f^a-^ry^-mi NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS TECHNICAL MEMORANDUM 1371 APPARATUS FOR MEASUREMENTS OF TIME AND SPACE CORRELATION By A. Favre, J. Gaviglio, and R. Dumas Translation of "Appareil de Mesures de la Correlation Dans le Temps et L'Espace.* La Recherche Aeronautique No. 31, Jan. -Feb. 1953. ■^SITY OF FLORIDA ^;; DEPARTMENT GAINtSMU£,a326//.rono'SA Washington April 1955 2^of 'rW3 ~^'ioin(^ NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS TECHNICAL MEMORANDUM 1571 APPARATUS FOR MEASUREMENTS OF TIME AND SPACE CORRELATION*! By A. Favre, J. Gavlglio, and R. Dumas SUMMARY These researches are made at the Laboratoire de Mecanique de 1 'Atmosphere de I'l.M.F.M., for the Office National d'Etudes et de Recherches Aeronautiques (O.N.E.R.A.) ^ with the aid of the Ministere de I'Air, and of the Centre National de la Recherche Scientifique (C.N.R.S.)» We have alxeady explained in previous communications (refs. 1 to 22) the principle and have given description of the apparatus for statisti- cal measurements of time and space correlation between two random vari- ables considered with a relative delay T in time, which we have designed with a special view to the study of tiorbulence. We shall briefly review now the improvements brought to the experi- mental apparatus, the control of the measurements, and a few particulaj* applications . EXPERIMENTAL APPLIANCES Wind Tunnel (Refs. 2, 5, ^4-, 6, 12, and 15) The low- turbulence wind tunnel. Installed indoors, has been trans- formed (fig. 1). The test section A is 80 x 80 X 270 cm; the cone B with low gradients has a contraction ratio of 15- It is preceded by a settling chamber C, in which are set five removable damping screens, and by a rapid expansion diffuser D with a screen analogous to those of the low-tvirbulence wind tunnel of the R.A.E. (ref. 25). The intensity of turbulence is of the order of 0.00210 with the diffuser screen and *"Appareil de Mesures de la Correlation Dans le Temps et L'Espace." La Recherche Aeronautique No. 51, Jan. -Feb. 1955, PP- 57-^' -'-A Commiinication to the 8th International Congress on Theoretical and Applied Mechanics, Istanbul, Aug. 1952. NA.CA TM 1571 of 0.00150, 0.00090, 0.00055, 0.00014-5, and O.OOO58 with 1, 2, 5, ^, and 5 damping screens, respectively. At the entrance of the test section may be placed one of the two tiorbulence grids similar to those of the NBS with elements of O.626 inch and 0.196 inch in diameter and with meshes M of 5 lA inches and 1 inch, respectively. A flat plate of 1,9^0 x 80 cm can be set in the test section for the study of the boiindary layer . Hot-Wire Anemometers (Ref s . 2, 3, 5, 7, 8, 11, I7, and 20) Two hot wires can be moved along the axis X^ of the test section and along the orthogonal axis X5 . The amplifiers reproduce the oscillations with an approximation of ±6 percent in energy and for the band pass 1 to 6,000 cps, more recently, for 1 to 3,500 cps with tk percent. The compensation is made by the sqiiare waves method. Figure 2 shows the two amplifiers A, the power supplies B, the square waves generator C, and a generator of sine waves from 0.6 to 30,000 cps D. Apparatus for Statistical Measurements of Time and Space Correlation (Refs. 1, 2, 3, 5, 8, 9, 10, 11, and I3) The apparatus records simultaneously and reproduces with a relative delay T the two voltages coming, for instance, from the two anemometers and measures the time- correlation coefficient (refs. 1, 2, and 5). It must be borne in mind that, for this measurement, it is necessary and sufficient that the phase shifts of the component waves due to the inevitable transformations should be identical in the two channels for each frequency; the difference T of the delays systematically intro- duced being the same for all the frequencies . The voltages are recorded on magnetic tape: (a) directly for the waves of