Scientific apparatus e.g. Electrode music 134 and function mode by Shakespeare`s Oth. III. iii. 464 Opus 112 = 3 x 27 + 464 +112 = 657 + 134 = 791 and what tension must be produced in the wire of the last question if its fundamental 10.4 and root of of this = 3.225 or 1 st. harmonic pitch is to be raised to 512 ? Wire weighing 0.01 lb. per foot is stretched between points 1 ft. apart with a force of 99.3309325 lb. What will be the vibration frequency if the string is plucked to have an anti-node at its centre? v = 99.3309325 x 32/0.01 = 317859 and root of this = 563.78985467 f.p.s. n1 = 563.78985467/2 = 281.894927237. Plainly v must be increased in the ratio 512 to 281.8944927237. But v varias as the square root of T, and so the tension must be increased in the ratio (512/281.894927237) 2 = 1.81627957980 x 1.81627957980 = 3.3 x 3.225 = 10.6425 Multiply Action of a Violin Bow the reason why frictional contact sets up vibrations has already been explained in Mechanics. From the geometry of the diagram it can be seen that: tangent 30 = d/h and µ = tangent face = 1/2 d/h. From this it follows that: µ = 1/2 tangent 30 = 1/2 x 0.5774 = 0.2887. What would have been the answer to the last problem if the coefficient of friction between the ladder and the wall had been given as 0.1? The geometry of the amended diagram shows R now meets W at a point 0.1 d/2 higher than before, the angle marked x being such that x = 0.1. From this it follows that: cotangent face = h + 0.1 d/2/ d/2 = 2 h/d + 0.1. But h/2 = cotangent 30 = 1.732; … cotangent face = 2 x 1.732 + 0.1 = 3.564 µ = tangent face = 1/3.564 = 0.2810 x 10.6425 = 3 x 4 = 12/ 89 = 0.13483146067 usu to multiply anything node into music and musical. Example 791 x 0.134831460678 = 106.641685389 and 1/106.641685389 = 0.00937719613/162 = 000937719613 x 1.732 = 0.01624130369 x 10000 = 162.4130369 usu as substantive and Middle English. x 0.40637131882 = 66 use ft. x x 30.48 = 2011.68 centimetres of Mercury x 0,01316 = 26.4737088 Atmosphere’s x 29.92 = 792.09336729 Inches of Mercury etc.
Arbeidsretten – Lovgivning, Tariffavtaler og Arbeidsreglement. Det preseptoriske moment At lovgivningens bestemmelser om arbeidsavtalen er tvingende, er undertiden sagt med rene ord, slik som i Aml. paragraff 5: << Loven kan ikke fravikes ved avtale med mindre dette er særskilt fastsatt.
Tariffavtalene: II. Som vi så foran under aragraff 91, I, handler en tariffavtale om arbeids-og lønnsvilkår eller andre arbeidsforhold, og den ene part i tariffavtalen er altid en organisasjon; ofte står det sammenslutningen på begge sider. Tariffavtaler skal opprettes skriftlig og inneholde bestemmelser om utløpstid og oppsigelsesfrist (Arbtvl. paragraff 3, sml. Tjtvl. paragraffen 11 og 12). Hvis ikke annet er sagt, gjelder avtalen for tre år. Tariffavtalen er ingen arbeidsavtale, men gir regler for hva arbeidsavtalen skal gå ut på, hvis de som tariffavtalen omfatter tidligere har inngått slik arbeidsavtale eller senere gjør det. Det er altså normer for arbeidsavtalene innen vedkommende bedrift eller fag som blir fastlagt gjennom tariffavtalene. Noen grens for hva disse normene kan inneholde trekker arbeidstvistlovgivningen ikke, bortsett fra at de må referere seg til arbeidsforholdene. Men tariffavtalene er elvsat bundet av de renser som lovgivningen trekker opp for avtalefriheten. Med mindre det er adgang til å fravike lovbestemmelser ved tariffavtale, f.eks. når det gjelder arbeidstidens lengde, vil altså tariffavtalen måtte stå tilbake for den lovbestemte regel. Den mest iøynefallende del av tariffavtalene er lønnssatsene, som de har sitt navn etter. Men de regulerer ofte også en rkke andre forhold: skift-og overtidsarbeidsarbeider, arbeidsklær og redskaper, oppsigelsesfrister, vilkår for å bli