Table Of Content

HANDBOOK OF METEOROLOGY EDITED BY F. A. BERRY, JR. Captain, U.S.N., Officer-in-Charge, U.S. Naty Weather Central, Washington, D.C. E.BOLLAY Lieutenant Commander, U.S.N.R NORMAN R. BEERS ^VA^ afe*^ New York London McGRAW-HILL BOOK COMPANY, INC. 1 9 4 5 HANDBOOK OP METBOKOLOGY COPYBIGHT, 1 9 4 5 , BY THE M C G B A W - H I L L BOOK COMPANY, INC. PRtNTEP IN THE UNITED STATES OF A M B B I C A All rights reserved. This book, or parts thereof, may not he reproduced in any form without-permission vf* the publishers.' vii THE MAPLE PRESS COMPANY, YORK, PA. PREFACE The "Handbook of Meteorology" is designed to furnish the student and the professional meteorologist a convenient text reference for data, fundamental theory, and weather analysis and forecasting. The empha- sis has been conscientiously placed on the scientific and engineering aspects of meteorology, rather than on current techniques. This emphasis is desirable at any time in a handbook, and particularly so at this time in view of recent and forthcoming changes in the methods of analysis and in the display of synoptic data (especially at upper levels). The editors' intent has been that this handbook contain practical meteorological information. Their interpretation of what is "practical" is based on their collective experience and on their interpretation of the experience of returning students who have forecast the weather in the field under trying conditions. Accordingly the "Handbook of Meteor- . ology" contains not only sections on fronts, air masses, upper air, etc., which are immediately suggested by its title, but also those fundamentals of mathematics and of the physical sciences on which meteorology is dependent. Some of these topics are frequently considered to be theo- retical. When, however, they are written up in compact form and in meteorological language so as to be "available, useful, in practice or action," then they are rightly included in a book that is designed for daily use. The practice of meteorology (by which is meant some direct or indirect aspect of weather forecasting) is like the other engineering sciences in that an answer to a problem is required in a specified time, often from meager data. Moreover, as is sometimes overlooked in the stress of war, "an engineer is one who can do at reasonable cost what almost any man can accomplish with unlimited resources at his dis-" posal."* It is the editors' considered belief'.that the practice of meteor- ology is inevitably to become accepted as an engineering science.. The variety of problems that arises in meteorological practice is endlessly complicated by both space and time intervals. An aviator' may stand by and demand to know precisely when he will have sufficient ceiling to take off. A constructor may save lives and money by knowing with some accuracy what will be the maximum rainfall over a large watershed. These and many other meteorological problems are not *GrLKET, J. r., Journal 0/Engineering, January, 1945. V VI PREFACE yet completely solved, though fine progress has been made with recent advances. Many meteorological problems are in fact not yet clearly stated as problems, nor can much be done to overcome present inade- quacies until many men and women understand not only the basic principles of meteorology, but also the principal problems of at least one other activity, e.g., aviation, agriculture, manufacture, transpor- tation, distribution, communications, etc. The editors desire to acknowl- edge these problems even though the present editioii of the handbook is limited in scope to aviation and hydrometeorology in this respect. Perhaps greater cooperation is required among individuals and among nations in the practice of meteorology than in any other social effort of man. This is so, simply because even short-period forecasts often depend on synoptic data that are beyond the reach of the indi\'idual meteorologist or the individual nation. Problems involving longer periods and greater areas require even more data, from the surface and from upper levels of the atmosphere. Recognition of the cooperation required for successful weather services appeared at least a hundred years ago when John Ruskin wrote, "The metec^ological Society, there- fore, has been formed, not for a city, nor for a kingdom, but for the world." The editors are deeply indebted to their contributors especially and to many others who have also cooperated generously to produce this' handbook. , . • Mr. Charney wishes to acknowledge his indebtedness to Professor J. Kaplan for his introduction to the subject (Section IV), and for the kind encouragement he received in the preparation of the manuspripli. The editors assume full responsibility for the selection and arrange- ment of topics. Each section has been read by one or more critics, but individual authors were final judges as to how their contributions should be covered. Much desirable material was omitted for security reasons at the time of writing, but it is believed the integrated result of all that has been available provides the engineering science needed by a trained meteorologist in the practice of his profession. For the rules and'regu- lations of the various meteorological services it is generally necessary to make reference to their individual publications. For the art of fore- casting the weather according to the needs and desires of his audience, the meteorologist must defer to the association of his fellows and to experience. T H E EDITORS. ANNAPOLIS, MARYLAND, September, 1945. LIST OF CONTRIBUTORS li. A. BAUMGARTNER, Lieut., U.S.N.R., Postgraduate School, United States Nerval Academy, X. NORMAN R . BEERS, Lieut., U.S.N.R., Postgraduate School, United States Naval Academy, I, V, X. F. A. BERRY, JR., Capt., U.S.N., Staff Comair 7th Fleet, X. E. BoLLAY, Lieut. Comdr., U.S.N.R., Fleet