the force of gravity on the remaining ball1 and this acceleration was harmonic4 ,the clock1 therefore1 was immensely improved as a time-keeper4 ,still1 however1 the acceleration remained partly due to the driving power1 and this was partly non-harmonic and introduced errors4 ,most of the old clocks were converted shortly after the time of ,huygens4 ,as there was in general no room for the pendulum inside the clock-case1 they usually brought the axle on which the pallets were mounted outside the clock and made it vibrate in front of the face4 ,many old clocks exist1 of which the engraving in the frontispiece is an example1 that have been thus converted4 ,a true old verge escapement clock is now a rarity4 ,the type of escapement invented by ,galileo never came into vogue for clocks1 on account of its imperfections1 except till after a long interval1 when1 with certain modifications1 it became the basis of a new improvement at the hands of ,sir ,george ,airey4 ,the crown wheel fell into disuse and was replaced by the anchor escapement1 which was employed in that popular and excellent timepiece used throughout the eighteenth and the early part of the nineteenth century1 and is now known as 8,the ,grandfather's ,clock40 ,it was after all the crown wheel in another shape4 ,the wheel1 however1 was flattened out1 the teeth being put in the same plane4 ,this made it much easier to construct4 ,the pallets were fixed on an axis1 and were a little altered so as to suit the changed arrangement of the teeth4 ,the pendulum was no longer hung on the axis which carried the pallets4 ,a cause of a good deal of friction and loss of power was thus removed4 ,the pendulum was hung from a strip of thin steel spring1 which allowed it to oscillate1 and which supported it without friction4 ,this excellent manner of suspending pendulums is now universal4 ,it enabled the pendulum to be made very heavy4 ,the bob was usually some eight or nine pounds weight4 ,by this means the acceleration on the pendulum was due almost entirely to gravity acting on the bob1 and thus the motion of the pendulum became almost wholly harmonic4 ,whence it followed that variations in the pendulum swing became of secondary importance1 and did not greatly alter the going of the clock4 ,illustration3 ,,fig4 #dd4 ,therefore when the wheels became worn1 and the pivots choked with old oil and dust1 the old clock still went on4 ,if it showed a tendency to stop for want of power1 a little more was added to the driving weight1 and the clock kept as good time as ever4 ,the swing of the pendulum was by this escapement enabled to be made small1 so that the arc of swing of the bob differed but little from a cycloid4 ,the secret of the time-keeping qualities of these old 8,grandfather0 clocks is the length of pendulum4 ,this renders it possible to have but a small arc of oscillation1 and therefore the motion is kept very nearly harmonic4 ,for practical purposes nothing will even now beat these old clocks1 of which one should be in every house4 ,at present the tendency is to abolish them and to substitute ,american clocks with very short pendulums1 which never can keep good time4 ,they are made of stamped metal4 ,when they get out of order no one thinks of having them mended4 ,they are thrown into the ash-pit and a new one bought4 ,in reality this is not economy4 ,good 8,grandfather0 clocks are not now often made4 ,the last place ,i remember to have seen them being manufactured is at ,morez1 in the district of the ,jura4 ,an excellent clock1 enclosed in a dust-tight iron case1 with a tall painted case of quaint old design1 can be bought for about #ees4 ,the wheels are well cut1 and the internal mechanism very good4 ,i visited the town of ,morez in the year #ahic4 ,the clock industry was declining4 ,the farmers of ,france seemed to prefer small clocks of hideous appearance1 made in ,germany and in ,america1 to the excellent work of their own country4 ,probably by now the old clockmaking industry is extinct4 ,one ,i purchased at that time has gone well ever since4 ,,chapter ,,iv4 ,it is now time to give a description of the various parts of an ordinary pendulum clock4 ,we will take the 8,grandfather0 clock as an example4 ,we shall want an hour hand and a minute hand in the centre of the face1 and a seconds hand to show seconds a little above them4 ,there will be a seconds pendulum #ciad inches long1 and the centre of the face of the clock will be about seven feet above the ground1 so as to give practically about five feet of fall for the weight4 ,illustration3 ,,fig4 #de4 ,in the first place1 we have to consider the axle which carries the minute hand1 and which turns round once in each hour4 ,this is usually made of a piece of steel about one-sixth of an inch in diameter4 ,clockmakers usually call an axle an 8arbor10 or 8tree10 whence our word axletree4 ,this 8arbor0 is turned in the lathe1 so as to have pivots on each end1 fitted into holes in the clock plates1 that is to say1 the flat pieces of brass that serve as the body of the clock4 ,the adjoining diagram shows ,s ,t the clock faces1 and ,c1 the arbor of the minute hand4 ,inasmuch as the seconds hand is to turn round sixty times while the minute hand turns round once1 it is obvious that the arbor of the minute hand must be connected to the arbor of the seconds hand by a train of cogwheels so arranged as to multiply by sixty4 ,this of course involves us in having large and small cogwheels4 ,illustration3 ,,fig4 #df4 ,the small cogwheels usually have eight teeth1 and are for convenience of manufacture1 as also to stand prolonged wear1 cut out of the solid steel of the arbor4 ,they are nicely polished4 ,the easiest pair of wheels to use will be two pinions of eight teeth1 or 8leaves10 as they are called1 and two cogwheels1 one of sixty-four teeth1 the other of sixty teeth4 ,it is then clear that if the arbor ,a turns round once in an hour1 the arbor ,b will turn round eight times in an hour1 and ,c will turn round 7#fj #fd7_/7h #h7 #fj times in an hour1 or once in each minute4 ,by having #dhj teeth on the cogwheel on ,a1 you could1 of course1 make ,c go round once in a minute without the use of any intermediate arbor such as ,b4 ,illustration3 ,,fig4 #dg4 ,but this would not be a very convenient plan4 ,for as the wheel on ,a is usually about two and a quarter inches in diameter1 to cut #dhj teeth on so small a wheel would involve us in cutting about sixty teeth to the inch4 ,the teeth would thus be microscopically small1 and would have to be set so fine that the least dirt would clog them4 ,moreover1 the pinion of eight leaves would have to be microscopic4 ,for these reasons1 therefore1 it is usual in clocks not to use wheels with teeth more than sixty or sixty-four in number1 and to diminish the motion gradually by means1 where needful1 of intermediate arbors4 ,we have next to consider how the weight is to be arranged so as to turn the arbor ,a once round in an hour4 ,we know that we have five feet of space for the weights to fall in4 ,if we arrange to have what is called a double fall1 as shown in the sketch1 then1 allowing room for pulley wheels1 we shall find that our string may be practically about nine feet in length4 ,illustration3 ,,fig4 #dh4 ,the clock will be wanted to go for a week without winding1 and as people may forget to wind it at the proper hour of the day1 we will give it a day extra1 and make an 8eight-day0 clock of it4 ,hence then1 while nine feet of cord is being pulled out by a weight which falls four and a half feet1 the minute hand is to be turned round as many times as there are hours in eight days1 viz41 #aib times4 ,this could be accomplished1 of course1 by winding the cord round the arbor of the minute hand4 ,but this would require #aib turns4 ,if our cord is to be ordinary whipcord1 or catgut1 say one-twelfth of an inch in diameter1 in order that the cord could be wound upon it1 the arbor would have to be #aib_/ab inches long #ad inches long4 ,this would make the clock case unnecessarily deep4 ,we must therefore again have recourse to an intermediate wheel4 ,illustration3 ,,fig4 #di4 ,if we put a pinion of eight leaves on the minute hand arbor c1 and engage it with a wheel of sixty-four teeth on another arbor b1 then b will obviously turn round once in eight hours1 that is to say1 twenty-four times in the period of eight days4 ,and1 if we fix on b a 8drum0 or cylinder two inches long1 the twenty-four turns of our cord will just fit upon it1 since1 as has been said1 our cord is to be one-twelfth of an inch in diameter4 ,the diameter of the drum must be such that a cord nine feet long can be wound twenty-four times round it4 ,that is to say1 each lap must take 7#i #ab7_/bd #d inches of cord4 ,from this it is easy to calculate that the diameter of the drum must be rather less than one and a half inches4 ,from this then it results that we want for a 8,grandfather's0 clock a drum two inches long and one and a half inches diameter1 on this a cogwheel of sixty-four teeth working into a minute hand arbor1 with a pinion wheel with eight leaves1 and a cogwheel of sixty-four teeth1 an intermediate or idle wheel with an eight-leaved pinion1 and a cogwheel of sixty teeth1 engaging with a seconds hand arbor with a pinion of eight leaves4 ,this is called the 8train of wheels40 ,with it a weight such as can be arranged in an ordinary 8,grandfather's0 clock case will cause by its fall during eight days the second hand arbor to turn round once in each minute during the whole time1 and the minute hand arbor to turn round once in each hour4 ,illustration3 ,,fig4 #ej4 ,we must next provide an arrangement for winding the clock up4 ,it is obvious that we cannot do so by twisting the hands back4 ,it is true that this could be done1 but it would take about five minutes to do each time and be wearisome4 ,in order to save this trouble1 an arrangement called a ratchet wheel and pall must be provided4 ,a ratchet wheel consists of a wheel with a series of notches cut in it1 as shown in the figure ,a4 ,a pall is a piece of metal1 mounted on a pin1 and kept pressed up against the ratchet wheel by a spring ,c4 ,it is obvious that if ,i turn the wheel ,a round1 and thus wind up a weight1 fastened to a cord wound round the drum ,d1 that the pall ,b will go click-click-click as the ratchet wheel goes round1 but that the pall will hold it from slipping back again4 ,when1 however1 ,i take my hands away1 and let the ratchet wheel alone1 then the weight ,e will pull on the drum ,d1 and try and turn the ratchet wheel back the opposite way to that in which ,i twisted it at first4 ,if the pall ,b is held fast1 it is impossible to move it1 but if the pall is fixed to a cogwheel ,f1 which rides loose on the arbor of the drum ,d1 then the pull of the weight ,e will tend to twist the cogwheel ,f round1 and this1 if engaged with a pinion wheel on the minute hand arbor1 will therefore drive the clock4 ,as the clock arbors move1 of course the weight ,e gradually runs down1 and1 at last all the string is unwound from the drum ,d4 ,the clock is said then to have 8run down10 but if ,i take a clock key1 and by means of it wind the string up upon the drum ,d1 then the pall lets the drum and ratchet slip2 the clock hands are not affected4 ,when ,i have given twenty-four turns to the arbor1 the nine feet of cord will then be wound upon the drum again1 and the clock will be ready to go for eight more days1 and will begin to move as soon as ,i cease to press upon the clock key4 ,illustration3 ,,fig4 #ea4 ,i have thus described the winding mechanism4 ,it now remains