frequencies comprised between 200 and 2,500 cps NACA TM 1571 5 (b) on an amplitude modulated wave of 5,500 cps frequency, demod\ila- ted after reproduction, for the waves of frequencies comprised between 1 to 25 cps (c) by overlapping of the two devices from 25 to 200 cps. The band pass is therefore unbroken from 1 to 2,500 cps (refs. 8, 9, 10, and 11) , The apparatus consists of (fig. 2): The two recording preamplifiers E, with a common oscillB.tor of 3,500 cps, and on either channel the networks effecting the division of the respective spectra into waves of 200 to 2,500 cps for direct recording, of 1 to 25 cps for modulation of the 5>500 cps carrier, and of 25 to 200 cps for the aforementioned overlapping The two recording amplifiers F (with appended oscillators of 80,000 cps and of i+0,000 cps) and their power supplies G The two magnetic recorders-reproducers H, one of which has a device I for adjusting the length of the tape between the recording and play-back heads and, consequently, the delay T (refs. 2 and 5) The two play-back preamplifiers F The two play-back amplifiers J, with their networks effecting, after the detection of the carrier, the reconstitution of the initial spectrum on each channel The two power amplifiers K which, after adding on one hand and subtracting on the other, supply the thermocouples; the output voltages of these thermocouples represent the mean squares M^^ of the sum and Mh of the difference, respectively (Dryden method); two extra amplifiers for the oscilloscope The apparatus L, which gives the sum and the difference of M^ and M-)-, (and will soon reckon their quotient), together with an oscil- lator for 20, 200, 1,000 cps, by means of which may be effected a sup- plementary control of the phase and energy response of the two channels during the process of measurements; this oscillator is also used for the measurement of the delay T The power supplies N; the oscillograph 0; the galvanometer M with adjustable period (5 sec). The equality of phases on the two channels is checked for each frequency (refs. 2 and 3) • NACA TM 1571 When the two voltages correspond to two variables measured at two different points of space, one obtains the coefficient R of time and space correlation. In the particular case when it represents the same variable measured at the same point of space, one gets the autocorrelation coefficient from which the spectral function can be deduced. Spectral Analyser (Ref s . 9, 10, 15, Ik, 15, and l6) A selective feed-back ajnplifier has been designed in order to deter- mine the spectral function directly, apart from the autocorrelation method. The band-pass is in width 4.5 percent of the median frequency chosen for frequencies comprised between I.5 and 2,500 cps. The energy is measured by means of a thermocouple and a long-period galvanometer (19 sec). COIWROL OF THE MEASUREMENTS (REFS. 2 to I7, AND 21) I. The response curve of the amplifiers of the hot-wire anemometers (ref. 7) has been determined as regards energy and phase by means of sine waves and square waves of variable frequencies, and so has the band-pass of the spectral analyser. II. The total response curve of the apparatus for measurements of time correlation, together with the hot-wire anemometers, has been estab- lished with sine waves of variable frequencies, as regards the energy (fig. 5), the equality of phases on the two circuits for each elementary oscillation (refs. 2 and 5) (the delay T being a multiple of the period), and the autocorrelation function (refs. 2 to 15)- The energy is constant, variations not exceeding ±l6 or 19 percent of the standard deviation 0.05 for 1 to 2,500 cps (refs. 2 to 16) . Frequent checkings are made in the course of measurements especially in the case of 20, 200, and 1,000 cps oscillations frequencies. III. The spectra are obtained on one hand by Fourier transform of the autocorrelation curves and on the other hand directly by means of the spectral analyser and are then systematically compared. These measurements are made in the case of turbulence downstream of a grid NACA TM 1571 (refs. 9, 10, 15, 1^, and 2h) and also in the case of a boundary layer of a flat plate (examples: figs. ^4-, 5, and 8) (refs. I5 and 2k) e spectra are satisfactorily concordant from 5 "to 2,000 cps 4). Thes now (fig. 4) rV. The vibrations of the hot-wire holders (ref . 