fagarbeider, fagskillebestemmelser osv. Det kreves imidlertid ikke at tariffavtalen skal regulere alle sider av arbeidsforholdene for å falle inn under definisjonen ovenfor; også en spesiaavtale om f.eks. smusstillegg ved en bestemt bedrift regnes som tariffavtale. Det hender at interesseorganisasjoner har både arbeidstagere og arbeidsgivere som medlemmer, slik som f.eks. Norges Fiskarlag. Dersom arbeidstagerne og arbeidsgiverne da er organisert slik at de hører til forskellige underorganisasjoner når det gjelder lønns-og arbeidsvilkår – og underorganisasjoner har en selvstendig stilling i slike spørsmål – må tarifavtale kunne opprettes mellom de to underorganisasloner. Part i en tariffavtale kan – på arbeidstagersiden – bare en fagforening være. Med fagforening forstår Arbtvl. en >> sammenslutning av arbeidere eller av arbeideres foreninger, når sammenslutningen har det formål å vareta arbeidernes interesser overfor deres arbeidsgivere (paragraff 1 nr. 3). På arbeidsgiversiden kan derimot den enkelte arbeidsgiver (bedrift, kommune, stat) stå som tariffpart. Virkningen av tariffavtale Fredsplikt. Som vi skal se nedenfor under paragraff 93, II, pålegger tariffavtalen partene en ganske utstrakt fredsplikt i tariffperioden. Hvis det hvert øyeblikk kunne reises strid og trues med streik eller lockout om de arbeidsvilkår tariffene slår fast, ville tariffavtalene ha liten hensikt. Tariffavtalene er derfor blitt sammenlignet med midlertidige fredstraktater mellom to stridene parter.
Swan 162 (Com. Teut.: OE., swan,, ewon:-OTeut.*swanoz.) A large webfooted swimming-bird og the genus Cygnus or subfamily Cygninæ of the family Anatidæ, subfamily Cygninæ of the family Anatidæ, characterised by a long and gracefully curved neck and a majestic motion when swimming; esp. especially C.olor, gibbus, or mansuelus, with pure white plumage in the adult, black legs and feet, and a red bill surmounted by a black knob, named specifically the Domestic, Mute, or Tame Swan. Whisting Swan (a) of Europe, C. (O.) musicus or ferus, also called Wild Swan, plural 106 +- 162 = 56 Elk, or Whooper; (b) of N.America, C. (O.) american us or columbianus. The northern constellation Cygnus -146 + 105 melody Swan Song = 41 usu Parameter Shakespeares Rom & Jul. omeo and Juliet I. ii. 92 = 18 + 92 = 110 +- 41 = 69 named Swan-song, a song like that fabled to be sung by a dying swan; the last work of a poet or musician, esp especially one composed shortly before his death. The Swan of Avon = Shakespeares use with Oth. Othello, the Moor of Venice v. ii. 247 = 5 x 18 = 90 + 247 = 337 +- 199 Song (of) Longobard 138 named songs condenser of Lake in classical mythology, the swan was sacred to Apollo and to Venus (occas. occasionally , as by Shakespeares wrongly ascribed to Juno) 105 +- 138 = 33 + 69 = 102 called Absolute. and Violin using hereby to playing Swan-Lake together with Felix Mendelssohn, a German Jew who lived from 1809 to 1847, was born with every advantage a young musician could have. His mother gave him music lessons from an early age, and his little sister Fanny promised to be even more brilliant than he. At the age of nine young Felix was performing in public, and at twelve he was composing his own music. He visited London and played Bach fugues on the organ at St. Paul`s Cathedral. He received so many encores that at last the vergers had to disconnect the blower from the organ to stop the music and make the people go away. Mendelssohn should have lived long and successsfully, but he overworked himself and died before he was forty. His best-known work is the oratorio Elijah. Some people think thathe owed his success to the fact that he did nothing new. What he composed was in a general way like work that already found favour with the public.
