Wftrfr M- ^51Wi 
 
 . LEADOft 
 
 • RM E54G2Za 
 
 y 
 
 NACA 
 
 RESEARCH MEMORANDUM 
 
 RECOVERY CORRECTIONS FOR BUTT -WELDED, STRAIGHT -WIRE 
 
 THERMOCOUPLES IN HIGH-VELOCITY, HIGH-TEMPERATURE 
 
 GAS STREAMS 
 
 By Frederick S. Simmons 
 
 Lewis Flight Propulsion Laboratory 
 Cleveland, Ohio 
 
 UNIVERSITY OF FLORIDA 
 DOCUMENTS DEPARTMENT 
 120 MARSTON SCIENCE LIBRARY 
 P.O. BOX 117011 
 GAB4FM }..£, Fl 32511-7011 USA 
 
 NATIONAL ADVISORY COMMITTEE 
 FOR AERONAUTICS 
 
 WASHINGTON 
 
 September 24, 1954 
 
3f /of f?<f 
 
 NACA RM E54G22a 
 
 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS 
 
 RESEARCH MEMORANDUM 
 
 RECOVERY CORRECTIONS FOR BUTT-WELDED, STRAIGHT-WIRE THERMOCOUPLES 
 IN HIGH- VELOCITY, HIGH- TEMPERATURE GAS STREAMS 
 By Frederick S. Simmons 
 
 SUMMARY 
 
 Recovery corrections were experimentally determined for several 
 diameters of chromel-alumel and platinum 13 percent rhodium - platinum 
 butt-welded thermocouples in a gas stream at temperatures from ambient 
 to 2000° R and Mach numbers from 0.2 to 1.0. The recovery corrections 
 at various temperatures and pressures are reasonably correlated with an 
 empirical equation in which the correction is seen to be proportional 
 to the fifth root of the pressure and inversely proportional to the 
 fourth root of the temperature. 
 
 Probable errors in temperature measurement due to resultant uncer- 
 tainties in the corrections are presented and discussed. 
 
 INTRODUCTION 
 
 It is a familiar fact that a body immersed in a gas may attain 
 thermal equilibrium at a temperature other than that of the gas . For a 
 gas at rest or moving at a low velocity, this temperature is the result- 
 ant of a balance of convective heat transfer between the body and the 
 gas with the radiant and conductive heat transfer between the body and 
 the external surroundings. For a gas moving at a high velocity, how- 
 ever, an additional factor becomes important: the aerodynamic heating 
 effect, which is the result of friction and stagnation of the gas near 
 the body. 
 
 For temperature measurements involving the immersion of instruments 
 such as thermocouples in gas streams, corrections to the indicated tem- 
 peratures are frequently necessary, and usually the errors in the meas- 
 urements consist mainly of the uncertainty of the magnitudes of these 
 corrections. A bibliography of the subject is given in reference 1. 
 
 For conditions of high temperatures and high velocities such as 
 those encountered in jet-engine exhaust gases, the corrections for the 
 heat- transfer effects and for the aerodynamic effects are of the same 
 
NACA RM E54G22a 
 
 order of magnitude. Methods for the calculation of the former are given 
 in reference 2. The present work is concerned with the magnitudes and 
 probable errors of the latter and is part of a program of high- temperature 
 measurements being conducted at the NACA Lewis laboratory. 
 
 SYMBOLS 
 The following symbols are used in this report: 
 
 C-p specific heat at constant pressure 
 
 D diameter of wires 
 
 L length of wires 
 
 M Mach number 
 
 Pr Prandtl number 
 
 p static pressure 
 
 R gas constant 
 
 Re Reynolds number 
 
 r recovery factor 
 
 T total temperature 
 
 t static temperature 
 
 t = adiabatic temperature 
 
 v velocity of gas 
 
 A ^ tad 
 
 T 
 
 y ratio of specific heats 
 
 p density of gas 
 
 u viscosity of gas 
 
NACA RM E54G22a 
 
 ANALYSIS 
 
 The total temperature of a gas stream is defined by 
 
 The relation between the total temperature and the temperature of a 
 body immersed in the gas, for the case of zero heat transfer to exter- 
 nal surroundings, is usually given in terms of a recovery factor r, 
 which is defined by 
 
 r = tad ' t (2) 
 
 T - t V ; 
 
 or 
 
 v 2 
 *ad = t + r 2C" 
 
 where the adiabatic temperature t ^ is the temperature attained by the 
 body in the absence of external heat transfer. The recovery factor is, 
 in general, a function of the geometric configuration of the body and, 
 in order of decreasing importance, of the Prandtl, Mach, and Reynolds 
 numbers of the gas stream. A detailed discussion is given in refer- 
 ence 3. 
 
 For purposes of temperature measurement, it is more convenient to 
 deal with a ratio A defined by 
 
 A = ^ (3) 
 
 The relation of A and r is given by 
 
 A = (1 - r)(l - t/T) (4) 
 
 Since the ratio t/T is primarily a function of the Mach number, A is 
 a function of the Prandtl, Mach, and Reynolds numbers and of the geome- 
 try of the body. 
 
 Experience has shown that for the case of cylindrical wires in cross 
 flow, the Mach number becomes an important parameter and the function 
 may conveniently be assumed to have the form 
 
 A = f x (M, Pr)x(Re) n (5) 
 
NACA RM E54G22a 
 
 Substitution in the Reynolds number of the relations (ref. 4) 
 
 P = p/RT 
 v = mVtRt \ 
 
 n0.7 
 
 u oc T 
 
 (6) 
 
 J 
 
 shows that 
 
 Re oc 
 
 MDp 
 ipl.2 
 
 (7) 
 
 and A may be written 
 
 A = f 2 (M, Fr) D 11 -E 
 
 n 
 
 ml . 2n 
 
 (8) 
 
 If the Prandtl number is independent of temperature and pressure, equa- 
 tion (8) may be written 
 
 4 n 
 
 A= Aq 
 
 'JL 12 
 
 1.2n 
 
 D 
 
 where 
 
 n n n n 
 
 the subscript zero denoting reference conditions of pressure and tempera- 
 ture and a reference diameter. It may then be expected that for a given 
 wire diameter 
 
 '•stfrflr 
 
 0) 
 
 Similarly, at a given pressure and temperature the variation of 
 A with diameter should be represented by 
 
 A = Aq 
 
 D 
 
 (10) 
 
NACA RM E54G22a 
 
 From the definition of A, the total temperature T is equal to 
 the adiabatic temperature t ^ multiplied by a factor l/(l - A). 
 