2) and of the tiinnel walls (ref. W) have been examined and reduced; their effects are watched with the oscilloscope dioring the experiments. The effect on the measiorements of the acoustic resonances has been found to be negligible (refs. 6 and 12). V. Comparative measurements have been made (refs. \, 6, 9, 10, 12, and 15) at each stage of the transformations of the wind tunnel: (a) Length of the test section reduced from 400 to 270 cm, contraction ratio of the cone increased from GX to I5, the new settling chamber placed behind the diffuser with its screen, and five damping screens inserted successively in the bulge (b) Installation of the first paj-t of the retxirn circuit with two corners with vanes (c) Size of the test section reduced from 80 x 80 cm to 80 X 40 cm (ref. I5) . These comparisons have not shown any appreciable changes in the results from one stage to the other, as regards the turbulence behind a grid. One must except, however, the influence of the initial turbulence and, consequently, of the damping screens, which is very important in the case of the boundary layer and the shape of the grid. VI. The comparison of the time correlation curves, obtained with different hot wires, disclosed appreciable differences for wires of the same diameter and especially for wires of different diajneters . The improvement of the compensation by the squaire-waves method has made it possible to reduce those differences (fig. 6) (refs. 10 and 13). Aerodynamic taring attempts of the hot-wire anemomenter are in progress, the wire being placed in the field of a propeller (refs. I7 and 20) . The measurement errors seem to be mainly due to the hot wires; the comparative experiments are preferably made with practically identical wires . NACA TM 1571 VII. The results obtained for the turbulence behind a grid with the apparatus for time and space correlation measurements : transversely, i.e. at several distances Xj (refs. 9> 10> I6, 21, and 2k) longitudinally, i.e. at several distances Xi (refs. 1^, I6, and 21) the delay T being zero and agreeing with the results con- cerning the transverse and longitudinal space correlations ^ and f, respectively, (example: fig. 7) (refs. 9^ 10^ 21, and 2k). VIII. The comparison of the spectra (fig. 8) (refs. I5 and 2k) with those of H. L. Dryden (NBS) and of F. G. Simmons (NPL) established for the t\irbulence behind a grid in quite similar conditions is satisfactory. The measurements have been especially developed up to I.5 cps . The comparison with A. A. Townsend's spectra (ref . 22) is also satisfactory although the experimental conditions are slightly different. IX. The qualitative comparison of the spectra established for the turbulence of a flat-plate boiindary layer (fig. 9) (ref. I5) with those of A. A. Townsend is fairly satisfactory, although the experimental conditions present some differences (ref. 25). A FEW APPLICATIONS OF TIME CORRELATION MEASUREMENTS Among the applications which can be made of time- correlation measiore- ments between two variables or of autocorrelation for one variable, and, in addition, to those concerning the turbulence studied elsewhere (ref. 22), we shall mention some other experiments (refs. I8 and 19)- Application of Time Correlation to the Relative Increase of a Periodic Signal Disturbed by a Random Parasite (refs. 3, 18, and 19) 1. In a previous paper (ref. 3) we have considered