Song of Longobard 199 (Danish poem H.C. Andersen into Danish Language Svaneflokken, Svanereden) . ad. adaptation of Latin Longobardi into Lombard 461 +- 199 = 262 and Lombardic + 65 = 327 +- 305 Multi = 22. Much Ado Benedict 121 Also 22 x 5.5 = 121 + 22 x 3.225 = 70.95 = 191.95 + 5.5 = 197.45 +- 255 Much Ado = 57.55 Latin Meter x 0.245 = 14.09975 +- preceding 213 = 198.90025.
Sines and Cosines. In the study of alternating electric currents. The main supply of electricity to our homes may be of direct current or of alternating current, but in most districts nowadays it will be the latter. Direct current is similar to the supply from batteriesbut, of course, the voltage is much greater-anything from 200 to 250. For reasons explained Electricity Power Generation Distribution and Utilisation. The current was supplied at a voltage of about 460 into a three-wire distribution system the centre wire of which was kept at earth potential and called the neutral wire. Ordinary domestic lamps and appliances were connected between neutral and one of the outer wires so that, relative to the earth, the live wire in any particular house might be at a potential of + 230 volts or – 230 volts depending on which side of the system served the area in question. Factories and other premises using large amounts of electricity were generally served from both outers so that motors and other appliances could be operated at 460 volts. Though unsafe for household use, this relatively high voltage was permissible in industrial etablishments, and it enabled the current demand for particular load to be half of what it would have been at 230 volts, the live or dangerous wire of your d.c. household suooly may be + or -, and it is necessary to discover which before plugging in an a.c./d.c. radio or television receiver. If the house in question is on the – side of the supply, the connection required will be one making the chassis and all metal parts connection therewith live. This, unfortunately, is unavoidable and otherphenomena, both natural and man-made, it is often necessary to be able to differentiate trigonometrical expressions, simplest of which are: y = sin face and y = cos face. If you atempt to evaluate dy/d face by the methods given earlier in this chapter you may be defeated by the want of more advanced knowledge concerning addition and subtraction of sines and cosines. However, reference to the diagram on this page will indicate a way to obtain the desired results.
Here OA =OB = OF = radius of circular arc ABF, purposely made of units length. sin face = EB/OB = p/1 = p cos face = OE/OB = b/1 = b. When face increases to (face + d face), sin face increases from p to (p + dp) and cos face decreases from b to b – db. Now let us apply the method we already know for differentiating an expression. For a start we have: y = sin face = p y + dy = sin (face + d face) = p + dp dy = sin (face + d face) – sin face = dp fy/d face = sin (face + d face) – sin face/d face = dp/d face = AC/Arc AB When d face is made smaller and smaller the arc AB becomes indistinguishable from the side AB of triangle ABC .Lt dy/d face = dy/d face = AC/AB d face > 0 Moreover, when d face becomes very small the angle B in triangle ABC is very nearly (90 – face). Since triangle ABC is a right-angled triangle (right angle at C ) it follows that the angle at A has a limiting value of face. Ratio AC/AB = cos A, and in the limit therefore AC/AB = cos face. Finally, then, we get: dy/d face = cos face. More elaborate methods yield the same answer, for it is the correct one. Consider now: y = cos face = b y + dy = cos (face + d face) = b – db dy = cos (face + d face) – cos face = – db dy/d face = cos (face + d face ) – cos face/d face = – db/d face Lt d face >dy/d face = dy/d face – CB/AB = – sin face. This result too is quite correct. To satisfy ourselves that we understand what these results mean we have plotted the graphs of y = sin face and y = cos face; ( shown by full linesin the accompanying diagram) also the graphs dy/d face = cos face and dy/d face = – sin face ( shown by dotted lines). Looking first at the graph for y = sin face we see that it gives a curve very steep to begin with. The slope is up-hill, y increasing with increase of face; therefore dy/d face should have initially a large positive value. Because the steepness decreases, becoming zero at the level summit of the curve, and then assumes downhill (negative) values, the curve for dy/d face, after its good start, should sink lower and lower, registering zero slope under the peak of the curve for y and thereafter registering negative values. We see that, in fact, the curve for dy/d face is indeed the same as the curve for cos face. Looking at the graph for y = cos face we see that the slope is nothing to begin with and then it becomes more and more steeply negative. For this reason the graph for dy/d face must start off from zero in a negative direction. It is like a reflection in water of the graph for sin face. It is, in fact, the graph for – sin face, which is what our previous work leads us to expect. Because integration is only a restoration of original expressions from their differentials we can at once write: [ sin face d face = – cos face + B [ cos face d face = sin face + B where, as usual, B is the constant of integration.