 Since in practice A is much less than unity, this factor can also be 
 expressed as (l + A) so that A represents a fractional correction 
 factor. 
 
 The present work was directed toward determination of whether for- 
 mulas like equations (9) and (10) could adequately describe the depend- 
 ence of A upon pressure, temperature, and diameter and, if so, toward 
 evaluation of the exponent n. Considerable experimental data, accu- 
 mulated over a period of years in the course of other research work, 
 were analyzed for that purpose. 
 
 EXPERIMENTAL PROCEDURE 
 
 The recovery characteristics of thermocouples at elevated gas tem- 
 peratures were obtained from tests made in the high-temperature tunnel 
 described in reference 5 with a modified test section, shown schemati- 
 cally in figure 1. The modified test section consisted of three con- 
 centric Inconel cylinders 24 inches long, the outer one 6 inches in 
 diameter, the inner one forming a nozzle approximately 2 inches in di- 
 ameter. Gas flowed between the cylinders, and 12 thermocouples welded 
 to the inner surface of the inner liner indicated that this surface was 
 within a few degrees of the gas temperature under all conditions, thus 
 establishing that net radiation between the test thermocouples and the 
 surroundings was negligible. The gas temperature was measured with a 
 0.020-inch-diameter chromel-alumel thermocouple in the stagnation region. 
 Preliminary tests showed this thermocouple to indicate the same as a 
 high-recovery probe with a chromel-alumel thermocouple and as a plati- 
 num 13 percent rhodium - platinum thermocouple 0.020 inch in diameter 
 placed nearby, to within wire calibration accuracies. The temperature 
 was steady to within ±5 R, and no measurable gradients existed in the 
 stagnation region or in the nozzle exit. The pressure ratio across the 
 nozzle was measured with tubes in the stagnation region and in the plane 
 of the nozzle exit as shown. The Mach number was calculated by using 
 values for the specific heat ratio at the various temperatures obtained 
 from reference 6. The test thermocouples were butt-welded and tne junc- 
 tion reduced to wire diameter; they were installed with the wires ex- 
 tending across the jet as shown in figure 1. In all cases, a differen- 
 tial in temperature was measured between identical thermocouples in the 
 stagnation region and nozzle exit with a sensitive recording potentiom- 
 eter. The sizes of the wires tested were 0.032-inch- and 0.020-inch- 
 diameter chromel-alumel and 0.020- inch- and 0.010- inch-diameter platinum 
 13 percent rhodium - platinum. In these tests the variation of the 
 ratio A with Mach numbers from 0.2 to 1.0 was obtained at four ap- 
 proximate temperature levels: ambient, 1000 , 1500°, and 2000° R. In 
 all tests for a given wire, the gas temperature was controlled to with- 
 in +15° R. 
 
NACA RM E54G22a 
 
 To determine the effect of pressure on recovery characteristics, 
 chromel-alumel and platinum 13 percent rhodium - platinum thermocouples 
 of various diameters were installed in a similar manner and tested at 
 ambient temperature in a 3- inch air jet discharging into a receiver of 
 controlled pressure. In these tests, the Mach number was varied from 
 0.2 to 1.0 at the approximate pressure levels of 15, 30, and 50 inches 
 mercury absolute. 
 
 RESULTS AND CONCLUSIONS 
 
 Effect of Pressure and Temperature 
 
 The experimentally determined values of A at various temperatures 
 are shown in figures 2 to 5 and at various pressures in figures 6 and 7; 
 in each case, the values of A are plotted against the Mach number of 
 the stream. Analysis of the data gives an average value of 0-2 for the 
 exponent n in the expression obtained for A in the preceding section. 
 Upon substitution of this value into equation (9), the equation becomes 
 
 A=A (p/ Po ) 1 /5 ( To/T )lA (11) 
 
 The degree of correlation may be seen in figures 2 to 7 where the data 
 are presented as plots of A-, against M, Aq for this purpose being 
 taken as 
 
 P \ l/5 / T \ 1/4 , 
 
 '_ x (measured A) 
 
 P / VoJ 
 
 The correlation appears sufficiently good to justify use of equation (ll) 
 for purposes of temperature measurements. 
 
 Effect of Wire Diameter 
 
 The diameter effect is noted in figures 8 and 9, where the results 
 in tests on carefully welded and machined chromel-alumel and platinum 
 13 percent rhodium - platinum wires of various diameters at ambient 
 pressure and temperature are presented. Analysis of the data similarly 
 gives an average value of 0.2 for the exponent n in equation (10), 
 which becomes 
 
 A= Aq (d/Dq) 1 / 5 (12) 
 
NACA RM E54G22a 
 
 The correlation represented by equation (12) appears strictly applicable 
 only at Mach numbers below 0.8. However, use of the equation at higher 
 Mach numbers will not introduce errors greater than errors arising from 
 other causes. 
 
 Effect of Fabrication Quality 
 
 Figure 10 shows the extent of variations of A with M from tests 
 on several 0.040- inch and 0.020- inch chromel-alumel thermocouples which 
 had not been precisely welded and had been hand-filed to approximate 
 wire diameter. From these and similar tests it has been qualitatively 
 observed that, in general, the poorer the construction of the junction, 
 the lower the values of A throughout the range of Mach number; the 
 variations, however, are quite unpredictable. This fact offers an 
 explanation for the difference in the values of A against M at 
 T = 540° R in the tests (figs. 2 to 5) performed in the high-temperature 
 apparatus as compared with those (figs. 6 and 7) performed in the air 
 jet. The former tests were performed at an earlier date when means were 
 not available for accurate welding and machining of thermocouple wires; 
 the latter tests were made when these means had become available but 
 the high-temperature test facility no longer existed. 
 
 In the case of machined wires at ambient temperatures, there appears 
 a pronounced maximum in the A against M curve at Mach numbers 
 around 0.75. This effect presumably is the result of changes in the 
 flow pattern around the wires and is related to similar effects observed 
 in drag measurements on circular cylinders (ref. 7). The effect is 
 noticeably reduced on the unmachined wires at low temperatures and ap- 
 pears to vanish at the higher temperatures. The reasons for this are 
 not obvious . 
 