to describe the escapement4 ,it is of course obvious that1 if the weight and train of wheels were simply let go1 the weight would rush down1 and the seconds-hand wheel would fly round at a tremendous pace2 but we want it to be so restrained as only to be allowed to go one-sixtieth part of its journey round in each second4 ,in fact1 we need an 8escapement0 and a pendulum4 ,the escapement usually employed in 8,grandfather0 clocks is the anchor escapement above described4 ,it is not by any means the best sort of escapement1 but it is the easiest to make2 and hence its popularity in the days sometimes called the 8dear1 good old days10 when people had to file everything out by hand1 and had to take a day to do badly what can now be done well in five minutes4 ,the escape wheel of an anchor escapement has thirty sharp angular teeth on its rim4 ,the wheel is made as light as possible1 so that the shock of stoppage at each tick of the clock may be as slight as possible1 for a heavy blow of course wastes power and gradually wears out the clock4 ,the anchor consists of two arms of the shape shown in the illustration 7,fig4 #dd74 ,as the escape wheel goes round in the direction of the arrow1 the anchor1 mounted on its arbor1 rocks to and fro4 ,the wheel cannot run away1 because the act of pushing one arm or 8pallet10 as it is called1 outwards1 and thus freeing the tooth pulls the other pallet in1 and this stops the motion of the tooth opposite to it1 but when the anchor rocks back again1 so as to disengage the pallet from the tooth that holds it1 then the opposite tooth is free to fly forward against the other pallet4 ,this tends to rock the anchor the other way1 but at that instant the pallet just engages the next tooth of the wheel1 and so the action goes on4 ,the anchor rocks from side to side2 the pallets alternately engage the teeth of the wheel1 making at each rock of the anchor the tick-tock sound with which we are so familiar4 ,if the anchor were free to rock at any speed it could1 the ticking of the clock would be very quick2 so1 to restrain the vivacity of the anchor1 we have a pendulum4 ,the pendulum might be simply hung on to the anchor4 ,but the disadvantage of doing this would be that the heavy bob of the pendulum would cause such a pressure on the arbor of the anchor that there would be great friction1 and the arbor would soon be worn out1 and the accurate going of the clock disturbed4 ,the pendulum therefore is hung on a piece of steel spring on a separate hook1 which lets it go backwards and forwards and carries the weight easily1 while a rod projecting from the anchor has a pin1 which works in a slot on the pendulum4 ,the pendulum is therefore able to control and regulate the movements of the escapement1 and thus the time of the clock4 ,of course it is clear that the heavier the driving weight put on the drum of the clock1 and the better the cut and finish of the wheels1 and the greater the cleanliness and oil1 the more will be the pressure tending to drive round the escape wheel1 and the harder the pressure on the pallets1 and hence the bigger the impulses on the pendulum1 and therefore the larger the amplitude of its swing4 ,if the amplitude of the pendulum's swing affected the time of its swing1 then the time kept by the clock would vary with the weight1 and the dirt and friction1 and the drying up of the oil4 ,but here precisely is where the value of the beautiful law governing the harmonic motion of the pendulum comes in4 ,the time of the pendulum is 7for small arcs7 independent of the length of swing1 and therefore of the driving force of the clock1 and hence within limits the clock1 even though roughly made and foul with the dirt of years1 continues to keep good time4 ,but the anchor escapement has imperfections4 ,the only way in which a pendulum can be relied on to keep accurate time is by leaving it unimpeded4 ,but the pressure of the teeth on the pallets in an anchor escapement constantly interferes with this4 ,illustration3 ,,fig4 #eb4 ,a little consideration will easily show that there are some times during the swing of a pendulum at which interference is far more fatal to its time-keeping than at others4 ,thus the bob of a pendulum may be regarded as a weight shot outwards from its position of rest against the influence of a retarding force varying as its distance from rest--in fact1 shot out against a spring4 ,the time of going out and coming in again will be quite independent of the force exerted to throw it out1 quite independent of its original velocity4 ,therefore a variation in the impulse given to the bob is of no consequence1 provided that impulse is given when the bob is near the position of rest4 ,this follows from the nature of the motion4 ,if a ball be attached to a piece of elastic thread1 and thrown from the hand1 so that it flies out1 and then stops and is brought back by the elastic force of the thread1 the time of the outward motion and the return is the same whatever be the force of the throw4 ,and so if a pendulum be impelled outwards from a position of rest1 the time of the swing out and back is the same1 however big 7within limits7 is the impelling force and the consequent length of the swing4 ,the use of a pendulum as a measure of time is to impel it outwards1 and then let it fly freely out and back4 ,but if its motion is not free1 if forces other than gravity act upon it while on its path1 then its time of swing will be disturbed4 ,it does not matter with what force you originally impel it1 but what does matter is1 that when it once starts it should be allowed to travel unimpeded and uninfluenced4 ,now that is what an anchor escapement does not do4 ,the impulse is given the whole way out on one of the pallets1 and then when it is at its extreme of swing1 and ought to be left tranquil1 the other pallet fastens on it4 ,but a perfect escapement ought to give its impulse at the middle point of the swing1 when the pendulum is at the lowest1 and then cease1 and allow the pendulum to adapt its swing to the impulse it has received1 and thus therefore to keep its time constant4 ,this is done by an escapement called the dead beat escapement1 which1 though in an imperfect way1 realises these conditions4 ,the alteration is made in the shape of the pallets of the anchor4 ,the wheel is much the same4 ,each pallet consists of two faces3 a driving face a b and a sliding face b c4 ,illustration ,when the tooth b has done its work by pressing on the driving face1 and thus driving the anchor over1 say1 to the left1 then the tooth on the opposite side falls on the sliding face of the other pallet4 ,this being an arc of a circle1 has no effect in driving the anchor one way or the other2 hence the pendulum is free to swing to the left as far as it likes and return when it feels inclined1 always with the exception of a little friction of the tooth on the faces of the pallets1 but when it returns and begins to move towards the right1 the tooth slides back along the face of the pallet till the pendulum is almost at the middle of its swing2 then an impulse is given by the pressure of the tooth upon the inclined plane a b4 ,as soon1 however1 as the tooth leaves b1 another tooth on the other side at once engages the sliding face b c of the other pallet1 and so the motion goes on4 ,this beautiful escapement is at present used for astronomical clocks2 the pallets are made of agate or sapphire1 and therefore do not grind away the teeth of the wheel perceptibly1 and the loss by friction on the sliding surfaces is exceedingly small4 ,there are several other ways even better than this for securing a free pendulum movement4 ,we have now to return to our clock4 ,the centre arbor moves round once in an hour1 and carries the minute hand4 ,in order to provide an hour hand1 which shall turn round once in twelve hours1 we fasten a cogwheel and tube ,n on to the minute hand arbor by means of a small spring1 which keeps it rather tight1 but allows it to slip if turned round hard 7see ,fig4 #de74 ,this spring is a little bent plate slipped in behind the cogwheel on which its ends rest2 its centre presses on a shoulder on the minute hand arbor2 it is a sort of small carriage spring4 ,the cogwheel n has thirty teeth4 ,this cogwheel engages another cogwheel o with thirty teeth1 on a separate arbor1 which carries a third cogwheel1 p1 with six teeth1 and this again engages a fourth cogwheel1 q1 with seventy-two teeth1 mounted on a tube which slips over the tube to which the cogwheel a is attached4 ,it is now easy to see that for each turn of the minute hand arbor the arbor p makes one turn1 and for each turn of the arbor p the cogwheel d1 makes one-twelfth of a turn4 ,from which it follows that for each turn of the minute hand arbor the cogwheel d with its tube1 or1 as it is sometimes called1 its 8slieve10 makes one-twelfth of a turn1 and thus makes a hand fastened to it show one hour for every complete turn of the minute hand4 ,the minute hand is attached to the tube or slieve which carries the cogwheel ,n4 ,the hour hand is attached to the tube or slieve which carries the cogwheel ,q1 and one goes twelve times as slowly as the other4 ,but if you want to set the clock it is easy to do so by reason of the fact that the minute hand is not fixed to the arbor1 but only to the slieve on the cogwheel that fits on the arbor1 and is held somewhat tight to the arbor by means of the spring4 ,the hands can thus be turned1 but they are a little stiff4 ,a washer on the minute hand arbor keeps the slieve on the cogwheel pressed tight against the spring1 being secured in its turn by a very small lynch-pin driven through a hole in the minute hand arbor4 ,it remains to explain a few subsidiary arrangements1 not always found upon all clocks1 but which are useful4 ,in order to prevent the overwinding of the clock 7see ,fig4 #dc71 which would cause the cord to overrun the drum1 an arm is provided1 fitted with a spring4 ,as the weight is wound up the free part of the cord travels along the drum or the fusee2 and the cord1 when it is near the end of the winding1 comes up against the arm and pushes it a little aside4 ,this causes the end of the arm to be pushed against a stop on the axis of the fusee1 and thus prevents the clock being further wound up4 ,the stop1 being ratchet-shaped1 does not prevent the weight from pulling the ratchet wheel round the other way1 and thus driving the clock2 it only prevents the rotation of that wheel when the string is near it1 and the winding is finished4 ,another arrangement is the 8maintaining spring40 ,it will be remembered that during the process of winding the clock the hand twisting the key takes the pressure of the ratchet wheel off the pall1 so that during that operation no force is at work to drive the clock4 ,in consequence the pendulum receives no impulse1 but swings simply by virtue of its former motion4 ,if the process of winding were done slowly enough the clock might even stop4 ,to avoid this1 a very ingenious arrangement is made to keep the cogwheel mounted on the winding shaft going during the winding-up process4 ,this is called a maintaining spring4 ,the arrangement shown in ,fig4 #ec will explain it4 ,illustration3 ,,fig4 #ec4 ,the cogwheel a and the ratchet wheel are both mounted loosely on the arbor carrying the drum4 a is linked to b by a spring c4 ,the ratchet wheel b is engaged by a pall fixed to some convenient place on the body of the clock frame4 ,when the weight pulls on the drum the pull is communicated to the ratchet wheel b1 and this acts on the spring c and pulls it out a little4 ,as soon as the spring c is pulled out as far as its elasticity permits1 a pull is communicated to the cogwheel a1 and the clock is driven round4 ,when the clock is wound the pressure of the weight is removed1 and therefore the ratchet wheel e no longer presses on the pall1 and thus no pressure is communicated to the ratchet wheel b1 or through it to the clock4 ,but here the spring c comes into play4 ,for since the ratchet wheel b is held fast by the pall d1 the spring c pulls at the wheel a1 and thus for a minute or so will continue to drive the clock4 ,this driving force1 it is true1 is less than that caused by the weight1 but it is just enough to keep the pendulum going for a short time1 so that the going of the clock is not interfered with4 ,if the reader can get possession of a clock1 preferably one that does not strike1 and1 with the aid of a small pair of pincers and one or two screwdrivers1 will take it to pieces and put it together again1 the mechanism above described will soon become familiar to him4 ,not every clock is provided with maintaining spring and overwinding preventer4 ,the cause of stoppage of a clock generally is dirt4 ,where possible1 clocks should always be put under glass cases4 8,grandfather0 clocks will go much better if brown paper covers are fitted over the works under the cases4 ,in this way a quantity of dust may be avoided4 ,to get a good oil is very important4 ,it will be noticed that pivot-holes in clocks are usually provided with little cup-like depressions4 ,this is to aid in keeping in the oil4 ,the best clock oil is that which does not easily solidify or evaporate4 ,ordinary machine oil1 such as used for sewing machines1 is good as a lubricant1 but rapidly evaporates4 ,olive oil corrodes the brass4 ,it is best to procure a little clock oil1 or else the oil used for gun locks1 sold by the gunsmiths4 ,the holes should be cleaned out with the end of a wooden lucifer match1 cut to a tapering point4 ,the pivots should be well rubbed with a rag dipped in spirits of wine4 ,if the pivots are worn they should be repolished in the lathe4 ,if the cogs of the wheels are worn1 there is no remedy but to get new ones4 ,old clocks sometimes want a little addition to the driving weight to make them go4 ,the weight necessary to drive the clock depends on its goodness of construction1 and on the weight of the pendulum4 ,if the clock is driven for eight days with a cord of nine feet in length with a double fall1 then during each beat of the pendulum that weight will descend by an amount #i_/7b #bd #fj #fj #h7 feet or #a_/abhjjth inch4 ,whence1 if the clock weight is #aj lbs41 the impulse received by the clock at each beat is equivalent to a weight of #aj lbs4 falling through #a_/abhjjth of an inch1 or to the fall of six grains through an inch4 ,the power thus expended goes in friction of the wheels and hands1 and in maintaining the pendulum in spite of the friction of the air4 ,the work therefore that is put into the clock by the operation of winding is gradually expended during the week in movement against friction4 ,the work is indestructible4 ,the friction of the parts of the clock develops heat1 which is dissipated over the room and gradually absorbed in nature4 ,but this heat is only another form of work4 ,amounts of work are estimated in pressures acting through distances4 ,thus1 if ,i draw up a weight of #a lb4 against the accelerative force of gravity through a distance of one foot1 ,i am said to do a foot-pound of work4 ,one pound of coal consumed in a perfect engine would do eight millions foot-pounds of work4 ,hence1 if the energy in a pound of coal could be utilized1 it would keep about #ajj1jjj grandfather's clocks going for a week4 ,as it is consumed in an ordinary steam engine it will do about half a million foot-pounds of work4 ,one pound of bread contains about three million foot-pounds of energy4 ,a man can eat about three pounds of bread in a day1 and1 as he is a very good engine1 he can turn this into about three-quarters of a million foot-pounds of work4 ,the rest of the work contained in the bread goes off in the form of heat4 ,illustration3 ,,fig4 #ed4 ,as has been previously said1 the power of the action of gravity in drawing back a pendulum that has been pushed aside from its position of rest becomes less in proportion as the pendulum is longer1 and hence as the pendulum is longer the time of vibrations increases4 ,in the appendix to this chapter a short proof will be given showing that the length of a pendulum varies as the square of the time of its vibration4 ,a pendulum which is #ciad inches in length vibrates at ,london once in each second4 ,of course at other parts of the earth1 where the force of gravity is slightly different1 the time of vibration will be different1 but1 since the earth is nearly a globe in shape1 the force of gravity at different parts of it does not vary much1 and therefore the time of vibration of the same pendulum in different parts of the earth does not vary very much4 ,the length of a pendulum is measured from its point of suspension down to a point in the bob or weight4 ,at first sight one would be inclined to think that the centre of gravity of the pendulum would be the point to which you must measure in order to get its length4 ,so that if ,b were a circular bob1 and the rod of the pendulum were very light1 the distance ,a ,b to the centre of the bob would be the length of the pendulum4 ,but if we were to fly to this conclusion1 we should be making the same error that ,galileo made when he allowed a ball to roll down an inclined plane4 ,he forgot that the motion was not a simple one of a body down a plane1 but was also a rolling motion4 ,the pendulum does not vibrate so as always to keep the bob immovable with the top side ,c always uppermost4 ,on the contrary1 at each beat the bob rotates on its centre and makes1 as it were1 some swings of its own4 ,therefore in the total motions of the pendulum this rotation of the bob has to be taken into account4 ,of course1 if the pendulum were so arranged that the bob did not rotate1 and the point ,c were always uppermost1 as1 for instance1 if the pendulum consisted of two parallel rods1 ,a ,b and ,c ,d1 suspended from ,a and ,c1 then we might consider the bob as that of a pendulum suspended from ,e1 and the pendulum would swing once in a second if ,a ,b ,c ,d ,e ,f were equal to #ciad inches1 for by this arrangement there would be no rotation of the bob4 ,but as pendulums are generally made with the bob rigidly fixed to the rod ,e ,f1 the rotation must be taken into account4 ,illustration3 ,,fig4 #ee4 ,it wants some rather advanced mathematical knowledge to do this4 ,but in practice clockmakers take no account of it4 ,the correction is not a large one1 so they make the rod as nearly true as they can1 arrange a screw on the bob to allow of adjustment1 and then screw the bob up and down until in practice the time of oscillation is found to be correct4 ,illustration3 ,,fig4 #ef4 ,the mode of suspension of a pendulum of the best class is that shown in ,fig4 #ef1 which allows the pendulum to fall into its true position without strain4 ,a is a tempered steel spring1 which bends to and fro at each oscillation4 ,it is wonderful how long these springs can be bent to and fro without breaking4 ,inasmuch as lengthening the pendulum increases the time1 so that the time of vibration t varies as the square of the length of the pendulum1 a very small lengthening of the pendulum causes a difference in the time4 ,in practice1 for each thousandth of an inch that we lengthen the pendulum we make a difference of about one second a day in the going of the clock4 ,if we cut a screw with eighteen threads to the inch on the bottom of the pendulum rod1 and put a circular nut on it1 with the rim divided into sixty parts1 then each turn through one division will raise or lower the bob by #a_/ajhjth of an inch1 and this first causes an alteration of time of the clock by one second in the day4 ,this is a convenient arrangement in practice1 for it affords an easy means of adjusting the pendulum4 ,we need only observe how many seconds the clock loses or gains in the day1 and then turn the nut through a corresponding number of divisions in order to rectify the pendulum4 ,illustration3 ,,fig4 #eg4 ,another needful correction of the pendulum is that due to changes in temperature4 ,if the rod of the pendulum be made of thoroughly dried mahogany1 soaked in a weak solution of shellac in spirits of wine1 and then dried1 there will not be much variation either from heat or moisture4 ,but for clocks required to have great precision the pendulum rod is usually made of metal4 ,a rod of iron expands about #a_/afjjjjth of its length for each degree ,fahrenheit2 and therefore for each degree ,fahrenheit a pendulum rod of #ciad inches will expand about #a_/djjj thousandths of an inch1 and thus make a difference in the going of the clock of about one-fourth of a second per day4 ,the expansion will1 of course1 make the clock go slower4 ,it would be possible to correct this expansion if some arrangement could be made1 whenever it occurred1 to lift up the bob of the pendulum by an amount corresponding to it1 as1 for instance1 to make the bob of some material which expanded very much more by heat than the material of which the pendulum rod was made4 ,illustration3 ,,fig4 #eh4 ,thus if we hang on to the end of a pendulum of iron a bottle of iron about seven inches long1 and almost fill it with mercury1 then1 as soon as the heat increases1 the iron of the rod and of the bottle expands1 and the centre of oscillation of the pendulum is lowered4 ,but as the linear expansion of mercury contained in a bottle is about five times that of iron1 the mercury rises in the bottle1 and thus the expansion downwards of the pendulum rod is compensated by the expansion upwards of the mercury in the bottle4 ,the rod may be fastened to the mouth of the bottle by a screw1 so that as the bottle is turned round it may be raised or lowered on the rod1 and thus the length of the pendulum may be adjusted4 ,the bottle is made of steel tube1 screwed into a thin turned iron top and bottom4 ,of course no solder must be used to unite the iron1 for mercury dissolves solder4 ,a little oil and white-lead will make the screwed joints tight4 ,this is an excellent form of pendulum4 ,another plan is to use zinc as the metal which is to counteract the expansion of the iron4 ,the expansion of zinc is about three times that of iron4 ,illustration3 ,,fig4 #ei4 ,hence a zinc tube1 about twenty inches long 7shown shaded in ,fig4 #ei71 is made to rest upon a disc fastened to the lower part of the iron pendulum rod4 ,on the top of the zinc rests a flat ring ,a1 from which is suspended an iron tube ,a1 which carries the bob ,b4 ,the expansion of the zinc tube is large enough to compensate the expansion both of the rod and the tube1 and the bob consequently remains at the same depth below the point of suspension1 whatever be the temperature4 ,there is1 however1 a new method which is far superior to all these1 and this is due to the discovery by ,m4 ,guilliaume1 of ,paris1 of a compound of nickel and steel which expands so little that it can be compensated by a bob of lead instead of by a bob of mercury4 ,this material is sold in ,england under the name of 8invar40 ,an invar rod with a properly proportioned lead bob makes an almost perfect pendulum1 the expansion of the invar and the lead going on together4 ,the exact expansion of the invar is given by the makers1 who also supply information as to the