Weather Central, X. JuLE G. CHARNEY, Lecturer, Department of Meteorology, University of California, iV. Civ;ilian Staff, Institute of Tropical Meteorology, Rjp Piedras, Puerto Rico, X. FREDERICK A. FICKEN, Professor of Mathematics, University of Tennessee (on leave); Office of Field Service Consultant, Operations Research Group, U.S.N., II. ALBERT S. PRY, Chief, Hydraulic Data Division, Tennessee Valley Authority, XIII. H. G. HOUGHTON, Professor of Meteorology, Massachusetts Institute of Technology, III. GEORGE R . JENKINS, Lieut., U.S.N.R., Postgraduate School, United States Naval Academy, IX, X. H. LANDSBEBG, Ph.D., Associate Professor of Meteorology, The University of Chicago, - XII. S. C. LOWELL, Lieut. Comdr., U.S.N.R., Postgraduate School, United States Naval Academy, III. K. B. MCEACHRON, Research Engineer, High Voltage Engineering Laboratory and Designing Engineer, Power Transformer Engineering Division, General Electric Company, Pittsfield, Mass.; Fellow, American Institute of Electrical Engineers, III. J. F. O'CONNOR, Lieiit., U.S.N.R., Postgraduate School, United States Naval Acad- emy, X. MILDRED B . OLIVER, Department of Meteorology, The University of Chicago, X. VINCENT J. OLIVER, Department of Meteorology, The University of Chicago, X. CAKL-G. ROSSBY, Andrew MacLeish Distinguished Service Professorship and Chair- man of the Department of Meteorology, The University of Chicago, VII. P. L. ScHBREScHEwsKY, Formerly Chief Weather Service, French Armies, X L A. K. SHOW ALTER, Meteorologist in Charge, Hydrometeorological Section, Office of Hydraulic Director, U.S. Weather Bureau, XIII. H. .J. STEWART, Daniel Guggenheim Aeronautical Laboratory, California Institute of Technology, VI. H. U. SVERDRUP, Professor of Oceanography, ^University of California; Director, Scripps Institution of Oceanography, XIV. LouvAN E. WOOD, Meteorological Engineer, Friez Instrument Division, Bendix Aviation Corporation, VIII. vu CONTENTS For the detailed contents of any section consult the title page of that section. For the alphabetical index see pp. 1057 to 1068. SECTION PAGE P E B F A C B . . -. V L I S T OF CONTRIBUTORS vii NUMERICAL AND GRAPHICAL D A T A I 1 METEOROLOGICAL MATHEMATICS AND CALCULATIONS . . II 123 PHYSICS OF ATMOSPHERIC P H E N O M E N A I l l 241 RADIATION. . ". IV 283 METEOROLOGICAL THERMODYNAMICS AND ATMOSPHERIC STATICS V 313 KINEMATICS AND DYNAMICS OF F L U I D F L O W VI • 411 T H E SCIENTIFIC BASIS OF M O D E R N METEOROLOGY . . . VII 501 METEOROLOGICAL INSTRUMENTS VIII 531 TRANSMISSION AND PLOTTING OF METEOROLOGICAL D A T A I X 573 SYNOPTIC METEOROLOGY AND W E A T H E R FORECASTING . X 601 CLOUDS AND STATES' OF THE SKY X I 881 CLIMATOLOGY XII 927 HYDROMETEOROLOGY X I I I 999 OCEANOGRAPHY. . . ' X I V 1029 INDEX 1057 SECTION I NUMERICAL AND GRAPHICAt DATA BY NORMAN R. BEERS AND THE A B R O L O G I C A L ENGINEERING S T A F F , POSTGRADUATE ScHOOL, UNITED STATES NAVAL ACADEMY CONTENTS Page Mathematical Tables 3 Units and Measures 25 Physical Data 34 Meteorological Tables and Graphs Wind 47 TaeTTjiodynamics TO Pressure 83 Atmospheric Statics 105 General 113 Bibliography 121 SECTION I NUMEIUCAL AND GRAPHICAL DATA BY NoBMAisr R. BEERS AND THE A E R O L O G I C A L ENGINEERING S T A P F , POSTGRADUATE ScHOOL UNITED STATES NAVAL ACADEJMY TABLE 1.—GBEEK PnBFtxBS micro 1/1,000,000 deka 10 milli 1/1,000 hecto 100 centi Hoo kilo 1,000 deci Ko mega 1,000,000 TABLE 2 . — G R E E K ALPHABET A a or a alpha N v '. nu B ,8 beta S f xi r 7 , gamma 0 o. ." omicron A S or d delta H w p i . E e epsilon P p 'rho Z f zeta So- sigma H T; eta T T tau e 9 or i> ^ theta T v _....,-. upsilon. I I iota * (^ or i p . . . . . . . .^ ... .^. .'....:. . phi K K "... kappa X x • . . . . . . , . ' chi AX lambda "i 4/ psi ' M li mu I Q cc) . .' ' omega Sec. I] MATHEMATICAL TABLES MATHEMATICAL TABLES TABLE 3.—RECIPROCALS OF NUMBERS* N 1.00 I 2 3 4 l.OS 6 7 8 9 1.10 I 2 3 4 1.18 6 7 8 9 1:20 1 2 3 4 1.26 6 7 8 9 1.30 I 2 3 4 1.85 6 7 8 9 1.40 1 2 3 4 1.4S 5 7 8 9 0 .9901 .9804 .9709 .9615 .9524 .9434 .9346 .9259 .9174 .9091 .9009 .8929 .8850 .8772 .8696 .8621 .8547 .8475 .8403 .8333 .8264 .8197 .8130 .8065 .8000 .7937 .7874 J8I2 .7752] .7692 .7634 .7576 .7519 .7463 .7407 .7353 .7299 .7246 .7194 .7143 .7092 .7042 .6993 .6944 .6897 .6849 .6803 .6757 .6711 1 .9990 .9891 .9794 .9699 .9606 .9515 .9425 .9337 .9251 .9166 .9083 .9001 .8921 .8842 .8764 .8688 .8613 .8540 .8467 - .8396 .8326 .8258 .8190 .8123 .8058 .7994 .7930 .7868 J806 .7746 .7686 .7628 .7570 .7513 .7457 -.7402 .7348 .7294 .7241 .7189 .7138 .7087 .7037 .6988 .6940 .6892 .6845 .6798 .6752 .6707 2 .9980 .9881 - .9785 .9690 .9597 .9506 .9416 .9328 .9242 .9158 .9074 .8993 .8913 .8834 .8757 .8681 .8606 .8532 .8460 .8389 .8319 ,8251 .8183 .8117 .8052 .7987 .7924 .7862 .7800 .7740 .7680 .7622 .7564 .7508 .7452 .7396 .7342 .7289 .7236 J184 .7133 .7082 .7032 .6983 .6935 .6887 .6840 .6793 .6748 .6702 3 .9970 .9872 .9775 .9681 .9588 .9497 .9407 .9320 .9234 .9149 .9066 .8985 .8905 .8826 .8749 .8673 .8598 .8525 .8453 .8382 .8313 .8244 .8177 .8110 .8045 .7981 .7918 .7855 .7794 .7734 J675 .7616 .7559 .7502 .7446 .7391 .7337 .7283 .7231 J179 .7128 .7077 .7027 .6978 .6930 .6882 .6835 .6789 .6743 .6698 4 .9960 .9862 .9765 .9671 .9579 .9488 .9398 .9311 .9225 .9141 .9058 .8977 .8897 .8818 .8741 .8666 .8591 .8518 .8446 .8375 .8306 ,8237 .8170 .8104 .8039 .7974 .7911 .7849 J788 J728 .7669 .7610 .7553 .7496 .7440 ' .7386 .7331 .7278 .7225 .7174 .7123 .7072 .7022 .6974 .6925 .6878 .6831 .6784 .6739 .6693 6 .9950 .9852 .9756 .9662 .9569 .9479 .9390 .9302 .9217 .9132 .9050 .8969 .8889 .8811 .8734 .8658 .8584 .8511 .8439 .8368 .8299 .8230 .8163 .8097 .8032 .7968 .7905 .7843 J782 .7722 J663 .7605 .7547 .7491 J435 .7380 .7326 .7273 .7220 .7168 .7117 .7067 .7018 .6969 .6920 .6873 .6826 .6780 .6734 .6689 6 .9940 .9843 .9747 .9653 .9560 .9470 .9381 .9294 .9208 .9124 .9042 .8961 .8881 .8803 .8726 .8651 .8376 .8503 .8432 .8361 .8292 .8224 .8157 .8091 .8026 .7962 .7899 .7837 J776 .7716 .7657 .7599 J541 .7485 J429 .7375 .B21 .7267 .7215 .7163 .7112 .7062 .7013 .6964 .6916 .6868 .6821 .6775 .6729 .6684 7 .9930 .9833 .9737 .9643 .9551 .9461 .9372 .9285 .9200 .9(16 .9033 .8953 .8873 .8795 .8718 .8643 .8569 .8496 .8425 .8354 1.8285 .8217 .8150 .8084 .8019 .7955 .7893 .7831 J770 .7710 .7651 .7593 .75:!6 .7479 .7424 .7369 .7315 .7262 .7210 .7158 .7107 .7057 .7008 .6959 .6911 .6863 .6817 .6770 .6725 .6680 8 .9921 .9823 .9728 .