 Probable Value of Aq and Its Probable Error 
 
 For the pressure range of 0-5 to 2 atmospheres, temperature range 
 of 500° to 2000° R, and diameter range of 0.01 to 0.04 inch, the most 
 probable value of Aq and the probable error in this value are given 
 in figure ll(a) for carefully machined wires and in figure ll(b) for 
 all wires, regardless of character of fabrication. 
 
 If the value of A is experimentally determined for a particular 
 thermocouple at room temperature and pressure, regardless of character 
 of fabrication, the probable error to be expected when the wire is used 
 at other temperatures and pressures and when correction equation (ll) 
 is applied is substantially the same as the probable error shown in 
 figure 11(a). The probable errors shown in figures ll(a) and (b) rep- 
 resent probable errors on the order of l/4 and l/2 percent, respec- 
 tively, in temperature measurements. 
 
NACA RM E54G22a 
 
 It should be pointed out that the, results reported herein are 
 strictly applicable only for butt-welded wires of great length compared 
 with their diameters (l/D > 50)-, perpendicular to the gas stream, and 
 in a region free from interfering bodies. Should thermocouple wires 
 be mounted in a holder of comparatively large diameter, large differences 
 may be observed in the relation of A to M as a result of the inter- 
 ference effects) such a configuration would require calibration. The 
 effect of the interference of the support is illustrated by the data 
 published in reference 8 for a particular design of bare-wire type 
 thermocouple probe. These data are also indicated in figure 11(a) for 
 comparison with the data on very long isolated wires. 
 
 Lewis Flight Propulsion Laboratory 
 
 National Advisory Committee for Aeronautics 
 Cleveland, Ohio, July 23, 1954 
 
 REFERENCES 
 
 1. Freeze, Paul D.: Bibliography on the Measurement of Gas Tempera- 
 
 tures. Circular 513, Nat. Bur. Standards, Aug. 20, 1951. 
 
 2. Scadron, Marvin D., and Warshawsky, Isidore: Experimental Determi- 
 
 nation of Time Constants and Nusselt Numbers for Bare-Wire Thermo- 
 couples in High- Velocity Air Streams and Analytic Approximation 
 of Conduction and Radiation Errors. NACA TN 2599, 1952. 
 
 3. Johnson, H. A., and Rubesin, M. W. : Aerodynamic Heating and Convec- 
 
 tive Heat Transfer - Summary of Literature Survey. Trans. A.S.M.E., 
 vol. 71, no. 5, July 1949, pp. 447-456. 
 
 4. Kennard, Earl H. : Kinetic Theory of Gases. First ed., McGraw-Hill 
 
 Book Co., Inc., 1938. 
 
 5. Scadron, Marvin D.: Analysis of a Pneumatic Probe for Measuring 
 
 Exhaust-Gas Temperatures with Some Preliminary Experimental Results. 
 NACA RM-E52A11, 1952. 
 
 6. Pinkel, Benjamin, and Turner, L. Richard: Thermodynamic Data for the 
 
 Computation of the Performance of Exhaust-Gas Turbines. NACA WR 
 E-23, 1945. (Supersedes NACA ARR 4B25. ) 
 
 7. Gowen, Forrest E., and Perkins, Edward W.: Drag of Circular Cylin- 
 
 ders for a Wide Range of Reynolds and Mach Numbers. NACA TN 2960, 
 1953. (Supersedes NACA RM A52C20. ) 
 
 8. Scadron, Marvin D., Warshawsky, Isidore, and Gettelman, Clarence C: 
 
 Thermocouples for Jet-Engine Gas Temperature Measurement. Proc. 
 Inst. Soc. Am., Paper No. 52-12-3, vol. 7, 1952, pp. 142-148. 
 
MCA EM E54G22a 
 
 Pressure tubes 
 
 Alurael 
 
 Typical wall thermocouple 
 
 Insulating firebrick 
 
 Beference thermocouple 
 
 From combustor 
 
 1CD-5S05 | 
 
 Figure 1. - Schematic diagram of test apparatus showing typical thermocouple installation. 
 (Pressure tubes and reference thermocouple are shown in same plane as test 
 thermocouples for convenience. Actual installation was perpendicular.) 
 
10 
 
 NACA RM E54G22a 
 
 .04 
 
 .03 
 
 .02 
 
 .01 • 
 
 
 
 
 
 
 
 
 
 
 
 o o 
 
 
 
 n, C 
 
 O 
 
 
 
 
 
 
 
 
 
 
 C 
 
 ) 
 
 a 
 
 a 13 
 
 a c 
 
 
 
 
 
 
 
 
 
 
 
 
 o 
 
 a 
 
 
 o<> 
 
 O 
 
 > 
 
 A 
 
 
 
 
 
 
 
 
 c 
 o 
 
 D 
 
 ] 
 
 o. 
 
 > 
 
 £ A 
 
 A 
 
 
 
 
 
 
 
 
 □ 
 
 
 o < 
 
 ► 
 
 A 
 
 
 
 
 
 
 
 
 
 
 
 o ' 
 
 D 
 
 V 
 
 > 
 
 A 
 
 A 
 
 
 
 
 
 
 
 
 
 
 o 
 
 ° < 
 
 C 
 > 
 
 A 
 
 
 
 
 
 
 
 
 
 
 
 
 o 
 
 < 
 
 > 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .05 
 
 .04 
 
 03 
 
 *0 
 
 . 32 
 
 .01 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 r 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 
 □ 
 
 C 
 
 u ■ 
 < 
 
 >o 
 
 a C 
 
 .> o 
 
 ) A 
 
 
 
 
 
 
 
 
 
 
 c 
 
 a 
 
 > 
 
 I 
 
 A 
 
 A 
 
 
 
 
 
 
 
 
 
 
 c 
 n 
 
 ] 
 
 A 
 
 
 
 
 
 
 
 
 
 
 
 
 
 O 
 
 p < 
 
 > 
 
 
 
 
 
 Total 
 
 
 
 
 
 
 
 
 < 
 "to 
 
 > 
 
 
 
 
 
 
 o 
 
 8 
 
 T, 
 OR 
 
 540 
 
 960 
 14 cn 
 
 
 
 
 C 
 
 
 
 D 
 
 V A 
 
 
 
 
 
 
 
 9 
 
 □ < 
 
 > 
 
 > 
 
 A 
 
 
 
 
 
 
 
 
 A 
 
 19 
 
 60 
 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .5 .6 
 
 Mach number, 
 
 .9 
 
 1.0 
 
 Figure 2. - Unmachined 0. 040-Inch chromel-alumel at various temperatures. 
 Static pressure, 30 Inches mercury absolute; reference total tempera- 
 
 pres 
 ture, 540° R 
 
NACA EM E54G22a 
 
 11 
 
 .04 
 
 
 
 
 
 
 
 
 
 
 
 
 O 
 
 C 
 
 c 
 
 I 
 
 3 
 
 
 
 
 
 
 
 
 
 
 
 O 
 
 
 
 
 
 '? 
 