size and suspension of the bob proper to use with it4 ,it has been already shown that the uniformity of time of swing of a pendulum is only true when the arc through which it swings is very small4 ,if the total swing from one side to another is not more than about two inches very little difference in time-keeping is made by putting a little more driving weight on the clock1 and thus increasing its arc of swing2 but when the arc of swing becomes say three inches1 or one and a half inches on each side of the pendulum1 then the time of vibration is affected4 ,at this distance each tenth of an inch increase of swing makes the pendulum go slower by about a second a day4 ,the resistance of the air1 of course1 has a great influence on a pendulum1 and is one of the chief causes that bring it ultimately to rest4 ,even the variations of pressure of the atmosphere which the barometer shows as the weather varies have an effect on the going of a clock4 ,attempts have been made by fixing barometers on to pendulums with an ingenious system of counter balancing to counteract this1 but these refinements are not in common use1 and are too complicated to be susceptible of effective regulation4 ,,appendix ,,to ,,chapter ,,iv4 ,it may be useful to give a simple form of proof of the law which governs the time of oscillation of a pendulum whose length is given4 ,unfortunately1 it is impossible to give one so simple as to be comprehended by those who know nothing whatever of mathematics4 ,it is1 however1 possible to give a proof that requires very little mathematical knowledge4 ,we know that when a mass of matter is whirled round at the end of a string it tends to fly outwards and puts a strain on the string4 ,the faster the speed at which the mass is whirled1 the stronger will be the strain on the string4 ,suppose that the length of the string equals ,r1 the velocity of the mass as it flies round equals ,v4 ,let a be the body whirled round by a string o a from a centre at ,o4 ,the body always1 of course1 tends to fly on in a straight line from the point at which it is at any instant4 ,but that tendency is frustrated by the pull of the string which constrains it to take a circular path4 ,it is1 of course1 all one whether the force that tends to pull the body inwards towards ,o is a string or an attractive force of any kind acting through a distance without any string at all4 ,evidently if the body keeps its place in the circle it must be because the centrifugal force tending to whirl it out is equal to the centripetal or attractive force tending to pull it in4 ,illustration3 ,,fig4 #fj4 ,the strain on the body1 due to the force tending to pull it inwards1 we shall designate by ,f1 meaning by ,f the number of feet of velocity that would in one second be imparted to the body by the attractive force4 ,suppose that at some given instant of time the body is at a point a4 ,at that instant its direction will be along a b1 tangential to the circle at a1 and that is the path it would take if the centripetal or attractive force ceased to act just as the body got to a4 ,in that case the body would be whirled off like a stone from a sling along the line a b1 and would at the end of a given time1 let us suppose a second1 arrive at b4 ,but it is not so whirled off2 it is attracted towards ,o and pulled inwards1 and comes to c4 ,hence1 then1 the attractive force acting during one second must have been sufficient to pull the mass in from b to c4 ,but we know that if an accelerating force 7,f7 acts on a body for a second it produces a final velocity equal to ,f at the end of the second1 and an average velocity half ,f during the second4 ,hence1 then1 the space b c1 by which the body has been pulled in1 is represented by half ,f1 but a b1 the space which the body would have travelled forwards1 will be represented by ,v1 the velocity of the body in a second2 but if the motion be such that the distance b c travelled in a second is very small1 then the triangles a b d and a b c are approximately similar1 and the smaller a b is the more nearly similar they are4 ,whence then 7a b7_/7b c7 7a d7_/7a b71 that is to say 7a b7 a d b c4 ,but a b represents the space which would have been traversed by the body in one second at the rate it was going1 and hence is equal to ,v2 a d is the diameter of the circle1 and hence equals #b ,r2 b c is the space through which the body has been drawn in the second by the attractive force ,f1 and therefore equals half ,f4 ,whence then ,v #b ,r half ,f ,r ,f4 ,we took a second as the limit of time during which the motion was to be considered4 ,of course any other time could have been taken4 ,now what is true of the motion of a body during a very short time is also true of the body during the whole of its path1 assuming that the path is a circle1 and that ,f remains constant1 as it obviously will if the path is a circle1 and the velocity is uniform4 ,whence then we may generally say that if a body is being whirled round at the end of a string the strain ,f on the string is directly proportional to the square of the velocity1 and is inversely proportional to the length of the string4 ,the time of rotation1 is of course length of the path velocity 7#b,r7_/,v 7#b,r7_/7,r ,f7 #b7,r_/,f74 ,whence then we see that for motion in a circle of a mass under the attraction of a centripetal force1 or pull of a string1 the time of rotation will be uniform1 provided that the centripetal force always varies as the radius of the path4 ,from this it is evident that a body fixed on to an elastic thread where the pull varies as the extension would make its rotations always in equal times4 ,if your sling consists of elastic1 whirl as you will1 you can only whirl the body round so many times in a second1 and no more4 ,any increase in your efforts only makes the string stretch1 and the circle get bigger4 ,the velocity of the body in its path of course increases1 but the time it takes to go once round is invariable4 ,it also follows that if a body hung by a string of length l1 under the action of gravity1 be travelling in a circle round and round1 then1 if the circle is a small one compared with the length of the string1 the inward acceleration f towards the centre will be approximately proportional to the radius r of the circle1 and the time of rotation will be t #b7r_/f74 ,but in this case f1 the inward acceleration1 is to g the acceleration downwards of gravity as ,a ,b3,a ,p or f_/g 7,a ,b7_/7,a ,p7 7,a ,p7_/7,o ,p7 r_/l4 ,illustration3 ,,fig4 #fa4 ,illustration3 ,,fig4 #fb4 ,whence then the time of rotation of this body would be if the circle of rotation was small #b7l_/g74 ,and if you try you will find that this is so4 ,for instance1 take a thread #ci-a_/g inches long1 that is #cbe feet4 ,hang anything heavy from one end of it1 and cause it to swing round and round in a small circle4 ,now g the acceleration of gravity #cbb feet per second4 the ratio of the circumference of a circle to its diameter #cad4 ,from which it follows that the time of rotation #b #cad7cbe_/cbb7 seconds #b seconds4 ,but if we look at the rotating body sideways1 it appears to act as a pendulum2 it matters nothing whether we swing it round and round or to and fro4 ,for in any case the accelerative force tending to bring it back to a position of rest is always proportional to the distance of displacement1 and1 therefore1 its time of motion must always be #b7l_/g7 and its motion harmonic4 ,the length of a seconds pendulum1 that is a pendulum that makes its double swing in two seconds1 will therefore be l #d_/77b77 g feet 7g #ab7_/ inches #ciad inches4 ,,chapter ,v4 ,i have thus described the principal features of ordinary clocks4 ,for the details many treatises must be studied1 and knowledge acquired which is not in any books at all4 ,i now1 however1 pass to watches4 ,it will be remembered that a verge escapement consists of a crown wheel with teeth1 engaging two pallets fixed upon a verge1 furnished with balls at its extremities4 ,as the crown wheel was urged forwards each pallet in succession was pushed till it slipped over the tooth which was engaging it4 ,then a tooth on the other side came into sharp collision with the other pallet1 and drove the verge the other way1 and so on4 ,now here we have a driving force1 and a sort of pendulum4 ,but how did the verge act as a pendulum to measure time8 ,it is not a body rocking under the action of gravity1 nor under the acceleration of a spring4 ,how then can it act as a regulator of time1 and what is the period of its swing8 ,the answer to this is1 that it is under the acceleration of gravity1 but that gravity does not act freely on the bobs or weights1 but only through the driving weight and teeth4 ,the impulse that drives the verge is really also the accelerating force upon it1 and the only accelerating force upon it4 ,and the worst feature about the movement is1 that as the teeth and pallets move1 the leverage of the teeth on the pallets alters1 and thus the bobs on the verge are under the influence not of a uniform or duly regulated force1 but of a constantly varying one1 and one that varies in a very complicated and erratic way4 ,it would be hopeless to expect much time-keeping from such a contrivance4 ,the most that could be expected would be by putting on a very big weight to reduce to comparative insignificance the friction1 and then hope that the swings would be uniform1 so that whatever went on in one swing would go on in the next1 and thus the time-keeping be regular4 ,but any course tending to diminish the driving force1 such as the thickening of the oil1 would greatly affect the going4 ,it was for this reason that ,huygens turned the verge into a pendulum by removing one of the bobs1 and letting gravity thus act on the other4 ,for watches1 however1 a different plan was contrived4 ,one end of a slender spiral spring was affixed to the verge4 ,the other end of the spring was made fast to the clock frame4 ,the verge was now1 therefore1 chiefly under the action of the acceleration of the spring4 ,to make the acceleration of the teeth of the 'scape wheel less embarrassing1 the teeth were so shaped as only to give a short push at stated intervals1 and not interfere with the free swing of the verge under the alternate to-and-fro accelerations and retardations of the spring4 ,by this means the verge became in every way an excellent pendulum1 not dependent on gravity1 and permitting the watch to be held in any position4 ,the verge thus fitted was turned into a wheel1 and became a 8balance wheel40 ,it was compensated for heat expansion by a cunning use of the unequal expansion of brass and steel1 in a manner analogous to the way this unequal expansion of metals had been employed to compensate the pendulum1 and became the beautiful and accurate time-measurer that we see to-day1 with its pivots mounted in jewels to diminish friction1 and with screws round the rims of the balance wheel to enable the centre of gravity to be exactly adjusted to its centre of rotation1 and with a delicate hair-spring of tempered steel that is a marvel of microscopic work4 ,but the escapement of the early watches left much to be desired4 ,in order to make it clear how imperfect that early escapement was1 we have to turn back and remember what has been said about the dead beat escapement4 ,it will then be remembered that it was shown that for small arcs the pendulum would keep good time provided you let it have as much swing as it wanted to use up the force which the escapement had applied to it1 but not otherwise1 so the pendulums only acted really well when