An Experimental Test of Einstein's Time Transformation Equation Citation Thorndike, Edward Moulton (1930) An Experimental Test of Einstein's Time Transformation Equation. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ah7t-b782. https://resolver.caltech.edu/CaltechTHESIS:08262024-222926273 Abstract No abstract. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Physics) Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Thesis Availability: Public (worldwide access) Research Advisor(s): Unknown, Unknown Thesis Committee: Unknown, Unknown Defense Date: 1 January 1930 Record Number: CaltechTHESIS:08262024-222926273 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:08262024-222926273 DOI: 10.7907/ah7t-b782 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16670 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 27 Aug 2024 23:01 Last Modified: 27 Aug 2024 23:04 Thesis Files PDF - Final Version See Usage Policy. 10MB Repository Staff Only: item control page

An Experimental Test of Einstein's Time Transformation Equation Thesis by Edward M. Thorndike In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy. California Institute of Technology Pasadena, California 1930 Summary The experiments which have been performed to test the fundamental equations of the .. special theory of relativity can be explained by the relativity theory or equally well by . a theory having a Lorentz contraction and a universal time~ The object of the work to be described is to test the Einstein time transformation equation. This is just as essential a part of the special theory of relativity as is the space transformation equation or Lorentz contraction. The apparatus used is a Michelson interferometer with -a large path difference. Light fro m an electrodele ss discharge in mercury is made to interfere and the resulting fringes photographed. It is shown that changes in the velocity of the apparatus because of the earth 1 s rotation combined with its total velocity should give no effect on the phase-difference of the recombining light rays on the basis of the theory of relativity and, on the theory with a fixed ether and a Lorentz contraction, should cause a shift in phase-difference of l. ;Yc.~y waves where 21 is the total difference in the path lengths, v is the total velocity of the earth in its equatorial plane, b..v is the change in velocity, A is the wave-length of the light used, and c is the velocity of light. The results are in complete agreement with the relativity theory and would conflict with the other theory if the general velocity were greater than about 100 kilometers per second. Introduction The special theory of relativity requires certain transformation equations for d istanc es and time intervals for systerns moving with respect to each other . Using t he customary - notation t h ey are: ilXV 1-f: b.y b.t V ,-~ ,6 t All theo1~ies agree that measurements in the Y and Z dir e ctions are not affected by the motion, hence the second and t h ird equations are not in question. The first equation has been s hown to be true by the Michelson-Morley experiment. (l) The la st equat ion has not been adequately investigated. It is the object of the present work to subject it to an experimental test. In order to know what to expect if the relativity time transformation is not valid, we shall consider a theory having a fixed ether and a Lorentz contraction. universal time for all observers, t 1 ~ t. It assumes a We shall show that it predicts a positive result for the present experiment while This experiment was suggested by R. J. Kennedy (Physical Review, Volume 20, 1922). The work de scribed here was done in collaboration with him. He is entirely responsible for the design and construction of most of the apparatus and for the measurement of the plates. Page 2 the theory of relativity requires a negative one, hence our results should decide between the two and thus test the relativity time transformation equation. The essential part of the apparatus used in this work is an interferometer of the Michelson type having a large difference in the lengths of its paths. Changes in the phase-dif- ference of the recombining light rays are determined by measure ments of the changes in the diameters of the interference fringes. Theory The special theory of relativity requires that the motion of the i nterferometer throu gh space produces no observable effeet on it. The diameters of the fringes andJthereforeJ the difference in phase of the recombining light must remain unchanged. This follows from the postulate t hat it is impossible to measure absolute motion through space• The theory with a fixed ether and a Lorentz contraction does not lead, to such a simple result• feet to be expected in this case. We must compute the ef- Consider a beam of light traveling down and back over some path 1 in the moving system. If the velocity of the moving system with respect to the ether is v, the path in the ether will be like that shown in Fi g . 