 
 
 
 
 
 
 
 
 O 
 
 
 
 
 
 3 <>A 
 O 
 
 <> 
 I* 
 
 
 02 
 
 
 
 
 
 
 
 o 
 
 C 
 
 i n 
 
 □ 
 
 O 
 
 ^A 
 
 O 
 
 A 
 
 A 
 
 
 
 
 
 
 
 
 
 
 
 u L 
 
 I 
 
 °A 
 
 A 
 
 
 
 
 
 
 
 .01 
 
 
 
 
 o 
 
 <>i 
 
 > 
 
 A 
 
 A 
 
 
 
 
 
 
 
 
 
 
 
 
 o 
 
 i ° 
 
 A 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .05 
 
 .04 
 
 .03 
 
 *o 
 
 .02 
 
 .01 
 
 
 
 
 
 
 
 1 
 
 
 
 1 
 
 1 
 
 
 
 < 
 
 > 
 
 
 
 
 
 
 
 
 
 
 
 
 a 
 
 
 °C 
 
 ] 
 
 
 
 
 
 
 
 
 
 o 
 
 o 
 
 o 
 
 o< 
 
 3 
 
 > AC 
 
 A° 
 
 
 
 
 
 
 
 
 
 
 C 
 
 <^ 
 
 °A 
 
 
 D 
 
 
 
 
 
 
 
 
 
 <2 
 
 !a d a 
 
 2 D 
 
 L 
 
 
 
 
 
 
 
 
 
 
 
 
 a 
 
 1 
 A 
 
 
 
 
 
 
 Total 
 
 
 
 
 
 
 
 O u 
 
 *o 
 
 ^A 
 
 
 
 
 
 
 T, 
 °R 
 
 
 
 <} 
 
 J D 
 
 A 
 
 
 
 
 
 
 
 
 O 540 
 □ 1010 
 
 
 
 o ° 
 
 
 
 
 
 
 
 
 
 
 A 
 
 i 
 2 
 
 31U 
 
 010 
 
 
 c 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .5 
 
 .6 .7 
 Mach number, M 
 
 1.0 
 
 Figure 3. - Unmachlned 0. 020-Inch chrorael-alumel at various temperatures. 
 Static pressure, 30 Inches mercury absolute; reference total tempera- 
 ture, 540° R. 
 
12 
 
 MCA EM E54G22a 
 
 
 
 
 
 
 
 
 
 
 
 
 o 
 
 
 
 O 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 o 
 
 n 
 
 o 
 
 o . q, v C[> 
 
 
 
 
 
 
 
 
 
 o° 
 
 
 <0 
 
 3 3 
 
 
 £ 
 
 
 
 Li 
 
 
 
 
 
 
 
 O 
 
 
 
 D 
 
 o 
 
 u 
 
 
 
 A " 
 
 
 
 
 
 
 
 
 
 
 O 
 
 6 
 
 
 
 > * 
 
 
 
 
 
 
 
 
 
 
 
 
 o<5 
 
 Ej> 
 
 
 a. A 
 
 
 
 
 
 
 
 
 
 
 
 
 C$ 
 
 o 
 
 > 
 
 A 
 
 4 
 
 
 
 
 
 
 
 
 
 
 
 
 n 
 
 O 
 
 
 A 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .05 
 
 .04 
 
 .03 
 
 .02 
 
 .0] 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 t 
 
 < 
 
 > 
 
 r 
 
 1 
 
 
 
 
 
 
 
 
 
 
 O 
 
 cO 
 
 [ 
 
 ] I 
 
 A 
 
 ] 
 
 o 
 
 
 
 
 
 
 
 
 
 
 o 
 
 o 
 
 ^ 
 
 k o 
 
 O 
 
 O 
 
 
 
 
 
 
 
 
 
 
 °^ 
 
 & 
 
 V 
 
 
 
 
 
 
 
 
 
 
 
 
 
 <*> 
 
 °fi 
 
 
 
 
 
 
 Total 
 
 
 
 
 
 
 
 
 rP 
 
 T 
 
 i * 
 
 
 
 
 
 T, 
 °R 
 
 O 525 
 D 960 
 
 
 
 
 
 n 
 
 
 
 
 
 
 
 
 
 
 
 
 $ 
 
 <A 
 
 
 
 
 
 
 
 
 
 A 
 
 1 
 
 960 
 
 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .3 .4 .5 .6 .7 .8 .9 
 Mach number, M 
 
 Figure 4. - Unmachlned 0. 020-Inch platinum 13 percent rhodium - platinum 
 at various temperatures. Static pressure, 30 Inches mercury absolute; 
 reference total temperature, 540° R. 
 