the impulse was given about the middle of the swing1 and they were free to go on and stop when they pleased1 and turn back at the end of it4 ,this essential condition was fairly approximated to in the dead beat escapement of clocks which left them at the end of their swing with only a very slight friction to impede their free motion4 ,but when you come to deal with a watch the case is quite different4 ,here the escapement is of a great size compared with the balance wheel1 and the friction even of the most dead beat watch escapement that could be contrived was so big compared with the forces acting on the balance wheel as seriously to derange its motion1 and render it far from a perfect time-keeper4 ,now about this time--,i am speaking of the early part of the eighteenth century--a demand of a very exceptional character arose for a really perfect watch4 ,the demand did not arise from gentlemen who wanted to keep appointments to play at ombre at their clubs1 or even from merchants to time their counting house hours4 ,for these the old-fashioned watch did very well4 ,the demand came from mariners4 ,but the seamen did not want to know the time merely to arrange the hours for meals on the ship or to determine when the watch was to be relieved1 but for a far more important purpose1 namely1 to find out by observation of the heavens their place upon the ocean when far out of sight of the land4 ,it will be very interesting to see how this problem arose1 and how the patient industry and ingenuity of man has solved it4 ,the ancient navigators never went very far from the shore1 for1 once out of sight of land1 a ship was out of all means of knowing where she was4 ,on clear days and nights the compass1 and the sun and stars would tell the mariner the direction he was sailing in1 but it was quite a problem to determine where he was on the surface of the earth4 ,illustration3 ,,fig4 #fc4 ,let us consider the problem4 ,suppose for convenience that the earth is divided up into 8squares10 as nearly1 at least1 as you can consider a globe to be so marked out4 ,let us suppose that it has been agreed to draw on it from pole to pole #cfj lines of longitude1 commencing with one through say ,greenwich ,observatory as a starting-point1 and going right round the earth till you come back to ,greenwich again4 ,also suppose that there have been drawn a series of circles parallel to the equator1 but going up at equal distances apart towards the poles4 ,let us have #agi of these circles1 so as to leave #ahj spaces1 a to b1 b to c1 etc41 from pole to pole4 ,this will divide the earth up like a bird-cage into squares1 as if we had robed it in a well-fitting ,scotch plaid4 ,the length measured along the equator of the side p q of each square at the equator is taken as exactly sixty nautical miles 7apart from a small error of measurement1 which makes it in actual practice #eiif74 ,this is equal to sixty-nine and a quarter ,english statute miles4 ,the side of the square leading towards the poles q s would also be sixty nautical miles were it not that the earth is not truly spherical1 which introduces a slight error4 ,we may1 however1 roughly say that at the equator each square measures sixty nautical miles each way4 ,illustration3 ,,fig4 #fd4 ,as we get towards the poles the squares become rectangular figures1 with the heights of latitude still sixty nautical miles1 but the widths becoming smaller4 ,thus in ,england our squares measure p q #cg nautical miles and q s #fj nautical miles4 ,now of course we can see at once that it is easy at any place on the earth's surface to find your latitude by a simple observation of the sun at noon1 if you know the day of the year1 and have got a nautical almanac4 ,for by an instrument called a sextant you can measure the angle he appears to be above the horizon1 and then1 as you know from a nautical almanac the angle he is above the equator1 you can soon determine your place ,a on the globe4 ,or at night1 if you measure the angular distance that the polar star ,p is from the zenith1 or point exactly over your head--that is1 the angle ,p ,o ,z--you can subtract it from a right angle and get your latitude1 ,a ,o ,e1 at once4 ,illustration3 ,,fig4 #fe4 ,but how are you to determine your longitude8 ,the pole-star1 or sun1 or any other star won't help you1 for as the earth is moving they keep shifting1 and at one time or another appear exactly in the same position to everyone on the same parallel of latitude1 as it is easy to see4 ,the fact is that you are on a ball turning round4 ,you know easily what latitude you are on1 but you cannot tell your longitude unless you can tell how many hours and minutes you get to a position before ,greenwich gets to the same position4 ,if when a particular star got to ,greenwich a gong were sounded which could be heard all over the earth1 then of course1 by seeing what stars were overhead1 everyone would know their longitude at once4 ,perhaps by means of the new electric waves this will before long be done1 and the ,greenwich hours will be sounded all over the world for the use of mariners4 ,but till this is accomplished all that can be done is to keep an accurate clock on board1 so as always to give you ,greenwich time4 ,early attempts were made to take a pendulum clock to sea1 suspending it so as to avoid disturbance to its motion by the rocking of the ship4 ,these proved vain4 ,it therefore became desirable that a watch with a balance wheel should be contrived to go with a degree of accuracy in some respects comparable with the accuracy of a pendulum clock4 ,to encourage inventors an ,act of ,parliament was passed in the thirteenth year of ,queen ,anne's reign 7chapter xv47 7#agac7 promising a reward of #bj1jjj to anyone who would invent a method of finding the longitude at sea true to half a degree--that is1 true to thirty geographical miles4 ,if the finding of the longitude were to be accomplished by the invention of an accurate watch1 then this involved the use of a watch that should not1 in several months' going1 have an error of more than two minutes1 which is the time which the earth takes to turn through half a degree of longitude4 ,this was the problem which ,john ,harrison1 a carpenter1 of ,yorkshire1 made it his life business to solve4 ,his efforts lasted over forty years1 but at the end he succeeded in winning the prize4 ,these instruments have been much improved by subsequent inventors1 and have resulted in the construction of the modern ship's chronometer1 a large watch about six inches in diameter1 mounted on axles1 in a mahogany box4 ,several of these are taken to sea by every ship4 ,the peculiarity of the chronometer is its escapement4 ,let ,a ,b be the scape wheel1 and ,c ,d a small lever attached to ,c1 the pivot on which the balance wheel and spring is fastened4 ,let ,e ,g be a lever1 with a tooth ,f which engages the teeth of the scape wheel and prevents it moving round4 ,let ,h be a spring holding the lever ,e ,g up to its work4 ,illustration3 ,,fig4 #ff4 ,the lever has a spring ,k ,e fastened to it at the point ,k4 ,this spring is very delicate4 ,if the lever ,c ,d is turned so that the little projection ,m on it strikes the spring ,e from left to right1 then1 as the spring rests on the lever1 the whole lever is pushed over1 and the teeth of the scape wheel set free4 ,at that instant1 however1 the escapement is so arranged that the arm ,c ,d is just opposite the tooth ,d of the scape wheel1 so that the scape wheel1 instead of running away1 leaps with its tooth ,d on to the lever ,c ,d and swings the balance wheel round4 ,the balance wheel is free to twist as much as it pleases1 but the moment it has twisted so much that the projection ,m passes the spring ,e1 then the lever ,g ,e flies back to its place1 and the scape wheel is again checked4 ,meanwhile the balance wheel flies round till at last it is brought to rest by the balance spring4 ,it then recoils and sets out on its return path4 ,this time1 however1 the projection ,m merely flips aside the spring ,e and the balance wheel goes back1 till again it is brought to rest and returns4 ,as soon as the lever comes opposite ,d the projection ,m then again hits the spring ,e1 and releases the catch at ,f1 and another tooth of the scape wheel goes by4 ,there then you have a completely free escapement1 and consequently an accurate one4 ,many watches are made with these escapements1 but they are more expensive than those in common use4 ,there is but little remaining in a watch that is not in a clock1 for the wheel-trains and general arrangements are very similar4 ,it is possible to apply the chronometer's detached escapement to a clock4 ,this was done by several clock-makers in the eighteenth and early part of the nineteenth century4 ,one method of doing it is as follows3 ,a is a block of metal fitted to the bottom of the pendulum1 ,b a light lever pivoted on it4 ,c is the scape wheel1 with four teeth2 ,d a tooth of the scape wheel1 which hops on to the projection of the pendulum the moment that the impact of the point ,e of the lever ,b ,e has pushed aside the lever ,g ,f1 and thus released the scape wheel4 ,the advantage is that it is a very easy escapement to make4 ,but it is in reality a detached 7that is to say1 a completely free7 chronometer escapement1 as can easily be seen4 ,illustration3 ,,fig4 #fg4 ,turret-clocks are open to considerable disadvantages1 for the wind blowing on the hands gives rise to considerable pressure1 so that the clocks are sometimes urging the hands against the wind1 sometimes are being helped by the wind4 ,and this inequality of driving force makes the pendulum at some times make a bigger arc of swing than at others4 ,but we saw above that though difference of arc of swing ought to make no difference in the time of swing of the pendulum1 yet this was only strictly true if the arc of swing were a cycloid4 ,but as for practical convenience we are obliged to make it a circle1 it follows1 as we saw1 that for every tenth of an inch of increase of swing of an ordinary seconds pendulum about a second a day of error is introduced4 ,to remove this difficulty a gravity escapement was invented by ,mudge in the eighteenth century1 improved by ,bloxam1 a barrister1 and perfected by the late ,lord ,grimthorpe4 ,the idea was to make the scape wheel1 instead of directly driving the pendulum1 lift a weight1 which1 being subsequently released1 drove the pendulum4 ,the consequence was1 that inequalities in wind pressure1 which affected the driving force of the scape wheel1 would not act on the pendulum1 which would be always driven by the uniform fall of a fixed and definite weight4 ,a movement of this kind has been fixed in the great clock at ,westminster1 and has gone admirably4 ,a description of its details will be found in the ,encyclopdia ,britannica1 written by ,lord ,grimthorpe himself4 ,all sorts of eccentric clocks and watches have been proposed4 ,for instance1 it seems wonderful to see a pair of hands fitted to the centre of a transparent sheet of glass go round and keep time with apparently nothing to drive them4 ,but the mystery is simple4 ,the seeming sheet of glass is not one sheet1 but four4 ,the two centre sheets move round invisibly1 carrying the hour hand and minute hand with them1 being urged by little rollers below on which they rest4 ,when you touch the glass the outside sheets appear at rest1 and you do not suspect that it is other than a single sheet4 ,but beware of dust1 for if dust gets on the inner plate you detect the trick4 ,in this way a mechanical hand was made that wrote down