1. For an observer moving with the apparatus, the length of the where xis the projection of 1 on the direction of motion and y is that perpendicular to the direction of motion. Page 3 For an obse rver stationary V with respect to the ether, the distances are given by: Now from the geometry of the fi gure, if t, is the time for the light to go from A to Bandt~ that required for it to go from Solving fort, and t~ -"I-. V "! c_vx::.y' t I - t ,_ Hence, we see that the tLne required for the light to travel down and back over any length 1 is independent of t he direction of 1 and is equal to ~t Consider an interferometer with path-lengths 1, and 1~ and difference in path-length 1. betvveen the mirrors. (fhese are the distances The li ght traverses these distances Page 4 The difference in time re- twice, once in each direction). quired for the light to traverse the two paths is: t= ?._ )_ The number of wave-lengths difference between the two paths will be: :: where L is the period of the light and /\ is its wave-length. Expanding in powers of r, ~ t : ~ ( I + ~ ~:+ ~f, ) Then n changes to n +An Now suppose that v chan ges to v+.l:lv. where: -+ J_ ~ Hence: This change in the number of waves is equivalent to a shift in the interference fringes of exactly the same amount. Hence, when the velocity changes by an amount 11v, the fringes will be shifted ~n fringe-widths. In the experiment, a change in velocity is furnished by the earth's orbital motion and by its rotation. It does not seem practical to use the change caused by the orbital velocity as this would require the apparatus to be kept in operation over a long period of time. The rotation, however•, takes Page 5 The velocity, v, now con- place in a day and can be used. sists of the orbital velocity combined with any general motion of the solar system through the ether- The effect to be ex- pected from the orbital motion alone is small and has the disadvantage of always occurring at the same solar time• be very difficult to observe. It would The effect from a general mo- tion of the solar.system might be expected to be larger and . has the added advantage that it would follow sidereal time and could, therefore, be separated from spurious effects which would It is impossible to tell the naturally follow solar time. exact velocity of the solar system through the ether, but we may reasonably expect it to be at least as large as the velocity with respect to the nebulae and other distant objects, several hundred kilometers per second• (2) If we take ll v to be zero when the velocity of the observer because of the earth's rotation has no component in the direction of the general motion, and if we consider Av to be the change in the general velocity because of the earth's rotation, we get: where w is the angular velocity of the earth, \~ is its radius, c{J is the latitude of the observer, t the time, and £ is a phase constant. Substituting this into our equation for An and putting in the values of the known constants we get: L:1.T1 -= i. l v w \~ W:> <{J "~')._ ~ ( wl +() Page 6 l-= I s.o ('_)'VI - !,- 7. 2__ ~ y.. IO <f -A-ec- '3 40 _, 3 e. <:.. ~· -!>- 5,4(, x JO C. )'Y) JO c.. -- s.ao.,. JO ~~ Se<:.. l\Y\ The displacement of the fringes will follow a simple sin curve with a period of one day, an amplitude depending on the velocity through the ether, and a phase constant depending on the direction of the motion and the zero of our time scale. If v, the velocity of the earth in the plane of its equator, were 425 kilometers per second, then the amplitude of the sin curve would be 1/1000 of a fringe-width. It will be shown later that this could easily be detected. Description of Apparatus The arrangement of the apparatus is shown in Fig. 2. 