%34 .9542 .9452 .9363 .9276 .9191 .9107 .9025 .8945 .8865 .8787 .8711 .8636 .8562 .8489 .8418 .8347 .8278 .8210 .8143 .8078 .8013 .7949 .7886 .7825 .7764 .7704 .7645 .7587 .7530 .7474 .7418 .7364 .7310 .7257 .7205 jri53 .7102 .7052 .7003 .6954 .6906 .6859 .6812 .6766 .6720 .6676 9 .9911 .9814 .9718 .9625 .9533 .9443 .9355 .9268 .9183 .9099 .9017 .8937 .8857 .8780 .8703 .8628 .8554 .8482 .8410 .8340 .8271 .8203 .8137 .8071 .8006 .7943 .7880 .7819 .7758 .7698 .7639 .7582 .7524 .7468 .7413 .7358 .7305 .7252 .7199 J148 .7097 .7047 .6998 .6949 .6901 .6854 .6807 .6761 .6716 .6671 Mia • 5 ^ -10 -9 -8 - 7 , -6 -5 l/jT = 0.318310 1/e = 0.367879 Moving the decimal point in either direction in. N requires moving it in the opposite directi?Jn in body of table (sea p. 5). * From. Marks, "Mechanical Engineers' Handbook," 4th ed., McGraw-HiU., New York, 1941. NUMERICAL AND GRAPHICAL DATA \ [Sec, I . N 1.60 1 2 3 4 1.BS 6 7 8 9 1.60 I 2 3 4 1.66 6 7 8 9 1.70 1 2 3 4 1.76 6 7 8 9 1.80 1 2 3 4 1.85 6 7 8 9 1.90 1 2 3 4 1.96 6 8 8 9 TABLE 3 0 .6667 .6623 .6579 .6536 .6494 .6452 .6410 .6369 .6329 .6289 .6250 .6.^11 .6173 .6135 .6098 .6061 .6024 .5988 .5952 .5917 .5882 .5848 .5814 .5780 J747 .5714 .5682 .5650 .5618 .5587 .5556 .5525 .5495 .5464 J435 .5405 .5376 .5348 .5319 Jim .5263 .5235 .5208 .5181 3155 .5128 .5102 .5076 .5051 .5025 1 .6662 .6618 .6575 .6532 .6489 .6447 .6406 ,6365 ,6325 .6285 ,6246 ,6207 ,6169 .6131 .6094 .6057 .6020 J984 .5949 J914 .5879 J845 J811 .5777 J744 3711 .5679 .5647 3615 3583 ,5552 .5522 .5491 3461. 3432 ,5402 .5373 .5345 3316 3288 ,5260 3233 ,5206 3179 3152 3126 ,5099 .5074 .5048 3023 —RECIPROCALS OF 2 .6658 .6614 .6570 .6527 .6485 .6443 .6402 .6361 .6321 .6281 .6242 .6203 .6165 .6127 .6090 .6053 .6017 3981 3945 .5910 .5875 3841 3807 .5774 3741 3708 3675 .5643 .5612 3580 .5549 .5519 .5488 3459 .5429 .5400 3371 3342 .5313 .5285 .5258 3230 .5203 3176 3149 3123 .5097 .507) .5045 .5020 3 .6653 .6609 .6566 .6323 .6481 .6439 .6398 .6357 .6317 .6277 .6238 .6200 .6161 .6124 .6085 .6050 .6013 3977 .5942 3907 3872 3838 3B04 .5770 3737 .5705 3672 3640 .5609 3577 .5546 .5516 .5485 3456 ,5426 3397 .5368 .5339 3311 .5283 .5255 3227 3200 3173 3147 3120 .5094 .5068 .5043 .5018 4 .6549 .6605 .6562 .6519 .6477 .6435 .6394 .6353 .6313 .6274 .6234 .6196 .6158 .6120 .6083 .60(6 .6010 .5974 .5938 3903 .5869 3834 •3800 3767 3734 .5701 .5669 .5637 .5605 3574 .5543 .5513 3482 .5453 3423 .5394 .5365 3336 3308 .5280 .5252 3225 3198 3171 3144 5118 .5092 .5066 .5040 , .5015 * NUMBEES.*— 5 .6545 .6601 .6557 .6515 ,6472 .5431 ,6390 .6349 .5309 .6270 .5231 .6192 .6154 .6116 .5079 .6042 .6006 .5970 3935 .5900 3865 3831 3797 3764 3731 .5598 .5666 .5634 .5602 3571 .5540 .5510 .5479 3450 3420 .5391 .5362 3333 3305 3277 .5249 3222 3195 3168 3141 3115 .5069 • .5053 • .5038 .5013 6 .6540 .6595 .6553 .6510 .6468 .6427 .6386 ,6345 .6305 ,6266 .6227 .6188 .6150 .6112 .5075 .6039 .5002 .5957 3931 3896 3862 3828 • 3794 3760 3727 3695 3653 .5631 .5599 3568 .5537 3507 3476 .5447 3417 .5388 .5359 3330 3302 3274 , .5247 .5219 3192 - 3165 3139 .5112 .5086 .5051 .5035 .5010 (Continued 7 .5636 .6592 .5549 .6505 .6454 .6423 .5382 .6341 .6301 .6262 .6223 .6184 .6146 .6109 .6072 .6035 3999 3953 3928 .5893 3858 .5824 3790 .5757. 3724 3592 .5659 3627 .5596 3565 .5534 .5504 3473 .5444 3414 .5385 .5355 .5328 3299 .5271 .5244 .5216 3189 3163 3136 '3110 .5084 .5058 .5033 .5008 8 .6631 .6588 .6545 .6502 .6460 .6418 .5378 .6337 .6297 .6258 .6219 .5180 .6143 .6105 .6068 ,6031 3995 .5959 3924 3889 3855 .5821 3787 3754 3721 .5688 ,5656 .5524 .5593 .5552 .5531 .5501 .5470 .5441 .5411 .5382 .5353 3325' 3297 .526? .5241 .5214 3187 3160 3133 3107 .5081 .5055 .5030 3005 9 .5627 .6583 .6540 .6498 .6456 .6414 .5373 .6333 .5293 ,6254 ,6215 ,6177 ,6139 .6101 .6064 .6028 .5992 3956 3921 3886 .5851 .5817 3784 3750 .5718 .5685 3553 3521 .5590 3559 .5528 3498 3467 .5438 .5408 3379 .5350 .5322- •3294 • 3266 .5238 .5211 3184 3157 3131 3105 3079 .5053 .5028 3003 4^ -4 , -3 • ''' - 2 , ]Moving the decimal point in. either direction iii N requires moving it in the opposite direction in bodj of table (see p. 5). Sec. I] MATHEMATICAL TABLES N 2.0 1 2 3 4 2.5 6 7 8 9 S.O 1 2 3 4 3.6 6 7 8 9 4.0 t 2 -3 4 4.5 6 7 8 9 TABLE 3 0 .5000 .4762 .4545 .4348 .4167 .4000 .3846 .3704 .3571 .3448 .3333 J226 .3125 J030 .2941 .2857 .2778 .2703 .2632 25M .2500 .2439 .2381 .2326 .2273 .2222 .2174 .2128 .2083 .2041 1 .4975 • .4739 .4525 .4329 .4149 .3984 .3831 .3690 3559 3436 .3322 3215 3115 .3021 J933 .2849 J770 J695 J625 0558 .2494 .2433 .2375 .2320 J268 .2217 .2169 2\li .2079 J037 .—RECIPROCALS 2 .4950 .4717 .4505 .4310 .4132 3968 .3817 3676 3546 3425 .3311 3205 3106 .3012 .2924 .2841 .2762 .2688 .2618 .2551 .2488 .2427 .2370 J!315 J262 J212 .2165 J119 .2075 J033 3 .4926 .4695 .4484 .4292 .4115 3953 .3802 .3663 .3534 3413 3300 3195 .3096 3003 J915 .2833 .2755 .2681 .2611 J545 .2481 .2421 J364 .2309 .2257 .2208 .2160 .2114 .2070 .2028 4 .4902 .4673 .4464 .4274 .4098 .3937 3788 3650 .3521 3401 3289 3183 3086 .2994 .2907 .2825 .2747 .2674 .2604 .2538 .2475 .2415 J358 .2304 .2252 .2203 .2155 .2110 .2066 .2024 OP NUMBERS.