answers to questions4 ,this plan can be applied to all sorts of tricks4 ,sir ,william ,congreve1 an ingenious inventor1 proposed to make a clock that measured time by letting a ball roll down an incline4 ,when it got to the bottom it hit a lever1 which released a spring and tipped the plane up again1 so that the ball now ran down the other way4 ,it is a poor time-keeper1 and the idea was not original1 for a ball had been previously designed for the same purpose4 ,sometimes clocks are constructed by attaching pendulums to bronze figures1 which have so small a movement that the eye is unable to detect it4 ,the figure appears to be at rest1 but is in reality slowly rocking to and fro4 ,it is necessary to make the movement as small as about one four hundredth of an inch in half a second1 if the movement is to escape human observation4 ,for a movement of one two hundredth of an inch per second is about the largest that will certainly remain unperceived4 ,in medival times clocks were constructed with all sorts of queer devices4 ,the people of the upper town at ,basle having quarrelled with those of the lower town1 fought and beat them4 ,to commemorate this victory they put on the old bridge at the upper town a clock provided with an iron head1 that slowly put out and drew in a long tongue of derision4 ,this clock may still be seen in the museum4 ,it is as though the council of the city of ,london put a clock of derision at ,temple ,bar to put out its tongue at the ,county ,council4 ,i do not propose here to describe the striking mechanism of clocks4 ,there are several different ways of arranging it4 ,they are rather complicated to follow out1 but they all resolve themselves into a few simple principles4 ,as the hour hand revolves it carries a cam so arranged as to be deeper cut away for the twelfth hour1 less for the eleventh1 and so on4 ,when the minute hand comes to the hour it releases the striking mechanism1 which1 urged by a weight1 begins to revolve1 and1 driving an arm carrying a pin1 raises a hammer1 which goes on striking away as the arm revolves4 ,this would continue for ever if it were not that at the same moment an arm is liberated which falls against the cam4 ,at each stroke the arm is 7by the striking apparatus7 raised a bit back into position4 ,when it comes back into position it stops the striking4 ,it thus acts as a counter1 or reckoner of the blows given1 stopping the movement when the clock has struck sufficiently4 ,if the counting mechanism fails to act1 we have the phenomenon which occasionally occurs of a 8,grandfather0 clock striking the whole of the hours for the week without stopping4 ,a chiming clock is simpler still4 ,for here we have a barrel covered with pins1 like the barrel in a musical box4 ,as the pins go round they raise hammers which fall against bells4 ,the barrel is wound up and driven by a spring or weight4 ,when the clock comes to the hour1 the barrel is released1 and rotating1 plays the tune4 ,if you want to make a clock wake you up in the morning it can be done by making the striking arrangement hammer away with no counting mechanism to stop it until the weight has run down4 ,if1 not content with that1 you want the sheets pulled off the bed or the bed tilted up1 or a can of water emptied over the person who will not rise1 a mechanical device known as a relay must be used4 ,it is very simple4 ,what is wanted is that1 after the lapse of a time which a clock must measure1 a considerable force must be exerted to pull off the bedclothes4 ,it would be absurd to make the clock exercise this pull4 ,it is obviously better to attach the clothes by a hook to a rope which passes over a pulley1 and from which hangs a weight4 ,a pin secures the weight from falling1 the pin being withdrawn by the clock4 ,the work is thus done by the weight when released by the clock4 ,in like manner1 if you have a telegraph designed to print messages at a distance1 you do not send along the wires the whole force necessary for doing the printing4 ,you only send impulses1 which1 like triggers1 release the forces by which the letters are to be stamped4 ,electric clocks of many kinds have been invented4 ,the principle of an electric escapement is similar to that of an ordinary escapement4 ,illustration3 ,,fig4 #fh4 ,the reader no doubt knows that1 when a circuit of wire is joined or completed leading to a source of electricity1 electricity flows through the wire4 ,if the wire is wound round a piece of iron1 then1 whenever the circuit is joined1 a current is set in motion1 and the iron becomes an electro-magnet4 ,when the circuit is severed the iron ceases to be a magnet4 ,if put at a proper position it would at each time an iron pendulum approached give it a small impulse provided that at that instant the current is turned on4 ,this can easily be made to be done by the pendulum itself4 ,for just as the pendulum is coming back to the central position a flipper ,p attached to the rod can be caused to make contact with a piece of metal fixed on its path4 ,then the electro-magnet1 becoming magnetised1 exerts a pull on the iron pendulum4 ,on the return beat of the pendulum the other side of the flipper ,r strikes the obstruction4 ,but if that side ,r is covered with ebonite or some non-conducting material no current will be set in motion1 and the electro-magnet will not 7as it would otherwise do7 retard the pendulum4 ,such a pendulum has therefore an impulse given to it every second beat4 ,such pendulums do not act very well1 because it is difficult to keep metallic surfaces like ,q clean1 and therefore misses often occur4 ,besides1 the strength of the current varies with the goodness of the contact and with other things4 ,what is now preferred is to make an arrangement by which an electric current winds the clock up every minute or so4 ,by this means the impulse which drives the clock is not a varying electric one1 but is a steady weight4 ,the most successful clocks have been made on these principles4 ,the advantage of electricity is1 that by means of the current that actuates the clock1 or winds it up1 you can at regular intervals set the hands in motion of a great number of clocks4 ,so that only one going clock with a pendulum is needed4 ,the other clocks distributed over the building have only faces and hands1 and a very few simple wheels1 to which a slight push is given by an electro-magnet1 say1 every minute or so4 ,the system is therefore well adapted for offices and hotels4 ,in ,america1 by means of electric contacts1 clocks have been arranged to put gramophones into action4 ,you will remember that it was pointed out that if a wire were dragged over a file a sound would be produced due to the little taps made as the wire clicked against the rough cuts on the file1 and that the tone of the note depended on the fineness of the cuts1 and hence the rapidity of the little taps4 ,you can imagine that1 if the roughnesses were properly arranged1 we might get the tones to vary1 and thus imitate speech4 ,this is the principle of the gramophone4 ,the roughnesses are produced by a tool1 which1 vibrating under the influence of human speech1 makes small cuts in a soft material4 ,this is hardened1 and then1 when another wire is dragged over the cuts1 the voice is reproduced4 ,in this way clocks are made to speak and tell the children when dinner is ready and when to go to bed4 ,on this simple plan1 too1 dolls can be made to speak4 ,the modern methods of clock and watch-making are very different from those in use in olden days4 ,in former times the pivots were turned up by hand on small lathes1 and even the teeth of the wheels were filed out4 ,each hole in the clock or watch frame was drilled out separately1 and each wheel separately fitted in1 so that the watch was gradually built up as one would build a house4 ,each wheel1 of course1 only fitted its own watch1 and the parts of watches were not interchangeable4 ,this has now all been altered4 ,by means of elaborate machinery the whole of the work of cutting out every wheel and the making of every single part is done by tools moved independently of the will of the workman1 whose only duty is to sit still and see the things made4 ,he is1 as it were1 the slave of the machine1 watching it and answering to its calls4 ,or shall we rather say that he is the machine's employer and master8 ,he has here a servant who never tires nor ever disobeys him4 ,all the machine requires is that its cutting edges should be exactly true and sharp and microscopically perfect2 then it will cut away and make wheel after wheel4 ,it oils itself4 ,it only wants the man to act as superintendent1 and stop it if any cutting edge gets unduly worn4 ,for this purpose he measures the work it is doing from time to time with a microscope to see that it is good and true and exact4 ,when all the parts have thus been made you have perhaps a hundred boxes1 each with a thousand watch parts in it1 each part exactly like its fellows4 ,you take one wheel or bit from each box indiscriminately1 and you then have the materials for a watch1 screws1 fittings1 pins1 and all4 ,all you have now got to do is simply to screw them all together1 like putting together a puzzle4 ,everything fits2 there is no snipping or filing4 ,in such a watch if a bit gets broken you simply send for another bit of the same kind and fit it into its place4 ,motor cars1 bicycles1 and many other machines are1 or ought to be1 made in this manner1 so that if a driver at ,york breaks a part of the car he simply sends to ,london for another4 ,it comes and fits into its place at once4 ,but for this sort of plan you must do work true to much less than a thousandth of an inch1 and1 of course1 no one must want to indulge his individual fancy as to the shape or appearance of the watch4 ,the whole advantage consists in dead uniformity4 ,but the cheapness is surprising4 ,you can have a better watch now for #cjs4 than could have been got for #cj twenty years ago4 ,artistic people are in the habit of condemning this uniformity as though it were inartistic and degrading4 ,in truth1 it is not degrading to get a machine to do what you want at the expense of as little labour as possible4 ,you pay #cjs4 for the watch1 but you have #bh #ajs4 left to spend on pictures4 ,only one ought not to confuse industry with art4 ,watches made in this way have no pretence to be artistic products4 ,they are simply useful4 ,to rule them all over with machine lines or to put hideous machine ornament on them is purely and simply base and degrading4 ,let your ornament be hand work1 your utility machine work4 ,thus then ,i have endeavoured to give a very brief sketch of the modes of measuring time1 and incidentally to introduce my readers to those laws of motion which are the foundation of so large a part of modern science4 ,it only remains that ,i should shortly describe modern apparatus by means of which it is possible to measure with accuracy periods of time so short as to appear impossible4 ,but when you see how it is done the method seems easy enough4 ,it is still by means of a pendulum1 only a pendulum beating time not once1 but hundreds and even thousands of times in a second4 ,and such pendulums1 instead of being difficult to make1 are remarkably simple1 and present no difficulty whatever4 ,for we have only to use the tuning fork which has been previously described4 ,the tuning fork consists of a piece of steel bent into a ,u shape4 ,the arms are set vibrating so as alternately to approach and recede from one another4 ,the reason why there are two arms is that1 if they come together and