'l'he interferometer and the optical system are mounted on a concrete bench. This is placed in a small room which can be made dark for changing plates, and which may be thermostated. Page 7 Let us follow the path of the light through the apparatus. It leaves the source, which will be described in detail later, passes through the aperture A,, and the lens L~ which makes it plane-parallel. Then the direct vision prism D and the lens L~ focus the green line of wave-length 5461 A on a second aperture A~. (A water cell was in front of this aper- ture in the run of January 1930, but not in the other two). The light is again rendered plane parallel by the lens L 3 • It is polarized with its electric vector parallel to the bench L, Fig. 2. Page 8 by a Nicol prism N, and enters the interferometer through the tube T, and the window w.. Here it strikes the half- platinized surface of the mirror M, at the angle of complete polarization. Half of the light is reflected to M~, and the remainder goes through the platinum film to M3 • After the light has recombined, it passes out through the window W~ and tube T :t to the photographic plate which is pressed lightly a gainst the end of the tube. (Since the light is polarized as stated above, there will be no trouble from light reflected at the glass side of the half-platinized mirror). The mirrors are mounted in invar supports which are ground into the heavy quartz disk Q. This rests on a felt pad which lies on the bottom of the vacuum chamber. The mir- rors M, and M'.l. are fixed, but Ivl 3 can be adjusted by three differential screws. These may be turned from outside the vacu- um chamber by three rods passing through ground joints in the cylinder C. diagram). (Only one of the three rods is shown in the The adjusting rods only touch the screws when ad- justments are being made. The vacuum line K connects the chamber to a mercury diffusion pump. A dischar ge tube connected to the line serves as a pressure gauge. The interferometer was placed in a steel tub which was filled with water in order to keep the apparatus at constant temperature. A thermo-regulator was placed at R, a small electrically-driven stirrer at S, a Beckman thermometer at T, Page 9 and heaters at H,,\;\,.,H'.l)., and H.p The thermo-regulator consist- ed of a pirex tube filled with toluene. A small amount of mercury was used to make contact with a piece of tungsten wire. The regulator was used to change the grid bias on a vacuum-tube in whose plate circuit was the relay which controlled the heating current. In this way practically no current was broken at the regulator contact, so the mercury did not become contaminated. The heaters were four 25 watt light bulbs connected in series-parallel. They could be operated either from the 115 volt a. c. supply or from storage cells. The light source caused soine difficulty. are: The requirements very homogeneous light of extremely constant frequency and reasonably great and constant intensity. During the first part of the work, an ordinary water-cooled mercury arc was used. This gave good interference, but the fringes were not steady. It appeared that the wave-length of the light was varying, perhaps because of Doppler shifts caused by the motion of the emitting particles. The type of source finally adopted was an electrodeless discharge in mercury. The contrast of the fringes is not quite so good here, but they are much steadier. The form of the tube employed is shown in Fig. 3. The main tube Mis surrounded by a jacket J, filled with carbon tetrachloride. This is co1mected to the atmosphere by the vertical tube T which is cooled by a water jacket J~, thus preventing the li.9.uid from escaping. When the lamp is in operation, the carbon tetrachloride is boiling gently, keeping Page 10 the temperature of the tube at 76° o. The back end of the main tube is connected to the mercury reservoir R, and to the pumps through the capillary c. The oil bath B which surrounds the mercury reservoir is kept at a constant temperature of about 60° 0 by a small mercury thermo-regulator and an electric heater. This keeps the vapor pressure of the mercury in the lamp constant. The front end of the lamp is heated with a Bunsen burner to prevent the mercury from condensing there and to drive off a coating which otherwise forms. The inductance coil of the high-frequency oscillator is wound around the main tube outside of the jacket. This type of source is quite intense and gives good interference; however the frequency and intensity do not seem to be quite constant. This will be discussed in the section on systematic errors. J, T M Fig. 3. Page 11 The circuit of the oscillator which furnished the power to drive the electrodeless discharge is shown in Fig. 4. This arrangement gave a wave-length of 20 meters. [ il Fig. 4. The filament transformer was supplied from the 115 volt a. c. line. A (UV-886) ballast tube was in series with it to smooth out voltage fluctuations. The plate transformer was connected to the 230 volt line. Here, two ballast tubes in parallel were used in series with the transfo~oor. The plate transformer ratio was 10 to 1. The small room in which the interferometer was housed was therrnostated at all times. pressure here were recorded. The