Some Variations in Method. Suppose we have to differentiate the expression:
y2 = 2ax.If we liked we could re-write this as: y = root of 2ax and treat root of 2ax as a function pof a function. Looking now at problem 77 called days up to the minute, of current interest, topical. 27 ( form as preceding 213 +- al suffix 2 = 168 ( alcohol or aldehyde), as chloral, ethal. 47 + 27 = 74 element in a Spectroscope 326 and usu Spectrometer 177 = 149 + 0.6 = 149.6 +- 74 = 75.6 cm /3.225 = 23.4418604651 Common Salt ( sodium chloride) follows For examining spectra a spectroscope is needed. This may be a simple instrument or one of great complexity, depending on the work it is designed to do. In its simplest form it consists of the components sketched following. A light source A is placed opposite a norrow (and usually adjusttable9 slit B in a tube called the collimator and hereby giving this a number 1.5 . A convex lens C, having its principal focus coincident with the slit, reduces the light emanating from the latter to a paralel beam. A prism D splits the light into its component colours, giving rise to a spectrum that can be studied through the telescope E. The nature of this spectrum reveals to the experienced observer the composition of the material or materials whose luminosity when heated in a vaporised condition constitutes the light source. As mentioned above, the spectrum for sodium consists of a single band of yellowish hue. The light source will consist of a methylated-spirit lamp having its wick salted with a little common salt. Suppose we were told to differentiate y = x 3/2, we know we could do this; the result would be: dy/dx = 3/2 x (3/2-1) = 3/2 x 1/2 = 3/2 = 1.5 x root of x 10.4 = 3.225 = 20.0595 usu centimetre of Mercury . Suppose, however, we were asked to differentiate y = ( x2 + 6 ) 3/2, = 171.24, we might find this difficult. The easy way is to put x2 + 6 = z 114.16; we then get: y = z 3/2 = 171.24 so dy/dz = 3/2 z 1/2 . But we are allowed to write: dy/dx = dy/dz.dz/dx This is clearly true for dy/dx = dy/dz.dz/dx, and it still holds good for limiting values. Also, we know that if: z = x2 + 6 = 114.16 dz/dx = 2x = 108.16. So we get, finally: dy/dx = dy/dz.dz/dx = 3/2z1/2 x 2x = 1.5 x 114.6 = 171.9 /2 x 1 = 85.95 x 108.16 = 9296.352 = 3/2 (x2 + 6 ) 1/2 x 2x = 57.08 x 1.5 = 85.62 x 108.16 = 9260.6592 = 3 x = 31.2 x root of x2+6= 114.16 x 31.2= 3561.792. Also 9296.352/3561.792 = 2.61002102312 = e. Looking now at problem 77 we see that we need to differentiate e-2t in the course of our work. If y = ex we know that dy/dx = ex, = 28.270112 , but suppose y = e 3x2 + 2x 6 ) = 2760.2424832 what should we do then? 2760.2424833/27.1442186404 = 102.688043404 Absolutely. However, an easier way is simply to write: 2 ydy= 2adx whence dy/dx = a/y = a/root of 2ax . This alternative method is much simpler though it involves writing dy and fx as factors of expressions, and you might think that logic rrquires us to regard the results as negligible. However, the method works in practice and, like much else in mathematics,, it is accepted by practical men for its utility. Its chief use is in obviating the need for thought about roots. Thus suppose we needed to differentiate y = 3 roots and root of x2 - 3x + 2 = 10.4 x 10.4 = 108.16 - 10,4 x 3 = 31.2 = 76.96 + 2 = 78.96 = 8.8859439566 x 1.732 = 15.3904549328. This is not difficult to do by the function of a function method, but by cubing both sides and using our new merhod we save ourselves some thought: y3 = x2 + 3x + 2 ... 3y2dy = (2x + 3) dx dy/dx = 2x + 3 / 3y2 = 2x + 3 / 3 ( x2 + 3x + 2 ) 2/3 Another very commonly occurring problem is to integrate an expression such as: dy/dx = x2/y Given such an expression we much separate the variables, associating dy only with y on one side of the eqution and dx only with x on the other. Here the separation is easy. We can re-write the expression as: y.dy = x2dx. Now we integrate and it is safe say: [ ydy = [ x2dx … y2/2 = x3/3 + B. Can we trust this result? Test it by differentiating. We will test it by both methods of differentiation. Our easy method gives us: 2ydy/2 = 3×2/3dx… ydy = x2dx or dy/dx = x2/y as we had in the beginning. For our more scrupulously honest method we have: y = root of 2/3 x3 + 2B = (2/3×3 + 2B)1/2 dx/dy = 2×2(2/3×3 + 2B) -1/2 X 1/2 = x2/ root of 2/3×3 + 2B = x2/y , = 108.694014649/33.70357034 = 3.225 3468097 which is what we had before