*— 6 .4878 .4651 .4444 .4255 .4082 3922 .3774 3636 3509 3390 .3279 3175 .3077 .2985 .2899 .2817 .2740 .2667 .2597 .2532 .2469 .2410 .2353 .2299 .2247 .2198 .2151 .2105 .2062 .2020 6 .4854 .4630 .4425 .4237 .4065 3906 .3759 .3623 3497 3378 .3268 3165 3067 .2976 J890 .2809 J732 .2660 .2591 u!525 .2463 .2404 .2347 .2294 .2242 .2193 .2146 .2101 .2058 .2016 -{Continued) 7 .4831 .4608 .4405 .4219 .4049 3891 .3745 .3610 3484 3367 3257 3155 .3058 .2967 J882 .2801 .2725 .2653 .2584 .2519 .2457 .2398 .2342 .2288 .2237 .2188 .2141 .2096 .2053 .2012 8 .4808 .4587 .4386 ,4202 .4032 .3876 .3731 .3597 3472 3356 .3247 3145 3049 .2959 J874 .2793 .2717 .2646 .2577 J513 J45I .2392 .2336 .2283 J232 .2183 .2137 .2092 .2049 .2008 9 .4785 .4566 .4367 .4184 .4016 .3861 .3717 .3584 3460 .3344 .3236 3135 .3040 .2950 .2865 .2786 .2710 .2639 .2571 .2506 .2445 .2387 .2331 .2278 J227 .2179 .2132 '.2088 .2045 .2004 Mia -24 -21 -20 -18 -17 -15 -14 -13 -12 -12 -II -10 -10 -9 -8 -8 -8 -7 -7 -6 -6 -6 -6 -5 -5 -5 -5 -4 -4 -4 I/TT = 0.31835 1/e = 0.367879 Explanation of Table of Reciprocals (pp. 3-6). This table gives the values of 1/N for values of N from 1 to 10, correct to four figures. (Interpolated values may be in error by 1 in th§ fourth figure.) To find the reciprocal of a number N outside the range from 1 to 10, note that moving the decimal point any number of places in either direction in column N is equivalent to moving it the same number of places in the opposite direction in the body of the table. For example: s i l T = °-31°8 3 ^ ^ = 0.000 3109 g ^ g ^ = 310.9 Computations are frequently simplified by careful arrangement of the problem and recognition of adequate mathematical approximations. For example: = 1 + X \x\<<l) \ ±x 1 (0.006944)»' NUMERICAL AND GRAPHICAL DATA [Sec. I TABLE 3.—RECIPROCALS OF NtrMBEKs.'*—{Cpniinuea) N 5.0 .1 .2 .1 .4 S.S .6 .7 .8 .9 6.0 .1 .2 .3 A 6.5 .6 .7 .8 .9 7.0 .r J .3 .4 7.6 _5 _7 _8 .9 8.0 .1 .2 .3 .4 86 .6 .7 .8 .9 9.0 .1 .2 .3 .4 S.8 .6 .7 .8 .9 0 .2000 .1961 .1923 .1887 .1852 .1818 .1786 .1754 .1724 .1695 .1667 .1639 .1613 .1587 .1563 .1538 .1515 .1493 .1471 .1449 .1429 .1403 .1389 .1370 .1351 .1333 .1316 .1299 .1282 .1266 .1250 .1B5 .1220 .(205 .1190 .1176 .1163 .1149 .1136 .1124 .1111 .1099 .1087 .1075 .1064 .1053 .1042 .1031 .1020 .1010 1 .1996 .1957 .1919 .1883 .1848 .1815 .1783 .1751 .1721 .1692 .1664 .1637 .1610 .1585 .1560 .1536 .1513 .1490 .1468 .1447 .1427 .(406 .1387 .1368 .1350 .1332 .1314 .1297 .1280 .1264 .1248 .1233 .1218 .1203 .1189 .1175 .1161 .1148 .1135 .1122 .1110 •.1098 .1086 .1074 .1063 .1052 .1041 .1030 .1019 .1009 a .1992 .1953 .1916 .1880 .1845 .1812 .1779 .1748 .1718 .1689 .1661 .1634 .1608 .1582 .1558 .1534 .1511 .1488 .1466 .1445 .1425 .1404 .1385 .1366 .1348 .1330 .1312 .1295 .1279 .1263 .1247 ,1232 .1217 .(202 .1183 .1174 .1160 .1147 .1134 .1121 .1109 .1095 .1085 .1073 .1062 .1050 .1040 .1029 .1018 .1008 3 .1988 .1949 .1912 .1876 .1842 .1808 .1776 .1745 .1715 .1686 .1658 .1631 .1605 .1580 .1555 .1531 .1508 .I486 .1464 .1443 .1422 .140} .1383 .1354 .1346 .1328 .1311 .1294 .1277 .1261 .1245 .1230 .1215 .(200 .1186 .1172 .1159 .1145 .1133 .1120 .1107 .1095 .1083 .1072 .1060 .1049 .1038 .1028 .1017 .1007 1 .1984 .1946 .1908 .1873 .1838 .1805 .1773 .1742 .1712 .1684 .1656 .1629 .1603 .1577 .1553 .1529 .1505 .1484 .1462 .1441 .1420 .1401 .1381 .1362 .1344 .1325 .1309 .1292 .1276 .1259 .1244 .1229 .1214 .1(99 .1183 .1171 .1157 .1144 .1131 .1119 .1106 .1094 . .1082 .1071 .1059 .1048 .1037 .1027 .1016 .1006 5 .1980 .1942 .1905 .1869 .1835 .1802 .1770 .1739 .1709 .1681 .1653 .1626 .1600 .1575 .1550 .1527 .1504 .1481 .1460 • .1439 .1418 ' .1399 .1379 .1361 .1342 .1325 .1307 .1290 .1274 .1258 ,1242 .1227 ,1212 ,1(98 .1183 .1170 .1156 .1143 .1130 .1)17 .1105 .1093 .1081 .1070 .I05S .1047 .1036 .1026 .1015 .1005 6 .1975 .1938 .1901 .1865 .1832 .1799 ,1767 .1736 .1706 .1678 .1650 .1623 .1597 .1572 .1548 .1524 .1502 .1479 • .1458 .1437 .1416 .(397 • .1377 .1359 .1340 .1323 .1305 .1289 .1272 .1256 .1241 .1225 .1211 .1196 .1182 .1168 .1155 .1142 .1129 .1116 .1104 .1092 .1080 .1068 ,1057 .1046 .1035 .1025 .1014 .1004 7 .1972 .1934 .1898 .1862 .1828 .1795 .1764 .1733 .1704 .1675 ,1647 .1621 .1595 .1570 .1546 .1522 .1499 .1477 .(456 .1435 .1414 .1395 .1375 .1357 .1339 .1321 .1304 .1287 .1271 .1255 .1239 .1224 .1209 .1(95 .1181 .1167 .:1153 .1140 .1127 .1115 .1103 .1091 .1079 .1067 .1055 .1045 .1034 .1024 .1013 .1003 8 .1969 ,1931 .1894 .1859 .1825 .1792 •• .1761 .1730 .1701 .1672 .1545 .1618 .1592 .1567 .1543 .1520 .1497 .1475 .1453 .1433 .1412 .1393 .1374 .1355 .1337 .1319 .1302 .1285 .1269 .1253 .1238 .1222 .1208 .1(93 .1179 .1166 .1152 .1139 .1125 .1114 .1101 .1089 .1078 .1066 .1055 .1044 .1033 .1022 .1012- .1002 9 .1965 .1927 .1890 .1855 .1821 .1789 .1757 .1727 .1698 .1669 .1642 .1616 .1590 .1565 .1541 .1517 .1495 .1473 .1451 .1431 .1410 .1391 .1372 .1353 .1335 .1318 .1300 .1284 .1267 .1252 .1236 .1221 .1206 .((92 .1178 .1164 .1151 .1138 .1125 .1112 .1100 .1088 .1076 .1065 .1054 .1043 .1032 .1021 .1011 .1001 |§ -4 -3 -2 -' ' •Moving the decimal point in either direction in N requires moving it in the opposite direction m body of table (see p. 5). Sec. I] MATHEMATICAL TABLES TABLE 4.—COMMON LOGABITHMS* {special table\.