temperature and barometric Du.ring the run in October 1929, the outside room was kept at roughly constant temperature, and Page 12 during the run in January 1930 it was quite carefully thermostated. The photographs of the interference fringes were at first measured on a recording microphotometer. ory results but was very tedious. This gave satisfact- In order to read the plates more quickly, Dr. Kennedy devised a comparator which is shown schematically in Fig. 5. This was used in all of the work de- scribed here. Len, H ~lf-5 ,lvered Su r hce <;-- M irro r Fig. 5. Two 45° prisms, one of which has been half-silvered on the diagonal face, are cemented together and mounted so that they move perpendicular to the paper in the diagram. A stan- dard plate is clamped ·to them while t h e plate to be measured is stationary. The observer sees a set of fringes, one half of which is fro m the standard plate and one half from the Page 13 other. By means of a micrometer, he moves the prisms until one fringe of the two systems coincides. 1'hen by setting on the same fringe on the opposite side of the center, he can measure the difference in the diameters of a standard fringe and of the one to be measured. In practice, settings are taken on nine fringes of a photograph and the results averaged by an automatic device. Accidental Errors The uncertainty of a measured quantity caused by purely random errors can easily be computed from the theory of probability. It may be made small by taking a large number of observations. Hence, random errors are serious only in that they make the work tedious. We are not very much concerned with them because they have already been made small compared with the systematic ones. If the systematic errors can be eliminated, the random ones will limit the precision of the experiment• Systematic Error•s The effect to be observed is a small change in the diameters of the fringes having a period of one day. Any other factor which produces such a daily shift will introduce a spurious result. It is errors of this sort which malrn the ex- periment particularly difficult. We shall first consider er- rors coming from the source, then from the interferometer, and finally from the measurement of the plates. Page 14 A change in the intensity of the source will naturally change the density o.f the photograph. This in turn changes the diameters of the fringes as will be shown later. Hence the intensity of the source must have no daily period. Now the intensity may depend on the lamp temperature, the pressure of the mercury vapor in the lamp, or the power supplied by the oscillator. The lamp temperature depends on the at- mospheric pressure, as this determines the boiling point of the carbon tetrachloride surrounding the lamp. Therefore, one might expect an error caused by changes in the atrnospheric pressure. There does not seem to be an appreciable one. The pressure of the mercury vapor in the lamp depends on the temperature of the little oil bath surrounding it, hence changes in this might affect the intensity. Tests do not show an appreciable effect of this sort. The final and important factor determining the intensity of the source is the power supplied by the oscillator. When the plate or filament voltages are changed, the density of the photograph does change. Since the line voltage has a daily period, this will introduce a serious error. The correction which nm.st be made for this will be discussed later. A change in the wave-length of the light will obviously cause a spurious effect. -o In fact, a change of 10 a shift of about 1/1000 of a fringe-width. 0 A will cause This might be caused by a Doppler effect if the emitting particles moved in the line of sight with a velocity of 50 cm. per second. Such Page 15 an effect would probably depend on the line voltage if it were pre sent. There might be a Zeeman effect from changes in the intenCareful tests showed sities of the magnetic fields present. t h at the fields present were not large enough to cause an appreciable error in the results. There might be a reversal of the lines depending on the temperature of the front end of the tube. No such effect was f OUJ.1.d • There might be Stark effects. In fact, the displacements do seem to depend on the oscillator voltage more than can be explained by the changes produced in the densities of the plates. The e xact re a son is not clear, but the fact is reason- ably certain. This is serious as the oscillator voltage has a period of one day. The data must be corrected for it. There are a number of things about the interferometer which might cause trouble. r.rhe optical system mi ght become slightly