 1.0 
 
KACA EM E54G22a 
 
 13 
 
 .05 
 
 .04 
 
 .03 
 
 .02 
 
 .01 
 
 
 .06 
 
 . 05 
 
 .04 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^oT 
 
 
 
 
 
 
 
 
 
 
 n 
 
 o 
 
 O 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 o 
 
 O 
 
 3 % 
 
 I 
 
 'v 
 
 
 
 
 
 
 
 
 
 
 
 8 
 
 u 
 o 
 
 
 A 
 
 
 
 
 
 
 
 
 
 
 
 o 
 6 
 
 
 i 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 ,o<* 
 
 §> 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 §> 
 
 < 
 
 >° 
 
 A 
 
 
 
 
 
 
 
 
 
 
 
 
 
 o 
 
 
 
 
 1 
 
 1 
 1 
 
 
 
 
 
 
 
 
 
 .02 
 
 . ~>: 
 
 
 .2 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 < 
 
 o 
 
 > 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 c 
 
 ] c 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 O 
 
 O t 
 
 
 
 — 
 
 
 
 
 
 
 
 
 
 
 
 
 o0 
 
 r 
 
 
 ] 
 
 
 
 
 
 
 
 
 y\ 
 
 
 o 
 
 3 □ 
 A 
 
 L 
 
 
 
 
 
 
 
 
 
 
 
 
 o 
 
 i OH 
 
 
 
 
 
 
 
 
 
 
 
 
 
 O 
 
 3 
 
 
 
 
 
 
 1 
 
 otal 
 
 
 
 
 
 
 
 O 
 
 ot 
 
 
 
 
 
 
 
 T, 
 °R 
 
 
 
 < 
 
 > 
 
 o 
 
 
 
 
 
 
 
 
 O 525 
 
 □ 960 
 /\ , . — 
 
 
 $ 
 
 □ 
 
 
 
 
 
 
 
 
 
 A 
 
 IS 
 
 60 
 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .3 
 
 .4 
 
 .5 
 
 1.0 
 
 Mach number, M 
 
 Figure 5. - Unmachlned 0.010-inch platinum 13 percent rhodium - platinum 
 at various temperatures. Static pressure, 30 inches mercury absolute; 
 reference total temperature, 540° R. 
 
14 
 
 NACA EM E54G22a 
 
 .06 
 
 .05 
 
 .04 
 
 .03 
 
 .02 
 
 .01 
 
 
 
 Static pressure. 
 
 
 
 
 
 
 
 
 
 
 
 
 p, 
 
 In. Hg abs 
 
 O 15 
 
 □ 30 
 
 . O 50 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 < 
 
 > n 
 
 [] 
 
 
 
 
 
 
 
 
 
 
 
 
 
 c 
 
 
 o 
 
 o 
 
 O 
 
 
 
 
 
 
 
 
 
 
 < 
 
 > 
 
 
 
 
 
 
 D 
 r 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 > 
 
 U i 
 
 'J 
 
 
 
 
 
 
 
 
 
 
 
 
 
 □ 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 <h 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 O 
 
 
 
 
 
 
 
 
 
 
 
 
 
 o 
 
 3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 <kj 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .05 
 
 .04 
 
 . 03 
 
 A 
 
 .02 
 
 .03 
 
 
 
 
 
 
 
 
 
 
 
 J-L n i 
 
 [ 
 
 ] 
 
 0° 
 
 
 
 
 
 
 
 
 
 
 
 
 
 c 
 
 o 
 
 > 
 
 v> 
 
 
 c 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 °c 
 
 
 
 
 
 
 
 
 
 
 < 
 
 } 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 n 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 n ( 
 
 >° 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 <P 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 o 
 
 □ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 <M 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .3 
 
 .5 .6 .7 
 Mach number, M 
 
 1.0 
 
 Figure 6. - Machined 0. 025-Inch chromel-alumel at various pressures. Total 
 temperature, 540° R; reference static pressure, 30 Inches mercury absolute. 
 
NACA EM E54G22a 
 
 15 
 
 .05 
 
 .04 
 
 .03 
 
 .02 
 
 .01 
 
 
 
 i 
 
 Static 
 
 
 
 
 
 
 
 < 
 
 > ^ 
 
 0[] 
 
 1 
 
 
 
 
 pressu] 
 
 P. 
 In. Hg 
 
 } 15 
 : 30 
 
 lbs 
 
 
 
 
 
 < 
 1 
 
 >° 1 
 
 2 
 
 ] 
 
 □ 
 
 O 
 
 
 
 
 c 
 
 
 
 
 
 < 
 
 □ 
 
 > 
 
 c 
 
 
 
 
 o 
 
 o 
 
 
 
 
 <, 
 
 > 
 
 50 
 
 
 
 
 
 
 D 
 
 □ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i 
 
 i 
 
 ) 
 n 
 
 > 
 
 
 
 
 
 
 
 
 
 
 
 
 
 n 
 
 a c 
 o 
 
 ) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 n 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 o 
 c 
 
 i 
 
 
 
 
 
 
 
 
 
 
 
 
 6 
 
 
 u 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .05 
 
 .04 
 
 .03 
 
 .02 
 
 .01 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 c 
 
 n^ 
 
 ?o 
 
 u ° 
 Ol 
 
 3 
 
 n 
 
 
 
 
 
 
 
 
 
 
 < 
 
 > < 
 > 
 
 > 
 
 
 
 o 
 
 
 
 
 
 
 
 
 
 
 c 
 
 > n 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 I 
 
 r 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 nn 
 
 a 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 n 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 c 
 
 
 ) 
 
 
 
 
 
 
 
 
 
 
 
 
 J5 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .2 
 
 .3 
 
 .5 
 
 .6 .7 
 Mach number, M 
 
 .9 
 
 1.0 
 
 Figure 7. - Machined 0. 019-Inch platinum 13 percent rhodium - platinum 
 at various pressures. Total temperature, 540° R; reference static 
 pressure, 30 Inches mercury absolute. 
 
16 
 
 NACA EM E54G22a 
 
 .06 
 
 .05 
 
 .04 
 
 .03 
 
 . 02 
 
 .01 
 
 
 
 
 o 
 d 
 O 
 
 A 
 V 
 > 
 
 Diameter, 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 D, 
 In. 
 
 0.040 
 .032 
 
 .025 - 
 
 .019 
 
 .015 
 
 
 
 
 
 Q 
 
 8 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 A 
 
 o 
 
 3 
 
 
 
 
 
 
 
 
 
 fl 
 
 o 
 
 ^ 
 
 
 
 
 
 
 
 .0 
 
 L2 
 
 
 C 
 
 q 
 
 Bo 
 
 A 
 
 
 
 e > 
 
 u ^ 
 
 J§# 
 
 
 
 
 
 
 
 
 
 B £ 
 
 A^> 
 
 
 
 
 CV * 
 
 
 
 
 
 
 
 
 
 
 £ i 
 
 ^ 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Q 
 
 <y? 
 