the coefficient of time correlation R]^]^ 22 between two signals uj^ and U2 disturbed by two parasites e^ and 62, respectively, and the coefficient of time correlation Rj^q 20 between the nondisturbed signals^ and noticed that, if one can choose a delay T, such as the time correlation coefficient between the parasites and between the signals and the parasites, to be negligible With ui = U2 = e2_ = £2 = 0, q-^ = ^±/^±^} '^2 - ^2^ ^2 MCA TM 1571 u^eg = e 1U2 = u-^e-^ = U2e2 = £162 = (l) one finds that Rll,22 = 1^10,20 lAl^/l/(^ + I1) (^ + ^12) The coefficient of time correlation between the disturbed signals is proportional to the coefficient of time correlation between the non- disturbed signals, when the delay is such that the coefficients of time correlation between the parasites and between the signals and the parasites are zero . With periodic signals and random parasites, condition (l) is easily fulfilled; thus, these signals can be detected. With sine waves of the same frequency, the coefficient of time correlation R]_i 22 °r o^ auto- correlation Rxi 11 will be for appropriate delays a sine wave of the same frequency, which will constitute a time detection of these signals (ref. 18). In the case of a single signal, it may be preferable to replace the autocorrelation Rix ]^]_ by the time correlation B.-^^^ 12 with an iden- tical signal disturbed by a less intense parasite. 2. We have made trials of the detection of a sine wave by autocor- relation (refs. 18 and 19). For example, figure 10 (ref. I9) shows the autocorrelation curves of the parasite alone — the spectrum of which stretches mainly from UOO to 1,100 cps — and of the signal of ~ 6OO cps distiirbed by the parasite . It may be seen that, for a delay T superior to 8 ms, the latter is close to the sine wave of ~ 60O cps of amplitude O.k. Other tests have enabled us to verify the above formula and to detect the presence of the signal for very small values of q with a great sensitivity (ref. 19) . 8 NACA TM 1371 Reduction of Parasites Ratio With Reference to Disturbed Phenomena by Addition With Delay (Ref s . 18 and I9) 1. Let ut be the variable representing a phenomenon disturbed by a parasite e-^. Let us add the disturbed variable to itself with a time delay T; we then have^ Q ^ ^ + %0,10 ^ 1 + f'oi^oi Thus, it is possible to reduce the parasite disturbing a phenomenon by addition with delay. This reduction will be at its maxim\im when T is such that the ratio of the autocorrelation coefficients of the phenom- enon, and of the parasite, to both of which the unity has been added, will be at its maximum. In the case of a periodic variable u-t and of a random parasite, one may take a delay multiple of the period and such as Roi,oi«o then, Q, - »2 <1 It may be preferable to filter the parasite so that, for a T multiple of the period, one should have ^01,01 then '■> 1 The operation may be repeated in series, choosing the optimum delays; one may also make several additions in parallel with optimum delays . \ith £^2 = et+T^, ut2 = ut+T2, q = u^^U^^ , Q = (ut + n^+^f/[e^ + et+T)2 NACA TM 1571 9 2. We have made (ref. 18) some measurements, using a sine signal of frequency n and, for the parasite, the above-mentioned tiorbulent veloc- ity fluctuations . For a delay T such that ^01,01 - and ^10,10 ~ 1 n 157 180 210 500 570 570 570 Q/q 1.90 1.97 2.0^ 2.41 2.0i+ I.9I 2.22 the mean value 2.08 approximates the theoretical value 2. For a delay T such that 1^01,01 ~ -0-5 and ^10,10 ~ 1 and n = 80, the ratio Q/q reached 4.25, 4.52, and 4.42, slightly above the theoretical value 4. Translated by A- Favre 10 NA.CA TM 1571 REFERENCES 1. Favre, A.: Appareil de mesures statistiques de la correlation dans le temps. VI° Cong. Intern. Mecan. Appl . 19^6, Paris. 2. Favre, A.: Mesures statistiques de la correlation dans le temps. VIJO Cong. Intern. Mecan. Appl. 19^8, Londres. 