moved by the expansion of its parts. This would change the angle at which the light enters the interferometer and therefore produce a change in the diameters of the fringes• A computation based on the known variation of the temperature shows the effect to be negligible. -s A change in the distance between the mirrors of 3 x 10 cm. corresponds to a shift of about 1/1000 fringe width. This might be caused by a change in the bath temperature. Fortunate- ly a rough determination of the coefficient of expansion of the apparatus shows this to be negligible. Page 1 6 The length of the optical path depends upon the index of refraction of the air in the interferometer. Since the index · of refraction of a gas depends upon its pressure., this must be kept constant. -3 If it varies by 5 x 10 1Tu~. of mercury, t he fringes should shift 1/1000 of a fringe-width. In prac- tice the pres sure is such that there is no discharge visible in the pressure gauge. -'.! ways below 10 This indicates that the pressure is al- mm. of mercury. It is ha.rd to see how there could be a daily change greater thar1 a small fraction of this. Some other sources of errors which have been investigated are: changes in the camera magnification by expansion of its tube, the effect of the photographic plates not being plane, and the war.ping of the interferometer by stresses set up in the vacuum line• The first two a.re clearly negligible. The third is made as small as possible by keepine; the room temperature constant and by avoiding all jarring• To sum up, there does not seem to be anything about the interferometer which might cause an appreciable daily variation in the diameters of the fringes. The errors wh ich are introduced in the measurements of the plates are mainly accidental. However, there is a systematic one depending on the density, which has ca.used considerable trouble. In the first place, the plates become_ heated and ex- panded by the passage of light through them. This has be en shown by measuring a plate when it has first been put in the comparator and again after it has had time to warm up. Because of this effect, dark exposures will expand more than light ones Page 17 and therefore give readine:; s wh ich are too large. factor may also come in. A second Since any one frin ge is not synnnetri- cal, an i n crease in density may throw the center of gravity toward the side where the intensity falls off more slowly. Be- cause of this, one would expect dense plates to be too small. Plates taken to test this gave widely discordant results., perhaps because the importance of the first effect vms not appreciated at the time. To sum up the whole matter of systematic errors, we may say t h at the voltage on the oscillator transformers and the density of the plates are the thi n gs for which corrections must be applied• They are not i ndepe ndent as the density de- pends on the volt a ge., but one correction cannot be applied for them both as the density is also affected by the sensitivity of the plates, and t h is seems to vary quite badly. The volt a ge correction was found by actually changing it by a large amount, and noting the resulting change in the diameters of the fringes. This was not done very carefully, as a t h orough investigation would take considerable time and we hope to elimi nate the difficulty. However., the approximate value of the correction is known. (See appendix}. The corr e ction for density was made as follows• Since the plates are always denser at the ends and sin ce there is no reason why the displacements should have a period of this sort except for the changes in density (unless t here is some systematic creepage of the emulsion on the glass plate, which no (3) one has observed) , we assume that any difference in the Page 18 average displacement between the center and the ends of the plate is caused by the change in density. The densities of all of the exposures were measured for the runs of October 1929 and January 1930, so the relation between density and displacement could be found. (See appendix). for the two runs were in close agreement. The results They were averaged and used for all three runs. Method of Taking the Data rrhe interference fringes were photographed on astronomical green-sensitive plates made by the research laboratory of the Eastman Kodak Company. rrhe exposure time was one half of an hour, so that 48 photographs were taken each day, twelve on a plate. An automatic camera shifted the plates at the re- quired· times. If the external conditions remained absolutely constant, this would give all the required data, but of course many things which might affect the diameters