 A 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i* 
 
 Jy 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 f 
 
 & 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Q < 
 
 it 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 F 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 . 05 
 
 .04 
 
 .03 
 
 .02 
 
 .01 
 
 
 
 
 
 
 
 
 
 
 
 > 
 
 > 
 
 9 
 
 
 
 
 
 
 
 
 
 
 
 
 
 > 
 
 
 1 . 
 
 ^n 
 
 > 
 
 
 
 
 
 
 
 
 
 
 
 rs T3 
 
 S 
 
 
 
 A 
 
 t 
 
 V V 
 
 ^A A 
 
 
 
 
 
 
 
 
 
 1 
 
 1 
 
 
 
 
 S 
 
 C 
 
 O 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 < 
 ft 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 y 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 £ 
 
 V 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ft 
 
 1 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \\ i 
 
 P 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .5 .6 
 
 Mach number, M 
 
 .7 
 
 .9 
 
 1.0 
 
 Figure 6. - Machined chromel-alumel of various diameters. Static pressure, 
 30 Inches mercury absolute; total temperature, 540° R; reference diameter, 
 0.020 Inch. 
 
WACA EM E54G22a 
 
 17 
 
 .06 
 
 .05 
 
 .04 
 
 .03 
 
 .02 
 
 .01 
 
 o 
 
 D 
 
 O 
 
 A 
 V 
 > 
 
 Diameter, 
 D, 
 In. 
 
 0.040 
 .032 
 .025 
 .019 
 .017 
 .015 
 
 i 
 
 fc A 
 
 -e 
 
 o 
 
 9 
 
 .05 
 
 
 
 
 
 
 
 
 
 
 
 — A- 
 
 9 
 
 i o 
 
 n p* 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 si 
 
 8 
 
 o £ 
 
 C 
 
 <5 
 
 
 
 .04 
 
 
 
 
 
 
 
 
 
 {1 
 
 □ u 
 
 o 
 
 
 
 B 
 
 B 
 
 
 
 .03 
 
 
 
 
 
 
 
 
 □ 
 
 
 
 
 
 □ 
 
 
 
 u 
 
 o 
 
 
 
 
 
 
 
 
 
 
 J 
 
 w 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 & 
 
 
 
 
 
 
 
 
 
 
 
 
 .02 
 
 
 
 
 A 
 
 a 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 d 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4» 
 
 1 
 
 if 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .3 
 
 .5 .6 .7 
 Mach number, M 
 
 .9 
 
 1.0 
 
 Figure 9. - Machined platinum 13 percent rhodium - platinum of various diameters. 
 Static pressure, 30 inches mercury absolute; total temperature, 540° R; reference 
 diameter, 0.020 Inch. 
 
18 
 
 KACA EM E54G22a 
 
 .05 
 
 .04 
 
 .03 
 
 .02 
 
 .01 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 Jpper 
 
 \ 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 / Median 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 / / 
 
 
 . ''Lower 
 
 limit — - 
 
 *- 
 
 
 
 
 
 
 
 
 
 / 
 
 ' / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 S 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 s 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .05 
 
 .04 
 
 .03 
 
 .02 
 
 .01 
 
 (a) Diameter, 0.040 Inch. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Up 
 
 1 
 per llmlt__ 
 
 
 
 
 
 
 
 
 
 
 
 
 y ^ 
 
 -" 
 
 
 -^ IV 
 
 edlar 
 
 
 
 
 
 
 
 
 
 
 / 
 
 ' y 
 
 y 
 
 -" 
 
 s 
 
 «. 
 
 
 
 
 
 
 
 
 
 / 
 
 ' / 
 
 
 
 
 
 — 
 Low 
 
 er limit 
 
 
 
 
 
 
 
 / 
 / / 
 
 ' / 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 1/ / 
 V 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 /V 
 V 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 v y 
 
 
 
 
 
 
 
 
 
 
 
 
 
 """' 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .2 .3 .4 .5 .6 .7 .8 .9 1.0 
 
 Mach number, M 
 
 (b) Diameter, 0.020 Inch. 
 
 Figure 10. - Chromel-alumel wires of various character of fabrication. Static 
 pressure, 30 Inches mercury absolute; total temperature, 540° R. 
 
MCA EM E54G22a 
 
 19 
 
 *o 
 
 .05 
 
 .04 
 
 .03 
 
 .02 
 
 .01 
 
 
 .05 
 
 .04 
 
 .03 
 
 .02 
 
 .01 
 
 
 
 
 
 
 
 
 
 
 
 y "~ 
 
 r4 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 y 
 
 y 
 
 
 N* 
 
 
 
 
 
 
 
 
 
 
 / 
 
 y / 
 
 y y 
 
 f / 
 s 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 N 
 
 ^- 
 
 ~_=z. 
 
 
 
 
 
 
 
 / 
 
 / / 
 
 ' y 
 
 / 
 
 
 
 >plC£ 
 
 urobe 
 
 il cross-flow 
 (ref al 
 
 
 
 
 
 
 
 / 
 
 // 
 
 y 
 
 / 
 
 y 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 y / 
 
 / y 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 '4- 
 
 y 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^y 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 (a) Machined wires. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 y 
 
 y 
 
 y 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 S 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 z 
 
 / 
 
 / 
 
 
 y* 
 
 -- 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 / , 
 
 
 y 
 / 
 
 y 
 
 y 
 
 
 
 
 
 
 
 
 
 
 
 
 / / 
 
 / / 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 y 
 
 / 
 
 y y 
 
 y 
 
 s 
 
 y 
 
 
 
 
 
 
 
 
 
 
 
 
 ■ 
 
 y 
 
 y ,, 
 
 y" 
 
 y y 
 
 < y 
 
 ' y 
 
 y 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 y 
 y 
 
 y 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .5 .6 
 
 Mach number, M 
 
 .7 
 
 .9 
 
 1.0 
 
 (b) All wires regardless of character of fabrication. 
 
 Figure 11. - Mean curve and probable error at reference static pressure of 30 Inches 
 mercury absolute and reference total temperature of 540° R. Pressure range, 0.5 
 to 2 atmospheres; temperature range, 500° to 2000° R; diameter range, 0.01 to 0.04 
 inch; reference diameter, 0.020 inch. 
 