^. B " 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 i.n 1.12 1.13 I.I4 1.15 1.16 1.17 1.18 1.19 1.20 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29 1.30 1.31 1.32 1.33 1.34 1.35 1.36 1.37 1.38 1.39 1.40 1.41 1.42 1.43 1.44 1.45 1.46 .1.47 1.48 1.49 0 0.0000 0043 C086 0128 0170 0212 0253 0294 0334 0374 0.0414 0453 0492 0531 0569 0607 0645 0682 0719 0755 0.0792 ^ 0828 0864 0899 0934 0969 1004 1038 1072 1106 0.1139 1173 1206 1239 1271 1303 1335 1367 1399 1430 0.1451 1492 1523 1553 1584 1614 1644 1673 1703 1732 1 0004 0048 0090 0133 0175 0216 0257 0298 0338 0378 0416 0457 0496 0535 0573 0611 0648 0686 0722 0759 0795 0831 0867 0903 0938 0973 1007 1041 1075 1109 1143 1176 1209 1242 1274 1307 1339 1370 1402 1433 \ 1464 1495 1526 1556 1587 1617 1647 1676 1706 1735 2 0009 0052 0095 0137 BI79, 0220 0251 0302 0342 0382 0422 0451 0500 0538 0577 0615 0652 0689 0726 0763 0799 0835 0871 0905 0941 0975 1011 1045 1079 1113 1146 1179 1212 1245 1278 1310 1342 1374 1405 1436 1467 1498 1529 1559 1590 1620 1649 1679 1708 1738 3 0013 0056 0099 0141 ).0183 0224 0265 0306 0345 0386 0426 0465 0504 0542 0580 0618 0656 0693 0730 0765 0803 0839 0374 0910 0945 0980 1014 1048 1082 1116 1149 1183 1216 1248 1281 1313 1345 1377 1408 1440 1471 1501 1532 1562 1593 1623 1652 1682 1711 1741 4 0017 0060 0103 0145 0187 0228 0269 03)0 0350 0390 0430 0469 0508 0546 0584 0622 0660 0697 0734 0770 0806 0842 0878 0913 0948 0983 1017 1052 1086 1119 1153 1185 1219 1252 1284 1315 1348 1380 1411 1443 , 1474 1504 1535 1565 1596 1626 1655 1585 1714 1744 5 0022 0055 0107 0149 0191 0233 0273 0314 0354 0394 0434 0473 0512 0550 0588 0526 0663 0700 0737 0774 0810 0846 0381 0917 0952 0985 1021 1055 1089 1123 1155 1189 1222 1255 1287 1319 1351 1383 1414 1446 ' 1477 1508 1538 1559 1599 1529 1658 1588 1717 1745 6 0025 0039 0111 0154 0195 0237 0278 0318 0358 0398 0438 0477 0515 0554 0592 0630 0657 0704 0741 0777 0813 0849 0885 0920 0955 0990 1024 1059 1092 1126 '1159 1193 1225 1258 1290 1323 1355 1386 1418 1449 1480 1511 1541 1572 1602 1532 1661 1591 1720 1749 7 0030 0073 0115 0158 0199 0241 0282 0322 0362 0402 0441 0481 0519 0558 0596 0533 0671 0708 0745 0781 0817 0853 0888 0924 0959 0993 1028 1062 1096 1129 1163 1195 1229 1261 1294 1325 1358 1389 1421 1452 1483 1514 1544 1575 1605 1635 1664 1694 1723 1752 8 0035 0077 0120 0162 0204 0245 0285 0326 0365 0405 0445 0484 0523 0561 0599 0537 0574 0711 0748 0785 0821 0855 0892 0927 0962 0997 1031 1065 1099 1133 1165 1199 1232 1255 1297 1329 1361 1392 1424 1455 1485 1517 1547 1578 1608 1538 1667 1697 1726 1755 — 9 — - 0039 0082 0124 0166 0208 0249 0290 0330 0370 0410 0449 0488 0527 0565 0603 0641 0678 0715 0752 0788 0824 0860 0895 0931 0966 1000 1035 1069 1103 1136 1159 1202 1235 1268 1300 1332 1364 1396 1427 1453 1489 1520 1550 1581 1611 1641 1670 1700 1729 1758 i 4 3 Moving the decimal point n places to the right [or left] in the number requires adding + n [or —n] in the body of the table (see p. 9). * From Marks, "Mechanical Engineers' Handbook," 4th ed,, McGraw-Hill, New York, 1941.

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HANDBOOK OF METEOROLOGY EDITED BY F. A. BERRY, JR. Captain, U.S.N., Officer-in-Charge, U.S. Naty Weather Central, Washington, D.C. E.BOLLAY Lieutenant Commander, U.S.N.R NORMAN R. BEERS ^VA^ afe*^ New York London McGRAW-HILL BOOK COMPANY, INC. 1 9 4 5 HANDBOOK OP METBOKOLOGY COPYBIGHT, 1 9 4 5 , BY THE M C G B A W - H I L L BOOK COMPANY, INC. PRtNTEP IN THE UNITED STATES OF A M B B I C A All rights reserved. This book, or parts thereof, may not he reproduced in any form without-permission vf* the publishers.' vii THE MAPLE PRESS COMPANY, YORK, PA. PREFACE The "Handbook of Meteorology" is designed to furnish the student and the professional meteorologist a convenient text reference for data, fundamental theory, and weather analysis and forecasting. The empha- sis has been conscientiously placed on the scientific and engineering aspects of meteorology, rather than on current techniques. This emphasis is desirable at any time in a handbook, and particularly so at this time in view of recent and forthcoming changes in the methods of analysis and in the display of synoptic data (especially at upper levels). The editors' intent has been that this handbook contain practical meteorological information. Their interpretation of what is "practical" is based on their collective experience and on their interpretation of the experience of returning students who have forecast the weather in the field under trying conditions. Accordingly the "Handbook of Meteor- . ology" contains not only sections on fronts, air masses, upper air, etc., which are immediately suggested by its title, but also those fundamentals of mathematics and of the physical sciences on which meteorology is dependent. Some of these topics are frequently considered to be theo- retical. When, however, they are written up in compact form and in meteorological language so as to be "available, useful, in practice or action," then they are rightly included in a book that is designed for daily use. The practice of meteorology (by which is meant some direct or indirect aspect of weather forecasting) is like the other engineering sciences in that an answer to a problem is required in a specified time, often from meager data. Moreover, as is sometimes overlooked in the stress of war, "an engineer is one who can do at reasonable cost what almost any man can accomplish with unlimited resources at his dis-" posal."* It is the editors' considered belief'.that the practice of meteor- ology is inevitably to become accepted as an engineering science.. The variety of problems that arises in meteorological practice is endlessly complicated by both space and time intervals. An aviator' may stand by and demand to know precisely when he will have sufficient ceiling to take off. A constructor may save lives and money by knowing with some accuracy what will be the maximum rainfall over a large watershed. These and many other meteorological problems are not *GrLKET, J. r., Journal 0/Engineering, January, 1945. V VI PREFACE yet completely solved, though fine progress has been made with recent advances. Many meteorological problems are in fact not yet clearly stated as problems, nor can much be done to overcome present inade- quacies until many men and women understand not only the basic principles of meteorology, but also the principal problems of at least one other activity, e.g., aviation, agriculture, manufacture, transpor- tation, distribution, communications, etc. The editors desire to acknowl- edge these problems even though