of the fringes varied, so these were measured and recorded• (The data taken for the run of January 1930 are shown in the appendix). Method of Computation Some days of a run are more self-consistent than others. '11hese seem to deserve more weight. Hence, the data are weight- ed by days, the weights being determined by the deviations of the data of one day from its average• The deviations should strictly be taken from a prelimary sin curve, but this is labo- Page 19 rious and unnecessary. The wej_ghts are inversely proportional to the squares of the deviations. The weighted measurements of exposures talcen at the same times of day are averaged for all the days of a run• The problem then is to find the most probable sin curve through these data. We see by the equation developed in the theory that the displacement should be given by an equation of the form: ( 1) where u is the displacement. In practice we do not measure the displacement from an average plate but from one chosen at 1~andom, hence a constant nru.st be added. This gives for the complete equation: ( 2) If u. is any measured displacement, vve must have by the principle of least squares: I (U-L.(;f= ' (3) 0 O a mininru.m. L(<X~(e.·-c)-+-1-<-IA;) ~ 0 This requires that: iir I_1.p swi( and e;-(.) + l" -lAJ ~ ( f), -() :: o ( 4) 0 ?..lT [2-fo.s~(e;-z)-t-k-u] o.._ ~(e.-(:) ::o (5) t, From (4) L 'lJr ().__ -:: (4i-k) ~ (e;-~) z 0 I C fa-, "(e.--t) ( 6) Page 20 Now ~ L:'(19;-c) ?s ~ 1rr I'""'(1!.-d c.;;, 0 ( 7) where n is the number of observations per day. ,_ Tr o.._ ::: ~ L_(CA,-k) ~ (G.-l'.) ( 8) 0 (9) Expanding (5) vr oI_si:... ( ~;-t) er, (t9,-(_) =- ,:rr ur 0 0 .L ~. ~ (&;-t) - k I ~(e;-e) C Now () ,,.,. 2_ ~ (o;-{) ('.q? (0.--c)-::. o (11) 0 ~tr . ["1.-ew.(e.--() ~o ' . 0 (10) (12) (13) There is a correction which must be applied to this result. It arises from the fact that the interferometer mirrors are gradually changing their positions thus causing a drift in the displacements. This introduces a spurious effect which must be taken out. We seek the amplitude and phase of the first harmonic of f(e) = be where bis the increase in the displacement per radian. By Page 21 the usual Fourier analysis one gets: C<-:, ~ ~ b ::. Tl where a is the spurious amplitude and f: is the phase constant. Combining this with the previous result, we get the cornplete effect. The effect of the drift may be included in the first solution and the same result obtained, but the method followed here shows more clearly the exact effect of the drift of the mirrors. Results Three runs were taken in which the conditions were considered good enough to warrant measuring the plates. The first one, from April 19 to May 12, 1929, contained 19 good days out of the 24. In the second, from October 8 to 22, 1929, 14 days out of the 15 were good. The last one, from January 6 to 13, 1930, contained 7 good days and 1 that had to be discarded. The conditions of the experiment have been gradually improved so that the later runs are about as reliable as the early ones, in spite of the smaller amount of data taken. The results are tabulated below. Page 22 April 1929 f a -4 0 Displacement 3.58 X 10 fringe-widths 71. Correction for Slope 1.74 180. Correction for Density 1.56 87. Correction for Voltage 0.38 90. Correction for Room Temp.4.05 r-7 0 -o. 0 0 0 -+ The final amplitude obtained from these is 2.7 x 10 fringe-widths. The displacement is a maximum at 10 hrs. 20 min. civil time. The correction for room temperature comes from the fact that the outer room was not thermostated during this run. The ballast tubes used in the oscillator circuit are quite sensitive to temperature changes, hence the room temperature affects the voltage on the oscillator transformers, and thus the size of the fringes. October 1929 £. a -4 0 Displacement 3.47 x 10 Correction for Slope o.44 180 . Correction for Density 1.57 121. Correction for Voltage 0.42 -34. The final amplitude is 2.2 x 10 fringe-widths -28. 0 0 - 4 fringe-widths. 0 The displacement is a maximum at 17 hrs. 20 mino civil time. Page 23 January 1930 a -4 Displacement 2.79 x 10 fringe-widths Correction for Slope 0.80 180. Correction for Density 4.34 108. Correction for Voltage 2.07 145.