 NACA-Langley - 9-24-54 - 350 
 

 IS 5 
 
 t" 1 73 
 
 — O 
 
 CS l« 
 
 01 01 
 
 a < 
 
 c 
 x: 
 u 
 
 £ ^ 
 
 C U r- 
 
 s 
 
 3 
 
 O 
 
 eg 
 
 ■s o 
 
 oi a; -<r 
 
 ■- (K W 
 
 a u 
 
 tc O 
 
 2 (fl 2 
 - £§« 
 
 IS T> X <■ 
 
 u o e r; 
 
 ™ « 41 « C< 
 
 £ a««: ooZ 
 
 Q 
 
 W 
 
 • Q 
 
 .2 w 
 
 3=£ 
 cS i 
 
 oi a 
 
 < a 
 
 5? a 
 
 So 
 
 <u ^ 
 
 £ 00 
 
 s ^ 
 
 e2 
 
 o U 
 
 u w 
 
 t. K 
 o o 
 2u 
 
 W-oX 
 
 K - W 
 c ts > 
 
 < oO 
 
 u So 
 <: is w 
 
 Z Z K 
 
 a 
 
 00 
 
 s 
 
 . < . 
 
 — a — 
 KM _ 
 5 < « 
 
 M o2 
 
 « K S 
 S; s c 
 
 D H S 
 O < £~ 
 
 as . ■* 
 
 r" H o 
 
 ~ M <0 < 
 lL 3h" OT ? 
 
 ££■*- 
 
 H w " 2 
 co > w -a 
 
 o..S 
 
 ~ ts ^ is a 
 
 ■S 01 4) >, r- 
 
 5 .2 j, c « 
 
 a *- a oi OT 
 
 •a c 
 
 o <s 
 
 a) 
 
 01 g £ 
 
 £ >»» 2 
 
 0) 
 
 
 ^2° 
 
 o ° § 
 
 S " 2 
 
 O m 
 
 S££ 
 
 oi 2 
 £ <s 
 
 o S -a 
 
 lis 
 
 u to ' 
 
 o c 
 
 O « £ U „ 
 
 " S 2 s - 
 ? .S 2 
 
 0> 
 
 si 5 
 
 01 0} 
 
 " M 
 
 I Li 0) 
 
 O t. 
 
 - a. 
 
 - c u 
 x: o c 
 be-- o 
 
 £ 3 5 
 
 3 k. -n 
 
 t « 
 0) ki 
 ^ CD T3 
 
 — ™ 01 
 tS -S (D 
 
 eft 
 
 .2 a a 
 
 S« 3 
 
 ° 5 
 
 Q, CS 
 
 3 — X 
 
 a £ S 
 
 - e 
 
 < 
 
 < 
 
 .- a 
 
 — °° 
 
 c 5 - 
 
 cs 2 
 
 — o 
 
 CS t. 
 
 
 <^ CSI 
 
 no 
 
 
 3 ■ 
 
 
 DO 
 
 y 
 
 Techniq 
 
 OJ 
 
 c 
 
 
 
 a> 
 
 ° -s S 
 
 
 £ 
 
 IS t. >, 
 
 - 
 
 
 
 s 
 
 t. IS T3 
 
 u 
 
 O (1) O 
 
 ■Is 
 
 B 
 
 is a> a> 
 
 5 
 
 J OS < 
 
 M 
 
 a 
 
 a 
 w . 
 
 « J* 
 
 IS ■ -t- 
 
 '■cm 
 
 < O J 
 
 £o» 
 
 o-WO 
 ^Z° 
 
 -in ^ *r" 
 
 s2| 
 
 o U x 
 isUWh 
 
 *•» Ck w 
 
 O on « 
 
 S _ W 5- 
 B=rt >G 
 
 < §o? 
 
 UsOk 
 
 < is W h 
 Z Z Kot 
 
 00 
 
 S 
 
 < . 
 
 W a 
 K o> 
 H ""■ 
 
 00 
 
 00 'S" 
 
 < in 
 O 2 
 
 a ^ 
 
 K S 
 
 a-g 
 
 < " 1? 
 
 w to S! 
 
 ^ - z 
 
 fc; «" 
 <-> s „■ 
 
 o«? 
 
 i-J ^ bC 
 
 > b- T3 
 
 rt 
 
 DQ 
 
 01 IS 
 
 rt 2 
 
 IS 01 oj 
 
 « c & 
 
 IS o , 
 
 S — ■" 
 
 "" ° 3 
 
 i £ i. 
 
 01 o o 
 
 3 ° rt 
 
 c t - 
 r- 0) 01 
 
 01 01 01 
 
 r 3 2 
 
 ho a 
 
 .2 | ^ 
 
 > 2 u C' 
 
 »5 f. "5 
 
 c n - 
 
 > 3 
 O 
 
 i- a 
 
 = s 
 
 a) C 
 
 c rt 
 
 O CO 
 
 .2 3 
 
 0J CO 
 
 - CO 
 
 u a> 
 
 o ^ 
 
 u a 
 
 §83 
 
 o ° u 
 
 O <u 
 
 6££ 
 m -c a 
 £.a <n 
 «f £ 
 
 J. C rt 
 
 j: o c 
 tj>2 o 
 
 3 3-? 
 
 t. 3 u 
 
 i o- o 
 
 01 d> Q, 
 
 0) I 
 U CI 
 3 t, 
 
 <S 01 
 
 3 2 
 
 2-1 
 a c 
 a> a> 
 •^ u 
 
 o 2 
 
 £ g 
 
 r! G » 
 
 cr ° 
 -C - .2 
 t^ 01 "O 
 
 3 I.TI 
 
 o o S 
 
 "" £ § 
 
 jS (U T3 
 
 2: 2 S 
 
 - » « 
 
 is -a ai 
 c o fc, 
 
 .2 a a 
 
 t; — * 
 °33 
 
 O ^ CO 
 
 a 2 S 
 
 < 
 z 
 
 «-. °° 
 
 Ol 00 
 
 i2 i° >,H 
 
 3 m 
 ■So 
 
 oi a; -^ 
 
 •g i*. w 
 
 c ^ "!- § ->3 
 
 a» o -^ is oi ^ 
 
 S*-> u c ,- ft- 
 
 cs >-. >, - "• 
 3 t« ts -a 
 
 >- o a o _ 
 
 ■5; J 01 t, c y 
 
 2 « <" v .5 < 
 
 a a a « < 60 z 
 
 c r ^ 
 
 u 
 
 • -C " 
 