the present editioii of the handbook is limited in scope to aviation and hydrometeorology in this respect. Perhaps greater cooperation is required among individuals and among nations in the practice of meteorology than in any other social effort of man. This is so, simply because even short-period forecasts often depend on synoptic data that are beyond the reach of the indi\'idual meteorologist or the individual nation. Problems involving longer periods and greater areas require even more data, from the surface and from upper levels of the atmosphere. Recognition of the cooperation required for successful weather services appeared at least a hundred years ago when John Ruskin wrote, "The metec^ological Society, there- fore, has been formed, not for a city, nor for a kingdom, but for the world." The editors are deeply indebted to their contributors especially and to many others who have also cooperated generously to produce this' handbook. , . • Mr. Charney wishes to acknowledge his indebtedness to Professor J. Kaplan for his introduction to the subject (Section IV), and for the kind encouragement he received in the preparation of the manuspripli. The editors assume full responsibility for the selection and arrange- ment of topics. Each section has been read by one or more critics, but individual authors were final judges as to how their contributions should be covered. Much desirable material was omitted for security reasons at the time of writing, but it is believed the integrated result of all that has been available provides the engineering science needed by a trained meteorologist in the practice of his profession. For the rules and'regu- lations of the various meteorological services it is generally necessary to make reference to their individual publications. For the art of fore- casting the weather according to the needs and desires of his audience, the meteorologist must defer to the association of his fellows and to experience. T H E EDITORS. ANNAPOLIS, MARYLAND, September, 1945. LIST OF CONTRIBUTORS li. A. BAUMGARTNER, Lieut., U.S.N.R., Postgraduate School, United States Nerval Academy, X. NORMAN R . BEERS, Lieut., U.S.N.R., Postgraduate School, United States Naval Academy, I, V, X. F. A. BERRY, JR., Capt., U.S.N., Staff Comair 7th Fleet, X. E. BoLLAY, Lieut. Comdr., U.S.N.R., Fleet Weather Central, X. JuLE G. CHARNEY, Lecturer, Department of Meteorology, University of California, iV. Civ;ilian Staff, Institute of Tropical Meteorology, Rjp Piedras, Puerto Rico, X. FREDERICK A. FICKEN, Professor of Mathematics, University of Tennessee (on leave); Office of Field Service Consultant, Operations Research Group, U.S.N., II. ALBERT S. PRY, Chief, Hydraulic Data Division, Tennessee Valley Authority, XIII. H. G. HOUGHTON, Professor of Meteorology, Massachusetts Institute of Technology, III. GEORGE R . JENKINS, Lieut., U.S.N.R., Postgraduate School, United States Naval Academy, IX, X. H. LANDSBEBG, Ph.D., Associate Professor of Meteorology, The University of Chicago, - XII. S. C. LOWELL, Lieut. Comdr., U.S.N.R., Postgraduate School, United States Naval Academy, III. K. B. MCEACHRON, Research Engineer, High Voltage Engineering Laboratory and Designing Engineer, Power Transformer Engineering Division, General Electric Company, Pittsfield, Mass.; Fellow, American Institute of Electrical Engineers, III. J. F. O'CONNOR, Lieiit., U.S.N.R., Postgraduate School, United States Naval Acad- emy, X. MILDRED B . OLIVER, Department of Meteorology, The University of Chicago, X. VINCENT J. OLIVER, Department of Meteorology, The University of Chicago, X. CAKL-G. ROSSBY, Andrew MacLeish Distinguished Service Professorship and Chair- man of the Department of Meteorology, The University of Chicago, VII. P. L. ScHBREScHEwsKY, Formerly Chief Weather Service, French Armies, X L A. K. SHOW ALTER, Meteorologist in Charge, Hydrometeorological Section, Office of Hydraulic Director, U.S. Weather Bureau, XIII. H. .J. STEWART, Daniel Guggenheim Aeronautical Laboratory, California Institute of Technology, VI. H. U. SVERDRUP, Professor of Oceanography, ^University of California; Director, Scripps Institution of Oceanography, XIV. LouvAN E. WOOD, Meteorological Engineer, Friez Instrument Division, Bendix Aviation Corporation, VIII. vu CONTENTS For the detailed contents of any section consult the title page of that section. For the alphabetical index see pp. 1057 to 1068. SECTION PAGE P E B F A C B . . -. V L I S T OF CONTRIBUTORS vii NUMERICAL AND GRAPHICAL D A T A I 1 METEOROLOGICAL MATHEMATICS AND CALCULATIONS . . II 123 PHYSICS OF ATMOSPHERIC P H E N O M E N A I l l 241 RADIATION. . ". IV 283 METEOROLOGICAL THERMODYNAMICS AND ATMOSPHERIC STATICS V 313 KINEMATICS AND DYNAMICS OF F L U I D F L O W VI • 411 T H E SCIENTIFIC BASIS OF M O D E R N METEOROLOGY . . . VII 501 METEOROLOGICAL INSTRUMENTS VIII 531 TRANSMISSION AND PLOTTING OF METEOROLOGICAL D A T A I X 573 SYNOPTIC METEOROLOGY AND W E A T H E R FORECASTING . X 601 CLOUDS AND STATES' OF THE SKY X I 881 CLIMATOLOGY XII 927 HYDROMETEOROLOGY X I I I 999 OCEANOGRAPHY. . . ' X I V 1029 INDEX 1057 SECTION I NUMERICAL AND GRAPHICAt DATA BY NORMAN R. BEERS AND THE A B R O L O G I C A L ENGINEERING S T A F F , POSTGRADUATE ScHOOL, UNITED STATES NAVAL ACADEMY CONTENTS Page Mathematical Tables 3 Units and Measures 25 Physical Data 34 Meteorological Tables and Graphs Wind 47 TaeTTjiodynamics TO Pressure 83 Atmospheric Statics 105 General 113 Bibliography 121 SECTION I NUMEIUCAL AND GRAPHICAL DATA BY NoBMAisr R. BEERS AND THE A E R O L O G I C A L ENGINEERING S T A P F , POSTGRADUATE ScHOOL UNITED STATES NAVAL ACADEJMY TABLE 1.—GBEEK PnBFtxBS micro 1/1,000,000 deka 10 milli 1/1,000 hecto 100 centi Hoo kilo 1,000 deci Ko mega 1,000,000 TABLE 2 . — G R E E K ALPHABET A a or a alpha N v '. nu B ,8 beta S f xi r 7 , gamma 0 o. ." omicron A S or d delta H w p i . E e epsilon P p 'rho Z f zeta So- sigma H T; eta T T tau e 9 or i> ^ theta T v _....,-. upsilon. I I iota * (^ or i p . . . . . . . .