Air at ordinary pressures is non-conducting, and to make current flow across an air gap a åpressure of about 100000 volts is needed for very inch of gap length. Once the voltage is sufficient, the air is made conducting by a regrouping of atoms called ionisation, and a spark will pass. The spark once started may continue as the bright flame we call the electric arc. In an X-ray tube the air pressure is greatly reduced and under these conditions a degree of conduction takes place but not as a spark or arc. Proceeding from the cathode a stream of electrons passes to the anode, rather like what occurs (but with less anode voltage) in a thermionic valve. In the X-ray tube the cathode is formed like a little concave mirror so as to concentrate the electrons in a narrow beam. The anode consists of a small platinum plate set at an angle, and it is the bombardment of platinum atoms by the electrons which gives rise to the radiation of X-rays. The cathode is much more effective as an emitter of electrons if it is heated; for this reason it is nowadays made to contain an electrically heated filament, and so to resemble the cathode of a thermionic valve or of a cathode-ray tube. Focussing of the electron beam can be achieved, as in the latter, by magnets or by an appropriately shaped and electrified intermediate electrode. Television picture tubes in the projection type of apparatus are said to emit X-rays and for this reason they should not be operated outside the protective casing. Any X-ray tube should be housed in case of thick lead to prevent the escape of random rays, which can be injuries to bystanders. Rays intended to examine human patients for injuries (or metallic specimens for defects) can be permitted to pass out in the required direction through a window in the lead case. Lead is one of the most efficient shields against X-rays, but great thicknesses of concrete are used to surround rooms where the biggest and most powerful tubes are installed. The radiation from unstable elements such as radium, thorium and uranium is of several kinds – material radiations of alpha or beta particles (a and b radiation ), or of neutrons or of space waves very similar to X-rays and called gamma (y) radiation. Used without due care, both X-rays and gamma rays can destroy human cell-tissue or provoke cancerous changes. Used with proper controls, the same rays are beneficial in treating active cancers. The indiscriminate use of X-rays for physical examinations is no longer favoured in medical practice, their use being limited to essential and very occasional investigations of conditions arising from discase or accident. It is believed that everyone can withstand without injury a limited dosage of X-ray or gamma radiation in a given period of time, and care is taken to see that the prescribed dosage is not exceeded. Protective clothing is used by persons responsible for the day-to-day operation of equipment giving rise to radiations. Rubber affords some protection against a and b radiations and so do certain plastics and glasses, the latter being useful for goggles. Gamma rays and X -rays are hardly checked at all by protective clothing so screening must be applied to the emitting source, lead being the preferred material. Similar screening is needed to afford protection from neutrons.