recede1 they balance1 and hence the instrument as a whole does not shake on its base4 ,this balance of moving parts of a rapidly moving machine is very important4 ,some motor cars are arranged so that the engines are 8balanced10 and the moving parts come in and out simultaneously1 leaving the centre of gravity unchanged whatever be the position of the motion4 ,this makes the vibration of the car very small4 ,the tuning fork is therefore balanced4 ,being elastic1 it obeys ,hook's law1 8,as the force1 so the deflection40 ,and therefore1 as we have seen1 the vibrations of the fork are isochronous4 ,a fork with arms about six or seven inches long will make about fifty or sixty vibrations in a second4 ,how are we to record those vibrations1 and how keep the tuning fork vibrating8 ,illustration3 ,,fig4 #fi4 ,a train of wheels is almost an impossibility1 not perhaps so impossible as might be supposed1 but still very difficult4 ,so a different method is adopted4 ,a little wire projects from one tuning fork arm4 ,a piece of glazed paper is gently smoked by means of a wax taper1 and is stretched round a well-made brass drum4 ,the tuning fork is then put so that the little wire just touches the paper4 ,the tuning fork is then made to vibrate by a blow1 and while it is vibrating the drum is revolved4 ,thus a wavy line is formed on the drum by the wire on the tuning fork4 ,if the tuning fork made fifty complete vibrations to and fro in a second there would be one hundred such indentations1 fifty to the right and fifty to the left1 and by these the time can be measured as you would measure a length upon a rule4 ,illustration3 ,,fig4 #gj4 ,if an arm a b be fitted to move sideways when a little string c d is pulled1 and be also provided with a small wire1 so as to touch the drum1 then it also will trace a straight line on the drum as the wire lightly scratches away the thin coating of smoke4 ,now1 if it is suddenly jerked and flips back1 then a little indentation will be made in the line1 and if when we are to measure a rapid lapse of time a jerk is given at the beginning1 and another jerk at the end of it1 we should get a diagram like that in the adjoining figure1 where a is the trace of the tuning fork1 b that of the indicating arm4 ,the time which has elapsed between the jerk which produced the indentation c and that which produced the indentation d will be about three and three-quarter double indentations of the tuning fork line1 thus indicating three and three-quarter fiftieths of a second4 ,it is easy to see how delicate this means of measurement can be made4 ,with small tuning forks we can easily measure times to a thousandth part of a second1 and much less if desired4 ,the jerk may be given by electricity if it is wished4 ,when the current is joined a little electro-magnet pulls a bit of iron and gives a pull to the string4 ,so extremely rapid is the flight of electricity that no appreciable time is lost in its transit through the wires1 so that the impulse may be given from a distance4 ,thus we may arrange that when a cannon ball leaves a gun an electric impulse shall be given4 ,when it reaches and hits a target another electric impulse is given4 ,these make nicks in the tracing line on the drum from which we can easily compute the time that has elapsed between the leaving of the mouth of the gun and the arrival of the shot at its destination4 ,illustration3 ,,fig4 #ga4 ,such an apparatus is used in modern gunnery experiments4 ,it is an elaborate one1 but is based on the principle above described4 ,drums are sometimes driven by clockwork1 and tuning forks are also often kept vibrating by electricity1 thus constituting very rapidly moving electric clocks4 ,the arrangement is simple4 ,an electro-magnet ,e is put in the vicinity of the arm of the tuning fork4 ,a small piece of wire from the arm is in contact with a piece of metal ,q1 from which a wire runs to the electro-magnet1 thence to a battery1 and from the battery to the tuning fork1 through which the current runs to the wire ,r4 ,when the fork vibrates the arm1 being bent outwards1 makes the wire ,r touch ,q4 ,this at once causes the electro-magnet to give a small pull to the steel arm of the tuning fork1 and thus assists the swing of the arm4 ,the whole arrangement is exactly analogous to an electric clock1 as may be seen by comparing ,fig4 #ga with ,fig4 #fh4 ,there is another method of measuring rapid intervals of time which also merits attention4 ,it is to let a body drop at the commencement of the period of time to be measured1 and mark how far it falls in the time1 and then find the time from the equation given previously1 ,s #a_/b g t4 ,it is practically done by letting a piece of smoked glass fall and making a small pointer make two dots upon it1 one at the beginning1 another at the end1 of the time to be measured4 ,an interesting adaptation of this method can serve as a basis of a curious toy4 ,take a crossbow1 with a bolt with a spike on it2 fix it firmly in a vice so that the barrel points at a spot a on a wooden wall4 ,on the spot a hang a cardboard figure of a cat on to a nail so contrived that when an electro-magnet acts the nail is pulled aside1 and the cat drops4 ,thus let a be the cat1 b the loop by which it is hung over the nail c1 that is fixed to another piece of iron furnished with a hinge at c1 so that when the electric current is turned on the nail c is withdrawn and the cat drops4 ,carry the wires from the electro-magnet and battery to the crossbow1 and so arrange them that when the bolt leaves the muzzle one is pressed against the other1 and contact made4 ,now here you have an apparatus such that exactly as the bolt leaves the crossbow1 the cat drops4 ,now what will happen8 ,illustration3 ,,fig4 #gb4 ,when the bolt leaves the bow it is subject to two motions1 one a motion of projection at a uniform pace in the direction of b a from the bow to the target4 ,but it is also subject to another force1 namely that of gravity1 which acts on it vertically1 and deflects it in a vertical direction exactly as much and as fast as a body would do if dropped from rest at the same instant as the bolt leaves the bow4 ,but the cat is such a body4 ,hence1 then1 since by the electric arrangement they are both let go together1 they will both drop simultaneously1 and thus will always be on the same level1 and when the bolt reaches the wooden wall and has fallen vertically from a to c1 the cat will also have fallen vertically from a to c1 and the bolt will pin him to the wall4 ,it does not matter how far you take the bow from the wall1 nor how strong the bow is1 nor how heavy the bolt is1 nor how heavy the cat is1 nor whether a b is horizontal or pointing upwards or downwards4 ,illustration3 ,,fig4 #gc4 ,in every case1 if only the barrel is pointed directly at the cat1 then the bolt and cat fall simultaneously and at the same rate1 and the bolt will pin the cat to the wall4 ,in trying the experiment the bolt should be pretty heavy1 say half a pound1 and have a good spike2 but if carefully done the experiment will succeed every time4 ,it enables you also to measure the speed of flight of the bolt4 ,for if the distance of the bow from the wall be thirty feet1 and the cat have fallen three feet when it is struck1 then the time of fall is ,t 77#b,s7_/g7 7#f_/;g7 #dc seconds4 ,but the bolt in this time went thirty feet2 hence its velocity was thirty feet in #dc seconds1 or seventy feet per second4 ,of course if you make the bolt heavier the velocity of projection will become slower1 the time longer1 and hence the cat will fall further before it is transfixed by the bolt4 ,my task is now at a close4 ,i have endeavoured not merely to give a description of clocks and various apparatus for measuring time1 but to explain the fundamental principles of mechanics which lie at the root of the subject4 ,may ,i end with a word of advice to parents8 ,there is a certain number of boys1 but only a certain number1 who have a real love for mechanical science4 ,such boys should be encouraged in every way by the possession of tools and apparatus1 but in the selection of this apparatus the following principles should be borne in mind3-- ,first1 that almost everything a boy wants can be made with wood1 and metal1 and wire1 and string1 if he has someone to give him a little instruction how to do it4 ,a bent bit of steel jammed in a vice makes an excellent tuning fork4 ,second1 that he wants not toy tools1 but good tools4 ,if an expert wants a good tool1 how much more a beginner4 ,third1 that he ought to have a reasonably dry and comfortable place to work in1 and the help and advice of the village carpenter or blacksmith4 ,fourth1 that he ought not to be allowed to potter with his tools1 but to make something really sensible and useful1 and not begin a dozen things and finish none4 ,fifth1 that the making of apparatus to show scientific facts is more useful than making bootjacks for his father or workboxes for his mother4 ,and1 lastly1 that a little money spent in this way will keep many a young rascal from worrying his sisters and stoning the cat2 and when the inevitable time comes at which he must face the young man's first trial1 ,,the ,,examiner1 he will often thank his stars that he learned in play the fundamental formula ,s #a_/b g t1 and that he knows the nature of 8harmonic motion10 the two most important principles in the measurement of time4 ,,the ,,end4 ,,appendix ,,on ,,the ,,shape ,,of ,,the ,,teeth ,,of ,,wheels4 ,illustration3 ,,fig4 #gd4 ,the teeth of wheels for watches and clocks need particular care in shaping1 and it may be of interest if ,i describe briefly the principles upon which these wheels are made4 ,what is required is that the motion shall not be communicated by jerks as the teeth successively engage one another1 but that the motion shall be perfectly smooth4 ,the problem therefore becomes this3 ,how are we to arrange the teeth of the wheels so that as one of them turns and drives the other round the leverage or turning power exercised by the driving wheel on the driven wheel shall always be uniform8 ,now if the teeth were simple spikes one can easily see that this would not be the case4 ,for instance1 as the arm a c turned round1 driving before it the arm b d1 the point c would scrape along1 and the leverage between the two teeth would constantly alter4 ,evidently some other construction must be adopted4 ,before we can determine what it is to be1 we must inquire what the leverage would be between two rods1 a c and d b1 mounted on pivots at a and d4 ,the answer to this question is1 that when a lever such as a c presses with its end against another1 d b1 the power is exercised in a direction c e at right angles to d b4 ,hence the leverage between the two arms is in the ratio of a e to d c4 ,the system is just as if we had a lever a e united to a lever d c by a rigid rod e c at right angles to both of them4 ,illustration3 ,,fig4 #ge4 ,whence then the ratio of the power is as a e is to d c4 ,illustration3 ,,fig4 #gf4 ,but since the triangles a e f1 d c f1 are similar1 a e is to d c as a f to f d4 ,whence then we get this general proposition3 ,if one body mounted on an axis is pressing upon another body mounted on an axis1 the pressure exerted between them is always exercised in a direction1 shown by the dotted line1 at right angles to the two surfaces in contact2 and the ratio of the leverage is found by drawing a line from one axis to the other1 so as to cut the line of direction of pressure in f4 ,the leverage of one on the other is then as a f to f d4 ,our problem has