° 0 (] The final amplitude is 4.9 x 10- 4 fringe-widths. The displaceme nt is a maximum at 13 hrs. 40 min. civil time. In order to give an idea of the consistency of the data, the points from which the displacements were computed are shown in Fig. 6. They appear very rough, but when one con- siders the scale employed, this is not surprising. The prob- able error for the uncorrected displacement curve is about 0 6 /l (n oon) 18 C;v;\ Tim e Fig. 6. :l.4 Page 24 0.8 x 10- 1 fringe-widths in amplitude and 2 hours in phase. This was computed for the April data before they were weighted, but it will be roughly right for all of the runs. As has been mentioned in discussing the errors, this is not a serious difficulty at present. rections to be applied. The real trouble is in the corSome of these are of the same size as the displace ments, and they are not at all well-known. Because of this, we estimate that the uncertainty in the _amplitude is about 2.5 x 10-"\- fringe-widths. This corresponds to a velocity of about 100 kilometers per second. The data show that there is not an effect following sidereal time with an amplitude as large as this. Hence we conclude that, within the experimental error, the motion of the apparatus through space produces no opservable effect. The limit set by our experimental error is still high, but if one considers that the velocity of the solar system mi ght reasonably be expected to be several hundred kilometers per second, or more, it is evident that these results support the Einstein time transformation equation and form a real addition to the experimental evidence for the theory of relativity. ---o--- Bibliography 1. D. c. :Miller, R. J. Kennedy, Science, Volume 63, 1926. Proceeding s of the National Academy of Sciences, Volume 12, 1926. K. K. Illingworth, Physical Review, Volume 30, 1927. A. A~ Michelson, F. G. Pease, and F. Pearson, Journal of the Optical Society of America and Review of Scientific Instruments, Volume 18, 1929. 2. G. Stromberg, As trophysical Journal, Volume LXI, 1925. 3. F. E. Ross, Monograph on the The ory of Photography fro m the Eastman Kodak Company, No. 5. Appendix ( 1) Plate Trans~ormer Voltage Correction Exposure 1 2 3 4 5 6 7 8 9 -'t Transformer Yoltage Displacements X 10 in. fringe-widths Plate Filament First Reading Second Reading 18306 58.5 32 2 182.7 58.5 183.7 58.5 22 11 183.7 58.5 183_.8 58.5 -23 -19 183.5 58.7 178.0 58.5 -09 -17 177.6 58.7 177.8 58.4 -07 -18 177.5 58.5 177.9 58.7 03 -34 177.4 58.8 1'77.4 58.5 182.5 58.7 39 32 183.5 58.7 183.7 58.6 24 -12 183.5 58.6 183.5 58.6 32 15 183.5 58.6 ( 2) Averaging exposures 1,2,3,7,8, and 9 we get: Plate Transformer Voltage 183.4 Filament Transformer Voltage 58 o 6 Displacement 13 Averaging exposures 4,5, and 6 we get: Plate Transformer Voltage 177. 6 Filament Transformer Voltage 58.6 Displacement -14 An increase of 1 volt on the plate transformer causes an increase of 4.7 x 10-'I- fringe-widths. for the correction factor used. This is the basis ( 3) Densitx Correction From the data given in the following pages, we obtained the averages of the densities and the displacements for exposures in different positions on the plates. These are the results: Density in m.m. Displacement in of wedge fringe-widths End exposure 51.0 20.9 X 10-"t- Second exposure 45.4 17.6 Third exposure 40.9 16.8 Fourth exposure 37.9 16.0 Fifth exposure 36.8 15.1 Middle exposure 35.4 16.2 These ·are plotted against each other and a straight line drawn through the points. An increase of 1.0 m.m. of wedge -4 cor•responds to an increase in displacement of about 0.4 x 10 fringe- 1rddths. This and simila r date from the October run forms the basis for the density correction. (4) ~ of Janu ary 1930 Outer~ Temperat ure (In de g1.,ee s Centigrade) Time Jano 6 7 8 9 10 11 12 13 14 12:30 26 .7 26.7 26.8 2 6 .9 26.8 26.8 26.6 26.8 26.7 3:30 .8 6:30 .7 9:30 12:30(noon) .7 3:30 .7 6 :30 .4 .8 .8 .5 .7 .6 .8 .8 .7 .9 .8 .9 .6 .7 .7 .8 .7 .7 .8 . .8 .7 .8 .7 .7 .8 .7 .6 .7 .7 .8 .8 .7 .7 .6 .7 .7 .6 .9 .8 .7 .7 .8 .8 .7 .8 9 :30 .9 .6 Inner Room Temperat ure (In de gre e s Centi gr a de) Time Jan. 6 7 8 9 10 11 12 13 14 12:30 26.8 26.8 26.9 27.0 26.9 26.8 26.9 27.0 26.8 3:30 6 .9 6 :30 6 .9 6 .9 6 .9 6.9 6 .9 6 .9 6.9 6 .9 6 .9 9 :30 6 .9 6 .9 6 .9 6 .9 12:30(noon) 6 .9 6 .9 6.9 6 .9 6 .9 6.9 6.9 6 .9 6 .9 3:30 6.9 6 .8 6 .9 6 .9 6.9 6 .9 6 .9 6 .9 6 .9 6 .9 6 .9 6 .9 6 .9 6 .9 7.0 6 .9 6 .9 6 .3 6 .8 6 .9 9 :30 6 .9 6 .9 6.9 6 .9 6.8 6 :30 6 .8 6.8 (5) Interferometer Bath Temperature The left hand figures give the temperature at which the bath heaters went on and the right hand ones the temperature All temperatures are in--1... of 1000 at which they were shut off. a degree Centigrade. Time Jan. 6 8 9 10 11 12 13 14 6 6 7 7 4 6 6 6 7 8 6 7 7 7 7 7 7 7 7 7 7 7 12:30 6 6 3:30 6 6 6:30 - 9:30 6 12:30(noon) 6 6 6:30 6 6 9:30 6 6 6 6 6 - 66 7 6 7 - 7 7 7 6 6 5 6 7 7 6 8 6 6 - 66 6 6 5 6 . 6 7 5 7 - 5 6 6 4 6 6 7 6 7 6 8 5 7 7 8 6 8 6 7 6 3:30 7 7 - 6 8 - - 6 - 6 Lamp Bath Temperature ( In degrees Centigrade) Time Jan. 6 7 12,30 8 9 10 11 12 13 14 60.4 60.0 60.0 60.l 60.2 60.0 60.0 3:30 6:30 .5 9:30 .4 12:30(noon) .4 .2 .3 .3 .3 .4 .2 .5 .o .o .2 .o .3 .1 .4 .3 3:30 6:30 . 