5. Favre, A.: Mesiires statistiques de la correlation dans le temps. Premieres applications a 1' etude de mouvements turbulents en soiifflerie. 28/2/i)-9. k. Favre, A.: Perfectionnements a la soufflerie pour obtenir une tres faible turbulence. I5/7/U9, 5. Favre, A.: Mesures de la correlation dans le temps et I'espace en aval d'une grille de turbulence poxir la composante longitudinale de la Vitesse. 15/7/14-9. 6. Favre, A.: Etude sommaire de I'effet sur la turbulence des resonances acoustiques. 15/7/14-9. 7. Gaviglio, J.: Etude d'anemometres a fils chauds . 15/7/^9* 8. Favre, A.: Nouvelles mesures de correlation dans I'espace et le temps en aval d'une grille de ttirbulence avec appareillage modifie. 51/12/49. 9. Favre, A., Gaviglio, J., and Dumas, R.: Mesures de la correlation dans le temps et I'espace et spectres de la t\irbulence en soufflerie. Coll. Intern. Mecan. 1950^ Poitiers. Publ. Sc. et Techn. Minist. Air no 251. 10. Favre, A., and Gaviglio, J.: Mesures de la correlation dans le temps et I'espace, et spectres de la t\irbulence en soufflerie (develop- pements ) . 30/6/5O . 11. Favre, A., and Gaviglio, J.: Perfectionnements a 1' appareillage de mesures statistiques de la correlation dans le temps et I'espace. 50/6/50. 12. Favre, A., and Gaviglio, J.: Etude de I'effet sur la tiirbulence des resonances acoustiques. Influence des modifications de la soufflerie, 50/6/50. 15. Favre, A., Gaviglio, J., and Dumas, R.: Correlation dans le temps et spectres de la turbulence en veine reduite. Controle des mesures. 51/12/50. NACA TM 1371 11 Ik. Favre, A., Gaviglio, J., and Dumas, R.: Correlation dans le temps et dans I'espace longitudinalement en aval d'une grille de turbulence. 51/12/50. 15. Favre, A,, Gaviglio, J., and Dumas, R.: Mesures dans la couche limite des intensitels de turbulence, et des correlations dans le temps; spectres. 31/5/51' Coll. Intern. Mecan. Marseille, 3/1/52. lo. Favre, A., Gaviglio, J., and Dumas, R.: Correlation dans le temps et dans I'espace: transversalement, transversalement et longitudinale- ment avec retard compensateur du mouvement d' ensemble, en aval d'une grille de turbulence. 5O/6/5I • 17. Gaviglio, J.: Essais de tarage d'\in fil chaud dans le champ d'une helice. 50/6/5I. • 18. Favre, A., and Gaviglio, J.: Detection de signaux periodiques perturbes par des parasites aleatoires par autocorrelation. Coll. Nat. Me'can. Marseille, 3/1/52. • 19. Favre, A., and Gaviglio, J.: Applications des mesures de correlation dans le temps a la reduction des parasites aleatoires par rapport a des signaux periodiques. 12/7/52. 20. Gaviglio, J.: Nouveaux essais de tarage d'un fil chaud dans le champ d'une helice. 12/7/52. 21. Favre, A., Gaviglio, J., and Dumas, R.: Nouvelles raes\ires de correlation dans le temps et I'espace, longitudinalement, transversalement, longitudinalement et transversalement en aval d'lone grille de turbulence. 12/7/52. / 22.. Favre, A., Gaviglio, J., and Dumas, R.: Quelques mesiures de correlation dans le temps et I'espace, pour la turbulence en soufflerie. VI 11° Cong. Intern. Mecan. Th. et Appl., Istamboul 1952. Recherche Aeronautique no 52, 1955- J.A.S. 25- Schuli, H., and Winter, K. G.: Investigation of the Turbulence Characteristics of an Experimental Low Turbulence Wind Tunnel. Vlio Cong. Intern. Mecan. Appl. 19^8, Londres. 2h. Dryden, H. L.: A Review of the Statistical Theory of Turbulence. Quart, of Appl. Math., Vol. 1, no. 1, April 19^5. 25. Townsend, A. A.: The Structure of the Turbulent Boundary Layer. Proc. Cambridge Phil. Soc, Vol. hrj , Pt . 2, 1950. 12 NACA TM 1371 Figure 1.- Low -turbulence wind tunnel. Figure 2,- Apparatus for measurements of time correlation. NACA TM 1571 15 1 c c 000^ >| ^ f^ — ■" /- — ^^ •^^ -• — •- ^ 009 xt — •- • • / i .' Pr >: OOi. i \. •'xj- >s ^?^ > ?*•••> /• \ ^ -< N 'C » '5 u c b X t-t 5 u U '.