now become the following3 ,given a rod b d1 suppose that it is pressed upon by a curved surface mounted on an axis at a4 ,then the direction of the pressure that the curved surface 7called in engineering language a cam7 will exercise on the rod b d is shown by the dotted line2 and the ratio of the driving power to the driven power is as d f to a f4 ,now how can we shape the cam so that as it moves round1 and different parts of its surface come successively into contact with b c1 the ratio of the leverage is always the same2 that is to say1 the ratio of a f to f d shall always be constant2 that is to say1 the line drawn through the point of contact perpendicular to the curve at that point1 shall always pass through the point f8 ,illustration3 ,,fig4 #gg4 ,illustration3 ,,fig4 #gh4 ,evidently1 if this is to be so1 the point d must be on a semicircle1 whose diameter is f b1 for in that case the angle f d b will always be a right angle4 ,illustration3 ,,fig4 #gi4 ,the surface must then be so arranged that1 whatever be the position of the cam and of the rod b d1 the point of contact between them must always be on the semicircle f c d2 that is to say1 as the cam moves round the axis a its shape must be such that a line drawn from f to the point where it cuts the circle f d b is always perpendicular to the curve4 ,now suppose that we move a circle whose centre is at a1 and radius a f1 so as to roll the circle f d b by simple surface friction round its centre o1 then any point d on it would mark out a curve on a piece of paper attached to the moving circle whose centre is at a1 and the direction of motion of the curve would always be such that the point d on it would at any instant be describing a circle round f1 and the direction of the curve would thus at any point always be at right angles to the line d f for the time being4 ,illustration3 ,,fig4 #hj4 ,this curve1 caused by the rolling of one circle on another1 is called an epicycloid4 ,hence1 then1 for a clock1 if we make the pinion wheel with straight spokes and the driving wheel with its teeth cut in the form of epicycloids1 caused by rolling a circle with a diameter equal to the radius of the pinion upon the driving wheel1 we shall get a uniform ratio of leverage one upon the other4 ,the circles with radii a f1 b f1 are called the 8pitch circles10 and these radii are in the ratio of the movement that is required for the wheels1 usually six to one or eight to one1 as the case may be4 ,the sides of the teeth of the pinion wheels are straight lines radiating from the centre1 and rounded off at the ends so as to avoid accidental jambing4 ,the teeth of the cogwheel have epicycloidal sides4 ,the tips are cut off so as to be out of the way1 and spaces are left between them for the width of the leaves of the pinion wheel4 ,illustration3 ,,fig4 #ha4 ,both pinion wheels and cogwheels are cut by cutters rotating at a high speed1 about #c1ejj times in a minute1 the cutters being carefully shaped for the pinion wheels with straight edges1 for the cogwheels in epicycloids4 ,it is a pretty thing to see a wheel-cutting engine at work1 the cutter flying round with a hum1 cutting the rim of a brass wheel into teeth1 the brass coming off in flakes thinner than fine hairs and falling in fine dust4 ,when a tooth is cut1 the wheel is moved round one division of an apparatus called a 8dividing plate10 so as to present a new part of the wheel to the cutter4 ,of course1 the cutter and wheels must all be properly proportioned4 ,cutters are sold in sets duly shaped for the work they have to do4 ,wheel-cutting is a special branch of the clockmaking industry4 ,the reason the speed of cutting is so high is because it is desired to take off small portions of metal at a time1 and thus not strain the wheel and the cutting machinery4 ,if bigger cuts were made1 then the machine would have to go slower1 for it is a principle in the construction of cutting machinery that the speed of the cut must always be proportioned to the depth of it4 ,if you want to take deep cuts you must move the cutting edge slowly1 and vice vers4 ,the most modern method of making cogwheels of brass1 and the best1 is to stamp them out of solid sheet metal at a single punch of a punching machine1 and cheap watches are always made in this way4 ,in fact1 the whole method of watch and clock-making is undergoing a transformation4 ,before the time of the great engineering development which took place towards the end of the eighteenth century1 the making of machines was a sort of fine art4 ,cogwheels were cut by hand4 ,the circumference was marked out by means of compasses4 ,then holes were drilled round the rim1 and teeth cut out leading into them1 and shaped by means of special files constructed for the purpose 7,fig4 #hb74 ,big machinery was all shaped out at the forge and by the file4 ,the engineers complained that you could not get big work made true even to the eighth of an inch4 ,but watches and clocks were beautifully made1 though only at the cost of hours of patient measuring and filing4 ,the taste for ornament still existed4 ,the wheels and backs of watches were chased over with the most beautiful patterns2 the frames of the clocks were wrought into beautiful figures and forms4 ,even astronomical instruments were embellished4 ,illustration3 ,,fig4 #hb4 ,then came the era of severe accuracy4 ,men of science took the government of machine-making whose feelings were repugnant to art in any form4 ,they hated to see any effort expended in ornament4 ,with severely utilitarian aims1 they banished all appearance of beauty from instruments and tools of all sorts1 so that our modern machines1 from a steam engine down to a watch1 are now models of precise but perfectly unornamented workmanship4 ,they are the fitting implements of a nation that wears trousers and tall hats4 ,one has only to compare an old vessel of war1 with its sculptured prow and streamers1 with a modern ironclad to take note of the difference4 ,the art of ornamentation is now little more than a spasmodic imitation of the past1 with a historical interest only4 ,as a living entity it has almost ceased to exist4 ,but in precision of manufacture the present age is without a rival in the history of the world4 ,people believe no longer in the old methods of scraping and filing1 and hand-work directly exercised on metal is rapidly falling into desuetude4 ,it is possible1 of course1 with a file and scraper and days of labour to get two flat surfaces of metal so perfect that when put together one will lift the other like a sucker on a stone1 but it is waste labour4 ,a small machine will do it as well in a few minutes4 ,no longer is a watch built up as one would build a house1 fitting part to part4 ,by expensive machines thousands of watch parts are stamped and cut out to pattern1 and then a watch is made by taking one of each indiscriminately and just putting them into their places4 ,comparatively unskilled workmen can do this4 ,where the skill is wanted is to design and make the machinery and watch the cutters1 measuring them with microscopic gauges from time to time1 and at once remedying them if an edge is found to be a ten-thousandth part of an inch out of place4 ,so that the labour of man is becoming more and more a labour of design and of supervision4 ,machines are the slaves that do the work1 for in a good machine we have an eye and an arm that never tires1 and only needs to be kept in working order4 ,but machines are not artistic1 and thus art is lost while precision is gained4 ,at present a desperate attempt is being made to supply by means of machinery the craving of the human mind for art4 ,but it is destined to failure4 ,art of this kind is generally produced by the same brain that designs machines1 and therefore presents an appearance of rigid accuracy and uniformity1 which1 while essential to an engine1 is out of place in an artistic product4 ,the great manufacturers of our ,midlands do not seem to understand that there is no object in making a towel-horse as geometrically accurate as a turning lathe4 ,it will apparently be years before they learn to put art and precision each in the place where it is wanted--precision in the works of the watch1 art in the face and the case of it2 machine work in the inside of a watch1 hand work on the outside4 ,when the public taste is educated so as to see the odious character of the jumble of ,gothic1 ,egyptian1 and meaningless ornament on such an article as the case of an ,american organ1 one step will have been made towards the revival of artistic taste4 ,but to propose as a means of reviving art that we should discontinue the use of machinery or abandon our modern cutters of precision to go back to a hack-saw and file is ridiculous1 and could only be suggested by men quite destitute of scientific ideas4 ,art and precision each has its place3 there is room for both2 let neither intrude on the domain of the other4 ,,index4 ,acceleration1 #gc1 #gg ,almagest1 #ec ,anchor escapement1 #abj ,ancient science1 #ej ,aristotle's ideas1 #bc1 #eb ,attwood's machine1 #hc ,babylon1 temple of1 #bd ,balance wheel1 #aei ,candles to measure time1 #df ,chaldean day1 #ae ,chaucer1 #ef ,chronographs1 #agi ,chronometer1 #afe ,chronometer escapement1 #aff ,clock movement1 #abc ,copernicus1 #ef ,crossbow experiment1 #ahc ,crown wheel1 #aae ,cycloid1 the1 #aji ,dante's ,inferno1 #ed ,day1 length of1 #bi ,dead beat escapement1 #ace ,density1 #ab ,driving weight1 #abg1 #ada ,earth1 a sphere1 #ba ,earth's motion1 #eg1 #fi ,earth not at rest1 #fg ,egg-boiler1 #dc ,electric clocks1 #agi ,epicycloidal wheels1 #aia ,escapements1 anchor1 #abj crown1 #aae chronometer1 #aff dead beat1 #ace gravity1 #afi ,falling bodies1 laws of1 #fb ,force1 #gf ,forces1 revolution of1 #hi ,fusee1 the1 #aag ,galileo's 8,dialogues10 #eh clock1 #aaa ,grandfather's clock1 #aai ,gravity1 action of1 #ac1 #fe ,gravity escapement1 #afi ,greek day1 #af ,harmonic motion1 #ig ,hooke's law1 #ga ,isochronism of springs1 #ic ,lamps to measure time1 #df ,latitude and longitude1 #afa finding1 #afc ,mass1 nature of1 #aj ,mercury clock1 #de ,modern methods1 #agg1 #aig ,moments1 #aja ,moon's appearance1 #ag ,motion1 reliability of1 #eg ,musical notes1 #ie ,north pole1 days at1 #cc ,oscillations1 law of1 #aea ,parabola1 the1 #hg ,pendulum1 the1 #ajc1 #ade suspension1 #ade mercury1 #adg gridiron1 #adi theory of1 #aee free1 #acc ,pisa1 leaning tower of1 #fa ,planets1 names of1 #aa ,pulse measurer1 #ii ,ratchet wheels1 #abi ,roman clocks1 #dj ,sand-glasses1 #da ,space1 nature of1 #h ,speed of falling bodies1 #gi ,spring balance1 #ajg ,stevinus' theory1 #ha ,style of sun-dials1 #ce ,sun-dials1 #bg to make1 #dh ,synchronous clocks1 #age ,time1 #ac ,toothed wheels1 #abe1 #acg ,tuning fork1 #id1 #aha ,velocities1 composition of1 #he ,water pressure1 #cg ,water clocks1 #ci ,watches1 #aef ,week days1 names of1 #bd ,wheels1 shape of teeth1 #aij ,wheel-cutting machines1 #aic ,winding drum1 #aca ,winter sun1 #ca ,zodiac1 #ah ,,bradbury1 ,,agnew1 ,,co4 ,,ld41 ,,printers1 ,,london ,,and ,,tonbridge4 99 99 99 99 99 99 ,transcriber's note3 ,punctuation1 hyphenation1 and spelling were made consistent when a predominant preference was found in this book2 otherwise they were not changed4 ,simple typographical errors were corrected2 occasional unpaired quotation marks were retained4 ,ambiguous hyphens at the ends of lines were retained4 ,square roots are represented as 7values74 ,index not checked for proper alphabetization or correct page references4 ,page #af3 8six o'clock0 was printed as 8six clock02 changed here4