 ' bo 
 
 is 3 
 
 c 
 
 
 5 
 3 
 
 — O 
 
 (* 
 
 
 
 0> <D 
 
 
 X < 
 
 
 N f?oj 
 
 _ ts 
 3 rg 
 
 ■So 
 
 c 
 
 o « 2 ^ 
 
 2 >,Ha fe w 
 
 C "" r- S -^ 
 
 « o-c J » * 
 E3 2 £§« 
 
 3 sh ts -a 2 <■ 
 
 ■5; a 01 b c U 
 ™ is ai ai e •< 
 £ a K < 00 Z 
 
 Q 
 
 W 
 
 • Q 
 
 to a 
 
 .2 w 
 
 3& 
 IS 1 
 
 c H 
 
 2h 
 oi a 
 < o 
 
 u K 
 
 2o 
 
 01 w 
 
 £ 00 
 
 a z 
 
 S2 
 
 EH 
 
 oU 
 
 aOM 
 
 CM ^K 
 
 O o o 
 -r 01 i-j 
 m •- i_> 
 
 "■§>< 
 
 5; < a 
 < §0 
 
 U JU 
 <C is W 
 
 ZZK 
 
 00 
 
 i 
 
 , <! . 
 _ W a 
 
 |«s 
 
 a to _ 
 
 7»1« 
 
 a < "> 
 
 0002 
 
 W b3 h 
 •-I K 01 
 
 a d -g 
 dh S 
 o < £ — 
 u 2 °- « 
 
 as . •«• 
 
 a h o 
 
 S G ' c «; 
 
 5o^ £ 
 
 H n ^ 2 
 00 > b< -o 
 
 5 
 
 IS 
 
 •* T3 
 
 „ 01 
 
 IS X! 
 
 Ui oi 
 
 1 1 
 
 II 
 
 o o 
 
 a , u 
 
 3. ti 5 
 
 « 2 rt 
 
 •° » 3 
 
 r- 0> 01 
 
 Oi 01 01 
 
 5. OI 
 
 •r 2 2 
 
 bh a. 
 
 2 § « 
 
 > = 
 
 22 
 01 3 
 
 u a 
 
 m g 
 
 § £ 
 
 1 2 " Z 
 °- £ - 
 
 3 S o 
 
 C 
 
 o o 
 
 O 01 
 
 S££ 
 01 j= a 
 5 3 o 
 
 S 2 s- 
 oi s a ~ 
 
 oi 1 „ •-; 
 
 2- g 
 g c 
 
 01 Oi 
 
 «> 5 
 
 £ « 
 
 n 2 « 
 §1 3 
 "" = « 
 
 x: a .2 
 
 ti 01 "O 
 
 *J CU 
 
 cu JS 
 
 ^- J5 co 
 
 0^ 
 
 (U 
 
 iS 3 
 
 01 01 
 
 u 01 
 
 ' u 01 
 
 O ti 
 
 U Q. 
 
 a c rt 
 
 x: o c 
 
 3 2 
 2 3. a 
 
 053 
 
 &■£ o o a vi 
 
 a or o 
 01 01 o, 
 
 •■" 3 r- 
 
 o, 01 c 
 
 .«; 
 
 -K S 
 
 Q 
 
 w , 
 •Q 3= 
 
 O J" 
 
 .2u^a 
 
 3=sa 
 
 IS I -7 
 
 c H S3 
 
 C 
 t- E 00 
 
 <aa 
 u a a 
 
 oi^O 
 
 ago 
 s2| 
 
 SHw 
 
 o u as 
 
 «owh 
 
 cm Ck w 
 
 O 00 a 
 
 10 'S =s 
 
 5<«t 
 
 K 
 
 -Ms: 
 is > O 
 
 < isCdn 
 Z Z Boo 
 
 00 
 
 s 
 
 < . 
 
 W a 
 K o 
 H 
 00 
 
 00 i" 
 
 *£ ITS 
 
 o 2 
 
 ft- 01 
 
 3-g 
 
 s s-<s 
 
 w tn ,^ 
 
 a o 
 
 |ss 
 
 a e a 
 2 §2 
 a M d 
 
 r * 2. 
 
 « o 
 
 o 41 « 
 
 W t. 2 
 > b-^S 
 
 01 01 ■ 
 
 -* T3 
 „ 01 
 IS T3 
 X 01 
 
 r ^ « 
 
 ■" CJ ^1 
 
 3 
 
 o 
 
 « g£ 
 
 So « 
 
 ■" Jl 3 
 
 C 41 10 
 
 £ 01 01 
 
 5 .2 2 
 
 01 
 
 > 2 
 §2 
 
 (h 
 
 a 
 
 b£ 
 
 E 
 
 
 
 ai 
 
 § 
 
 — 
 
 -! 
 
 B 
 
 
 ri 
 
 to 
 
 iS =5 
 
 01 CO 
 f-> CO 
 
 j- a> 
 
 O tH 
 
 u a 
 
 1 1 
 
 01 o " 
 
 *f o 
 =• £ *- 
 
 6££ 
 01 £ a 
 £.2 0, 
 «,•§£ 
 
 i=^ 
 
 J, en 
 
 J3 O C 
 M^2 O 
 
 3 S '■? 
 
 U. 3 (1 
 
 01 01 a. 
 
 .01 
 3 l. 
 
 a 3 
 f 01 
 
 ^ IS 
 
 01 S 
 
 |S 
 
 01 01 
 
 *- u 
 
 4. £ 
 
 £ rt 
 o a"S 
 
 n 2 « 
 
 8 e e 
 
 J3 .5 .2 
 
 ti 01 "O 
 
 111 " 
 XT 41 T3 
 
 a 01 
 01 a 
 
 2 |S 
 
 — - S 01 
 
 IS -9 41 
 C ? t. 
 
 .2 3.°- 
 t: — 4 
 
 g.§3 
 
 O ^ CO 
 
 a 2 S 
 
 ira S 
 
 Xl 
 
 < 
 
 < 
 z 
 

UNIVERSITY OF FLORIDA 
 
 3 1262 08106 608 5 
 
 UNIVERSITY OF FLORIDA 
 DOCUMENTS DEPARTMENT 
 
 XRSTON SCIENCE LIBRARY 
 
 XX117011 
 
 •' *?«1 1.7011 I