9:30 .4 .o .2 ( 6) Atmospheric Pressure (In inches of mercury) Time Jan. 12:30 6 7 29.-- 8 9 .31 .40 10 .12 11 .16 .12 3:30 6:30 .37 .39 .13 .04 12 13 14 .40 .30 .33 .38 .21 .30 .40 .32 .28 .36 .31 9:30 .22 .43 .40 .16 12:30(noon) .20 .40 .32 . LL .12 .36 .36 .28 3:30 .18 .39 .22 .10 .13 .26 .34 .28 6:30 .22 .41 .18 .13 .22 .24 .34 .28 9:30 .28 .12 .18 .26 .34 .28 In the next table, the figures in() are not actual readings but the means of two exposures before and after that one. The densities and voltages correspond to the exposures used. (7) Displacements (In 10- fringe-widths) 8 9 10 11 12 13 12:30(noon) (18) 40 19 66 10 -12 -10 44 21 44 48 13 7 28 -14 29 46 21 5 21 25 19 36 28 18 32 -11 47 24 42 50 30 11 -22 16 -5 21 53 24 29 6 22 17 49 48 65 1 11 22 32 30 15 37 30 -3 -19 3 57 9 5 21 14 0 .43 (30) 32 21 24 5 -9 26 (30) 53 20 25 1 (-13) 17 (30) 36 53 41 6 (-14) 10 (30) 27 25 21 0 -31 ( 10) 19 (33) 34 12 0 -14 (10) 14 (33) 8 26 -4 -20 -7 17 27 10 8 10 12 21 25 43 16 32 -13 36 11 -5 30 21 8 11 15 -9 44 42 39 22 0 10 23 43 27 43 12 -o ... 29 21 17 39 22 12 -31 38 9 39 46 44 6 -1 57 18 36 (44) 19 -4 -29 -10 41 19 (44) 47 6 23 24 Time 6:30 Jan. 6 4 7 (8) Displ a cements (In 10--t frin ge-widths) Time Jan. 12:30 (midni ght) 6:30 8 9 10 11 12 17 45 (44) 40 -6 3 -13 -22 32 (44) 3 (-8) 24 33 17 44 26 29 (-8) -7 19 8 52 65 30 -20 -10 18 28 8 37 20 -13 -26 3 26 37 44 12 1 -28 -34 40 18 17 33 -13 16 13 41 49 21 18 20 -30 5 26 62 38 14 5 -9 -9 52 16 0 37 -8 -20 12 36 26 26 10 28 -13 27 47 (24) 56 40 21 -19 45 (32) (24) 32 (26) -31 -4 9 (32) 38 37 33 19 -8 -48 16 17 39 22 -30 -10 -58 28 8 61 45 -4 3 -10 27 15 20 21 -11 -13 -41 25 51 36 13 -11 -27 -10 11 10 13 6 12 -8 -18 24 17 51 (13) -12 -18 -20 16 58 10 (13) -1 -8 -2 46 50 36 (13) 24 3 (-10) 28 (43) 39 (13) -16 -12 (-10) 38 (43) 33 22 -22 7 13 -20 14 -8 (9) Density ( In m.m. of wed ge) Time 12:30 (noon) 6:30 J an. 6 8 9 10 11 12 13 64 120 112 35 74 11 16 69 114 80 29 62 14 24 68 105 52 24 52 9 21 55 103 44 35 54 10 27 60 103 44 28 46 9 24 54 100 50 36 50 8 32 60 91 45 34 45 8 30 50 92 52 47 47 11 36 55 87 47 37 44 11 38 46 55 56 55 44 21 46 66 55 54 55 34 26 38 43 55 79 70 35 35 38 101 55 157 103 39 31 33 78 104 95 73 24 33 35 65 72 95 34 23 28 30 39 62 96 32 30 28 37 36 50 50 22 31 21 32 52 31 28 32 22 35 35 45 27 18 29 18 31 23 45 18 18 36 13 36 30 40 23 12 31 10 24 22 38 21 16 35 16 26 34 33 47 14 35 14 21 27 36 47 12 40 19 22 32 7 -... (10) Density ( In m.rn. of wedge) Time Jan. 12:30 7 8 9 10 11 12 13 14 23 44 47 12 43 21 51 36 53 47 19 35 25 49 31 52 103 19 35 24 37 31 52 40 25 30 26 36 34 43 27 27 25 23 25 28 45 23 30 31 24 27 29 42 13 26 30 19 17 23 43 20 30 38 23 21 28 36 15 34 31 15 16 22 48 24 47 31 18 28 66 27 70 43 12 19 59 64 44 117 56 14 27 64 64 22 56 11 66 53 64 83 30 16 17 62 52 82 58 32 22 12 49 44 76 46 40 25 22 48 43 71 36 39 24 18 42 47 69 42 41 31 27 44 48 78 37 40 26 23 36 43 67 39 45 44 30 42 45 78 32 46 44 34 36 39 73 46 54 44 37 36 40 74 67 51 44 41 36 40 84 67 67 43 51 21 41 (midni ght) 36 6:30 -- (11) Plate Transformer Voltage (From recording voltmeter) Time 12:30 Jan. 6 8 9 10 11 12 13 163.2 2.2 3.4 2.7 2.6 1.8 2.4 3.2 2.1 3.8 2.8 3.0 2.7 2.4 3.0 2.2 3.2 2.8 2.8 2.6 2.4 3.9 3.0 2.5 2.6 3.0 2.8 1.3 3.8 2.7 2.7 2.8 3.0 2.6 1.4 3.9 2.2 3.0 2.8 3.0 2.7 1.3 3.9 2.4 3.0 2.3 2.9 2.1 1.4 3.8 2~3 3.1 2.7 3.0 2.3 1.4 3. 6 2.7 3.7 2.8 3.1 2.5 1.5 3.8 2.8 3.2 3.8 3.0 2.7 1.4 3.7 2.8 3.2 3.5 2.7 1.8 1.4 3.7 2.8 2.9 3.0 2.9 1.5 1.4 3.7 2.8 3.2 3.0 2.8 1.4 1.5 3.6 3.1 3.1 3.0 2.8 1.3 1.4 3.6 3.0 3.1 3.0 2.4 1.4 1.4 3.5 3.2 3.1 3.2 2.2 1.5 1.3 3.5 3.2 3.2 3.1 2.4 1.4 1.4 3.5 3.3 3.5 3.2 2.5 1.4 1.5 3.6 3.5 2.9 3.1 2.5 1.5 1.3 3.5 2.8 2.6 3.1 2.7 1.8 1.3 3.0 3.1 2.1 2.9 2.3 1.8 1.2 2.5 2.5 1.8 2.7 2.1 1.8 1.1 2.5 2.4 2.1 2.4 2.5 1.3 1.3 2.4 2.8 2.1 2.7 2.8 1.3 1.2 7 (noon) 6:30 (12) Plate Transformer Voltage (From recording voltmeter) Time Jan. 12:30 7 8 9 10 11 12 13 14 2.4 2.5 2.1 2.7 2.4 1.4 1.3 2.7 2.2 2.1 2.7 2.3 1.6 1.2 2.0 2.5 2.0 2.7 2.3 1.8 1.2 1.7 2.5 2.5 2.8 2.0 2.0 1.2 1.7 2.5 2.5 2.7 2.1 1.9 1.4 1.6 2.6 2.5 1.8 2.1 1.2 1.4 1.6 2.4 2.5 1.5 2.0 1.8 1.5 1.6 2.3 2.5 1.2 2.1 1.3 1.5 1.8 2.3 2.5 1.2 1.9 1.7 1.3 1.7 2.1 2.4 2.1 1.7 2.2 1.5 1.7 2.2 2.3 2.3 1.7 2.5 1.4 1.8 2.4 2.0 2.5 1.8 2.4 1.6 2.2 2.4 1.8 2.5 1.7 2.5 1.4 2.2 2.8 2.5 2.5 1.6 2.6 1.1 2.7 2.3 2.7 2.8 1.5 2.5 1.0 2.5 2.6 2.9 2.0 1.5 1.9 1.0 2.6 2.2 2.9 2.6 1.6 1.9 0.8 2.5 2.4 2.1 2.7 1.8 1.9 1.0 2.5 2.6 2.5 2.6 1.7 2.1 o.8 2.5 3.3 2.6 2.7 1.7 2.7 G.8 2.0 2.7 2.7 2.7 1.9 2.6 o.9 2.4 2.8 2.@ 2.7 1.8 2.6 o.9 3.0 3.2 2.6 2o7 1.8 2.5 o.9 2.8 3.2 2.6 3.0 1.6 2.5 o.9 (midnight) 6:30