^ ... .^. .'....:. . phi K K "... kappa X x • . . . . . . , . ' chi AX lambda "i 4/ psi ' M li mu I Q cc) . .' ' omega Sec. I] MATHEMATICAL TABLES MATHEMATICAL TABLES TABLE 3.—RECIPROCALS OF NUMBERS* N 1.00 I 2 3 4 l.OS 6 7 8 9 1.10 I 2 3 4 1.18 6 7 8 9 1:20 1 2 3 4 1.26 6 7 8 9 1.30 I 2 3 4 1.85 6 7 8 9 1.40 1 2 3 4 1.4S 5 7 8 9 0 .9901 .9804 .9709 .9615 .9524 .9434 .9346 .9259 .9174 .9091 .9009 .8929 .8850 .8772 .8696 .8621 .8547 .8475 .8403 .8333 .8264 .8197 .8130 .8065 .8000 .7937 .7874 J8I2 .7752] .7692 .7634 .7576 .7519 .7463 .7407 .7353 .7299 .7246 .7194 .7143 .7092 .7042 .6993 .6944 .6897 .6849 .6803 .6757 .6711 1 .9990 .9891 .9794 .9699 .9606 .9515 .9425 .9337 .9251 .9166 .9083 .9001 .8921 .8842 .8764 .8688 .8613 .8540 .8467 - .8396 .8326 .8258 .8190 .8123 .8058 .7994 .7930 .7868 J806 .7746 .7686 .7628 .7570 .7513 .7457 -.7402 .7348 .7294 .7241 .7189 .7138 .7087 .7037 .6988 .6940 .6892 .6845 .6798 .6752 .6707 2 .9980 .9881 - .9785 .9690 .9597 .9506 .9416 .9328 .9242 .9158 .9074 .8993 .8913 .8834 .8757 .8681 .8606 .8532 .8460 .8389 .8319 ,8251 .8183 .8117 .8052 .7987 .7924 .7862 .7800 .7740 .7680 .7622 .7564 .7508 .7452 .7396 .7342 .7289 .7236 J184 .7133 .7082 .7032 .6983 .6935 .6887 .6840 .6793 .6748 .6702 3 .9970 .9872 .9775 .9681 .9588 .9497 .9407 .9320 .9234 .9149 .9066 .8985 .8905 .8826 .8749 .8673 .8598 .8525 .8453 .8382 .8313 .8244 .8177 .8110 .8045 .7981 .7918 .7855 .7794 .7734 J675 .7616 .7559 .7502 .7446 .7391 .7337 .7283 .7231 J179 .7128 .7077 .7027 .6978 .6930 .6882 .6835 .6789 .6743 .6698 4 .9960 .9862 .9765 .9671 .9579 .9488 .9398 .9311 .9225 .9141 .9058 .8977 .8897 .8818 .8741 .8666 .8591 .8518 .8446 .8375 .8306 ,8237 .8170 .8104 .8039 .7974 .7911 .7849 J788 J728 .7669 .7610 .7553 .7496 .7440 ' .7386 .7331 .7278 .7225 .7174 .7123 .7072 .7022 .6974 .6925 .6878 .6831 .6784 .6739 .6693 6 .9950 .9852 .9756 .9662 .9569 .9479 .9390 .9302 .9217 .9132 .9050 .8969 .8889 .8811 .8734 .8658 .8584 .8511 .8439 .8368 .8299 .8230 .8163 .8097 .8032 .7968 .7905 .7843 J782 .7722 J663 .7605 .7547 .7491 J435 .7380 .7326 .7273 .7220 .7168 .7117 .7067 .7018 .6969 .6920 .6873 .6826 .6780 .6734 .6689 6 .9940 .9843 .9747 .9653 .9560 .9470 .9381 .9294 .9208 .9124 .9042 .8961 .8881 .8803 .8726 .8651 .8376 .8503 .8432 .8361 .8292 .8224 .8157 .8091 .8026 .7962 .7899 .7837 J776 .7716 .7657 .7599 J541 .7485 J429 .7375 .B21 .7267 .7215 .7163 .7112 .7062 .7013 .6964 .6916 .6868 .6821 .6775 .6729 .6684 7 .9930 .9833 .9737 .9643 .9551 .9461 .9372 .9285 .9200 .9(16 .9033 .8953 .8873 .8795 .8718 .8643 .8569 .8496 .8425 .8354 1.8285 .8217 .8150 .8084 .8019 .7955 .7893 .7831 J770 .7710 .7651 .7593 .75:!6 .7479 .7424 .7369 .7315 .7262 .7210 .7158 .7107 .7057 .7008 .6959 .6911 .6863 .6817 .6770 .6725 .6680 8 .9921 .9823 .9728 .%34 .9542 .9452 .9363 .9276 .9191 .9107 .9025 .8945 .8865 .8787 .8711 .8636 .8562 .8489 .8418 .8347 .8278 .8210 .8143 .8078 .8013 .7949 .7886 .7825 .7764 .7704 .7645 .7587 .7530 .7474 .7418 .7364 .7310 .7257 .7205 jri53 .7102 .7052 .7003 .6954 .6906 .6859 .6812 .6766 .6720 .6676 9 .9911 .9814 .9718 .9625 .9533 .9443 .9355 .9268 .9183 .9099 .9017 .8937 .8857 .8780 .8703 .8628 .8554 .8482 .8410 .8340 .8271 .8203 .8137 .8071 .8006 .7943 .7880 .7819 .7758 .7698 .7639 .7582 .7524 .7468 .7413 .7358 .7305 .7252 .7199 J148 .7097 .7047 .6998 .6949 .6901 .6854 .6807 .6761 .6716 .6671 Mia • 5 ^ -10 -9 -8 - 7 , -6 -5 l/jT = 0.318310 1/e = 0.367879 Moving the decimal point in either direction in. N requires moving it in the opposite directi?Jn in body of table (sea p. 5). * From. Marks, "Mechanical Engineers' Handbook," 4th ed., McGraw-HiU., New York, 1941. NUMERICAL AND GRAPHICAL DATA \ [Sec, I . N 1.60 1 2 3 4 1.BS 6 7 8 9 1.60 I 2 3 4 1.66 6 7 8 9 1.70 1 2 3 4 1.76 6 7 8 9 1.80 1 2 3 4 1.85 6 7 8 9 1.90 1 2 3 4 1.96 6 8 8 9 TABLE 3 0 .6667 .6623 .6579 .6536 .6494 .6452 .6410 .6369 .6329 .6289 .6250 .6.^11 .6173 .6135 .6098 .6061 .6024 .5988 .5952 .5917 .5882 .5848 .5814 .5780 J747 .5714 .5682 .5650 .5618 .5587 .5556 .5525 .5495 .5464 J435 .5405 .5376 .5348 .5319 Jim .5263 .5235 .5208 .5181 3155 .5128 .5102 .5076 .5051 .5025 1 .6662 .6618 .6575 .6532 .6489 .6447 .6406 ,6365 ,6325 .6285 ,6246 ,6207 ,6169 .6131 .6094 .6057 .6020 J984 .5949 J914 .5879 J845 J811 .5777 J744 3711 .5679 .5647 3615 3583 ,5552 .5522 .5491 3461. 3432 ,5402 .5373 .5345 3316 3288 ,5260 3233 ,5206 3179 3152 3126 ,5099 .5074 .5048 3023 —RECIPROCALS OF 2 .6658 .6614 .6570 .6527 .6485 .6443 .6402 .6361 .6321 .6281 .6242 .6203 .6165 .6127 .6090 .6053 .6017 3981 3945 .5910 .5875 3841 3807 .5774 3741 3708 3675 .5643 .5612 3580 .5549 .5519 .5488 3459 .5429 .5400 3371 3342 .5313 .5285 .5258 3230 .5203 3176 3149 3123 .5097 .507) .5045 .5020 3 .6653 .6609 .6566 .6323 .6481 .6439 .6398 .6357 .6317 .6277 .6238 .6200 .6161 .6124 .6085 .6050 .6013 3977 .5942 3907 3872 3838 3B04 .5770 3737 .5705 3672 3640 .5609 3577 .5546 .5516 .5485 3456 ,5426 3397 .5368 .5339 3311 .5283 .5255 3227 3200 3173 3147 3120 .5094 .5068 .5043 .5018 4 .6549 .6605 .6562 .6519 .6477 .6435 .6394 .6353 .6313 .6274 .6234 .6196 .6158 .6120 .6083 .60(6 .6010 .5974 .5938 3903 .5869 3834 •3800 3767 3734 .5701 .5669 .5637 .5605 3574 .5543 .5513 3482 .5453 3423 .5394 .5365 3336 3308 .5280 .5252 3225 3198 3171 3144 5118 .5092 .5066 .5040 , .5015 * NUMBEES.*— 5 .6545 .6601 .6557 .6515 ,6472 .5431 ,6390 .6349 .5309 .6270 .5231 .6192 .6154 .6116 .5079 .6042 .6006 .5970 3935 .5900 3865 3831 3797 3764 3731 .5598 .5666 .5634 .5602 3571 .5540 .5510 .5479 3450 3420 .5391 .5362 3333 3305 3277 .5249 3222 3195 3168 3141 3115 .5069 • .5053 • .5038 .5013 6 .6540 .6595 .6553 .6510 .6468 .6427 .6386 ,6345 .6305 ,6266 .6227 .6188 .6150 .6112 .5075 .6039 .5002 .5957 3931 3896 3862 3828 • 3794 3760 3727 3695 3653 .5631 .5599 3568 .5537 3507 3476 .5447 3417 .5388 .5359 3330 3302 3274 , .5247 .5219 3192 - 3165 3139 .5112 .5086 .5051 .5035 .5010 (Continued 7 .5636 .6592 .5549 .6505 .6454 .6423 .5382 .6341 .6301 .6262 .6223 .6184 .6146 .6109 .6072 .6035 3999 3953 3928 .5893 3858 .5824 3790 .5757. 