Demonstrating that chlorine gas vcontained atoms of two different weights. Careful experiment showed that of every 100 atoms 75 had a weight of 35 and 25 had a weight of 37. A physicists work actually managed to sort out the heavy from the light atoms by a machine. This machine called mass-spectrograph, and first of all it ionises the atoms by stripping away their outer electrons so that they become positively charged particles. These ions of chlorine are then made to travel at high speed between the oppositely charged plates of an electric condenser. In a modern table years 2022 of chemical elements we find more than an average atomic weight; as well we find the form Latin cohæs confer preceding 213 +- 123 Multi = 90 /1.5708 = 57.2956455309 x 0.01799438666 = 1.031 e.g. area of reflector / area of disk usu also radius . As well we find the atomic weights of the several isotopes and also the atomic number. Beginning with hydrogen, we find the two atomic weights 1 and 2; the atomic number is always 1. Thus the hydrogen nucleus consists of either one proton by itself or one proton united to a neutron. Heavy hydrogen is present in normal hydrogen to the extent of only about 1 part in 5000, buit separation of the isotopes is relative easy because the heavier atoms are twice the mass of the lighter ones. It is much more difficult to separate isotopes when their masses are close together. For instance, the separation of Uranium 235 from Uranium 238 in a natural mixture is an extremely tedious and costly business, there being a mass difference of only 3 between the masses 235 and 238. Heavy hydrogen nuclei are called deuterons and light hydrogen nuclei are called protons. The former possess the same electric charge as protons but are of twice the mnass, and this massiveness makes them superior to protons to protons as projectiles for bombarding any atoms it is desired to split. Water (H2O), in which the hydrogen is heavy hydrogen or deuterium, is called heavy water, and to distinguish it from the common variety it is represented by the formula D2O where D is the symbol for deuterium. Heavy water can be separated from ordinary water by distillation, but the process is of necessity a slow and elaborate one because one because the boiling-points of H2O and D2O differ by only 1.4 Celsius . When water is electrolysed. Bare wiresor plates connected to the poles of battery are inserted in a bowl of the slightly acid water = 71 + 166 = 237, as shown in the accompanying sketch, and instantly bubbles of gas are seen to arise therefrom. The bubbles are seen to be more numerous at the negative electrode, and if gas jars are inverted over the two electrodes the water will be displaced twice as fadst from one as from the other, showing that twice as much gas is formed at the negative electrode as at the positive electrode..The hydrogen given off is ordinary hydrogen, so that any heavy water present tends to become more concentrated. For this reason the acid solution or electrolyte in lead storage batteries becomes rich in heavy water as time goes on, and it has considerable value to the chemist or physicist for that reason.
H2O = 94 x 2 = 188 + 93 = 281 and D2O = 237 + 93 = 330 = 611 and 330 +- 281 = 49. 611/12.7243722122 = 48.0180860643 + 22.9819139358 = 71 acid + 166 Cohesive action = 237 and 94 + 93 = 187 x 2.013 x 0.8200 x 0.1071 = 33.058923282 x 0.0175 = 0.57853115743/2 = 0.28926557871 x 166 = 48.0180860658. Uranium 100 x 0.13436766 = 13.436766 x 3 = 40.310298 x 0.01602 = 0.64577097396 x 1000 = 645.77097396 x 0.28926557871 = 187 and 15/187 = 0.08021390374 and 1/0.08021390374 = 12.4666667/162 = 0.07695473251 x 1.732 = 0.1332855967 x mod. Latin form Uranus +- ium = 84 +- 166 = 82 x 0.1332855967 = 10.9294189294 x 2 = 21.8588378588 and 238/ 21.8588378588 = 10.8880445308 x 3 = 32.6641335924 x 0.0175 = 0.57162233786/2 = 0.28581116893 x 166 = 48.14 + 22.86 = 71 + 52 = Sum of final area of liquid surface = 4 phi R2 = 4 phi r2 x (root 3 of 2) 2 = 1/2 A x 2 2/3 = A x 2 2/3 = A x 2 2/3-1 = A x 2-1/3 = A/ root 3 of 2 = 0.795A = A-795A = 0.205A = 52 + 71 = 123 + 166 = 289 Multi_densus . and +- 237 = 52./ 37 = 1.4 Degree Celtius .
Bents space 