\ S V \ I / /■ 1 1 1 V 1 \ V \ \ \ \ \ • • • / • ■/ r r * • ( •" ^ • ' I V V •A 1 V •\. • __ Li >i-_ ^ ^_ ^_ ^^ ^^ __ Lj ^^ ^^^ ^^ <;o 0) m CD o ^1 O o CD W O cu ^1 a w c CO CD ^( ho 11+ NACA TM 1571 u o u o [in II o a u cu m (D O -a < o S 2 O O o ^•^ a; «^ T3 • t-H hD m O O LO •a f^ •1-1 '^r 0) II H CD Q NACA TM 1571 15 o 0) u m 0) •a I — I u CD o CD T3 p CTJ o :=! c/: CD TO •■*H > U CD 73 O O O CD CD CD c^ Xi JZ! CD tt; a " CD th S=! ^ m -O 8 < ^ y>b 1 CD >^ 1 ure 5. of aut turbul wall, ha 't-i S Ph 16 NACA TM 1371 Velocity = 12.20 nrps; M = 1 inj Distance to grid = lj-0 M Semiempirical conipensation |R(T U^■^•o T 1 - . . - Wire I > Diameter = 7 microns -' n Wire II J \ - UiT-f" TT \ 1 — 1 5 — r- L^ 1 1 1_J cz 1S iZ] i—i 1 , _ _ 3° _ _ _ _ ^ _2S z _ _ _ 30 I _ _ _ 35 I J L u 40 J _ _ T I1 R I: (T Velocity = 12.20 mpsj M = 1 in; Distance to grid = 40 M Wire Diameter = k microns 05 I ^ A Wire Diameter = 7 microns >t* rr _ f<^ 10 15 ^ A 13 as
    (b) HPL 0.001 0.01 0.1 0,01 ,. 0001 10 0.001 001 I; ^?i 10 (c) IMA square vave compensation, (d) j^ semlempirical ccoipensation. Figure 8,- Comparison of turbulence spectra downstream of a grid obtained at NBS, NPL, and LMA. NACA TM 1571 19 \ ^(^1 k a 'ot A • 5 = 0028 + C = 0020 O 5 = 00115 X 1=00073 A I = 00032 a 5=00007 iox j+4d-x— H^. o— X- 30 F Ei n) - — A (a) Tow 3 en 2 d. U Xj Ji - 6 ~' cm. ■ 2i ^ i^ ^ S i - 9. J ^- y A 15 mm A 3 mm 7 6 mm T 12 mm 006 012 .^ 025 — 050 —\ 075 100 — 562 p^ H i . — *■ o • 24 mm 135 mm — 1 4 tf^' ^4 IS — ■ — >-t\r 1 1 /ri^ i—'-l^^!"^ g.o- l^t% « — tT~" 1 1" 1^ -^ -♦A"-" — --of-- 4^\ - -Si* V" '&. ^ "^1: , - - — — -- — 1> ■^ — :^ h "-'-'- ^»- ^»sr ^'■^ ' ' — 1 5" *»"»ii-l- ixbx *0 f>i "> > "O « K«0>p «o W) Figure 9.- (b) IMA ]^ = 766000. Comparison of turbulence spectra in flat -plate boundary layer. Presented as a function of distance from the wall. 20 NACA TM 1371 CD ■i-i w u o T3 ^1 CTJ >> w •I-i I — I d ho (D a o •t-t +-> o 0) -t-J 0) Q I o T— I fciO NACA-Langley - 4-7-55 - 1000 CO -J M CO '"' D" a n c e x: CO o s •a c OJ •-s K OJ r a aT 3 .2* CO b c" •-5 o m 0) >> T3 O > o > CO s 3 < K U < n1 3 rt C O u CO k. a w -^ T3 3 5 < H S- < < g< U S ft < rt 0. ZZ< 2 3< •a g - _ o,t-i •;:§•£ 2< . a* W S -„- ' b "j t. a) eg f- TO I— I r* L, m CO . i to . -^ -^ a. m ^ bi ^ ■ 6 2 t< 3 < ' "- " to -g 2 H i; to (S . 5 " C 2 c •" ,-, 0) S ." << ■" K Q O o w4? 031 _ bD I a> ci < CC a c: 1 . o to ' -— < Q) ^ tS T3 QJ eg ^ J. "3 « ' n! ^ m a) to (U ^O c to £ , >-a ' u rt o 3 I T3 "^ -^ . C4 to <— < £ 3 O I m ^ >> rt 3 *§" •2 rt I. C c bo -° C M .,- 0) 0) <: aT3 c a o a ^■3 2 « < z E o 3 CO rr 0) (h 01 X to CJ £ TJ C 0) < >~i £C CO s u x: u x; c tu" .1 CO in fa -^ '. c- G CO •-3 a tH -o to t. oT u > "3) > mas, CA T Rec 3 01 rS tS 3 < S:o ft o . CO U 1-5 aJ T3 § g < - . 2< am — ' am <05 m — a<^ ti < a> tM t- u. in " en -^ -"s H w^ u 3 ■< a U ,»-J= nt "! a C c r a to a X t- c cj bD Lh Q) a (1) S^ , o to = £ " = * u 2 * o o ^ to to d) -Q dJ S a " S £ to = t; > T3 to o c . ta u rt OJ 0) g-S = " ego; C ^ 3 o ^ P 3 c o < J= • I" a a 0) P 3 •o -^ (« to >» £ 3 o ta 3 III ^ c "^ 'C £ 6 ■° 'C m <: aT3 £ to c °-2 a a o — 3 ■" o .2 S ^ 2 <« .S a < < 2 CO Q, M • 3 • ""I 0"t3i Q _o fc .2 S £5 CtJ < c ^ >. - ■a < fc CO d . r^ 0) in >-= . ^ i - M ^ £ 2 fc ? bo tn < CC 5,1 ca 3 < t«MU 5 " o ca 2 J <^ d -sa&> n -> <" ' 2 a; > - <:^ « £ to fc .» ,„• W OJ x .2 1 3 M « ° « ■D PK C ^ s < tional A PARAT ACE CC rrelatio Gavigli U < t« ft Q. . z 2<: wO'^ liJ . to lied 20 rom 953, n ex- elati a de nd a cal and App April 1955 Trans, f an. -Feb., 1 Bments to a space corr Included is urements a rt '-5 > T3 to 0! e^ ^ - t, CTJ Q; Q en '^ " £ £ 0) a, x"So t. 3 < a,- Of r ti rbu f th ons to -<.? made tus fc of tu trol c licati SK^S 3 ... ea >> c a ongi Stan OS. Bron 2 2 -o a nl 3 u «1 rief review mental app gned for st tion of the particular ^"o< ational hanics, rs., ph lerche -44). c bC u j- t- 0) rt S " -° Z « .2- > iiS^CC d