3724 3592 .5659 3627 .5596 3565 .5534 .5504 3473 .5444 3414 .5385 .5355 .5328 3299 .5271 .5244 .5216 3189 3163 3136 '3110 .5084 .5058 .5033 .5008 8 .6631 .6588 .6545 .6502 .6460 .6418 .5378 .6337 .6297 .6258 .6219 .5180 .6143 .6105 .6068 ,6031 3995 .5959 3924 3889 3855 .5821 3787 3754 3721 .5688 ,5656 .5524 .5593 .5552 .5531 .5501 .5470 .5441 .5411 .5382 .5353 3325' 3297 .526? .5241 .5214 3187 3160 3133 3107 .5081 .5055 .5030 3005 9 .5627 .6583 .6540 .6498 .6456 .6414 .5373 .6333 .5293 ,6254 ,6215 ,6177 ,6139 .6101 .6064 .6028 .5992 3956 3921 3886 .5851 .5817 3784 3750 .5718 .5685 3553 3521 .5590 3559 .5528 3498 3467 .5438 .5408 3379 .5350 .5322- •3294 • 3266 .5238 .5211 3184 3157 3131 3105 3079 .5053 .5028 3003 4^ -4 , -3 • ''' - 2 , ]Moving the decimal point in. either direction iii N requires moving it in the opposite direction in bodj of table (see p. 5). Sec. I] MATHEMATICAL TABLES N 2.0 1 2 3 4 2.5 6 7 8 9 S.O 1 2 3 4 3.6 6 7 8 9 4.0 t 2 -3 4 4.5 6 7 8 9 TABLE 3 0 .5000 .4762 .4545 .4348 .4167 .4000 .3846 .3704 .3571 .3448 .3333 J226 .3125 J030 .2941 .2857 .2778 .2703 .2632 25M .2500 .2439 .2381 .2326 .2273 .2222 .2174 .2128 .2083 .2041 1 .4975 • .4739 .4525 .4329 .4149 .3984 .3831 .3690 3559 3436 .3322 3215 3115 .3021 J933 .2849 J770 J695 J625 0558 .2494 .2433 .2375 .2320 J268 .2217 .2169 2\li .2079 J037 .—RECIPROCALS 2 .4950 .4717 .4505 .4310 .4132 3968 .3817 3676 3546 3425 .3311 3205 3106 .3012 .2924 .2841 .2762 .2688 .2618 .2551 .2488 .2427 .2370 J!315 J262 J212 .2165 J119 .2075 J033 3 .4926 .4695 .4484 .4292 .4115 3953 .3802 .3663 .3534 3413 3300 3195 .3096 3003 J915 .2833 .2755 .2681 .2611 J545 .2481 .2421 J364 .2309 .2257 .2208 .2160 .2114 .2070 .2028 4 .4902 .4673 .4464 .4274 .4098 .3937 3788 3650 .3521 3401 3289 3183 3086 .2994 .2907 .2825 .2747 .2674 .2604 .2538 .2475 .2415 J358 .2304 .2252 .2203 .2155 .2110 .2066 .2024 OP NUMBERS.*— 6 .4878 .4651 .4444 .4255 .4082 3922 .3774 3636 3509 3390 .3279 3175 .3077 .2985 .2899 .2817 .2740 .2667 .2597 .2532 .2469 .2410 .2353 .2299 .2247 .2198 .2151 .2105 .2062 .2020 6 .4854 .4630 .4425 .4237 .4065 3906 .3759 .3623 3497 3378 .3268 3165 3067 .2976 J890 .2809 J732 .2660 .2591 u!525 .2463 .2404 .2347 .2294 .2242 .2193 .2146 .2101 .2058 .2016 -{Continued) 7 .4831 .4608 .4405 .4219 .4049 3891 .3745 .3610 3484 3367 3257 3155 .3058 .2967 J882 .2801 .2725 .2653 .2584 .2519 .2457 .2398 .2342 .2288 .2237 .2188 .2141 .2096 .2053 .2012 8 .4808 .4587 .4386 ,4202 .4032 .3876 .3731 .3597 3472 3356 .3247 3145 3049 .2959 J874 .2793 .2717 .2646 .2577 J513 J45I .2392 .2336 .2283 J232 .2183 .2137 .2092 .2049 .2008 9 .4785 .4566 .4367 .4184 .4016 .3861 .3717 .3584 3460 .3344 .3236 3135 .3040 .2950 .2865 .2786 .2710 .2639 .2571 .2506 .2445 .2387 .2331 .2278 J227 .2179 .2132 '.2088 .2045 .2004 Mia -24 -21 -20 -18 -17 -15 -14 -13 -12 -12 -II -10 -10 -9 -8 -8 -8 -7 -7 -6 -6 -6 -6 -5 -5 -5 -5 -4 -4 -4 I/TT = 0.31835 1/e = 0.367879 Explanation of Table of Reciprocals (pp. 3-6). This table gives the values of 1/N for values of N from 1 to 10, correct to four figures. (Interpolated values may be in error by 1 in th§ fourth figure.) To find the reciprocal of a number N outside the range from 1 to 10, note that moving the decimal point any number of places in either direction in column N is equivalent to moving it the same number of places in the opposite direction in the body of the table. For example: s i l T = °-31°8 3 ^ ^ = 0.000 3109 g ^ g ^ = 310.9 Computations are frequently simplified by careful arrangement of the problem and recognition of adequate mathematical approximations. For example: = 1 + X \x\<<l) \ ±x 1 (0.006944)»' NUMERICAL AND GRAPHICAL DATA [Sec. I TABLE 3.—RECIPROCALS OF NtrMBEKs.'*—{Cpniinuea) N 5.0 .1 .2 .1 .4 S.S .6 .7 .8 .9 6.0 .1 .2 .3 A 6.5 .6 .7 .8 .9 7.0 .r J .3 .4 7.6 _5 _7 _8 .9 8.0 .1 .2 .3 .4 86 .6 .7 .8 .9 9.0 .1 .2 .3 .4 S.8 .6 .7 .8 .9 0 .2000 .1961 .1923 .1887 .1852 .1818 .1786 .1754 .1724 .1695 .1667 .1639 .1613 .1587 .1563 .1538 .1515 .1493 .1471 .1449 .1429 .1403 .1389 .1370 .1351 .1333 .1316 .1299 .1282 .1266 .1250 .1B5 .1220 .(205 .1190 .1176 .1163 .1149 .1136 .1124 .1111 .1099 .1087 .1075 .1064 .1053 .1042 .1031 .1020 .1010 1 .1996 .1957 .1919 .1883 .1848 .1815 .1783 .1751 .1721 .1692 .1664 .1637 .1610 .1585 .1560 .1536 .1513 .1490 .1468 .1447 .1427 .(406 .1387 .1368 .1350 .1332 .1314 .1297 .1280 .1264 .1248 .1233 .1218 .1203 .1189 .1175 .1161 .1148 .1135 .1122 .1110 •.1098 .1086 .1074 .1063 .1052 .1041 .1030 .1019 .1009 a .1992 .1953 .1916 .1880 .1845 .1812 .1779 .1748 .1718 .1689 .1661 .1634 .1608 .1582 .1558 .1534 .1511 .1488 .1466 .1445 .1425 .1404 .1385 .1366 .1348 .1330 .1312 .1295 .1279 .1263 .1247 ,1232 .1217 .(202 .1183 .1174 .1160 .1147 .1134 .1121 .1109 .1095 .1085 .1073 .1062 .1050 .1040 .1029 .1018 .1008 3 .1988 .1949 .1912 .1876 .1842 .1808 .1776 .1745 .1715 .1686 .1658 .1631 .1605 .1580 .1555 .1531 .1508 .I486 .1464 .1443 .1422 .140} .1383 .1354 .1346 .1328 .1311 .1294 .1277 .1261 .1245 .1230 .1215 .(200 .1186 .1172 .1159 .1145 .1133 .1120 .1107 .1095 .1083 .1072 .1060 .1049 .1038 .1028 .1017 .1007 1 .1984 .1946 .1908 .1873 .1838 .1805 .1773 .1742 .1712 .1684 .1656 .1629 .1603 .1577 .1553 .1529 .1505 .1484 .1462 .1441 .1420 .1401 .1381 .1362 .1344 .1325 .1309 .1292 .1276 .1259 .1244 .1229 .1214 .1(99 .1183 .1171 .1157 .1144 .1131 .1119 .1106 .1094 . .1082 .1071 .1059 .1048 .1037 .1027 .1016 .1006 5 .1980 .1942 .1905 .1869 .1835 .1802 .1770 .1739 .1709 .1681 .1653 .1626 .1600 .1575 .1550 .1527 .1504 .1481 .1460 • .1439 .1418 ' .1399 .1379 .1361 .1342 .1325 .1307 .1290 .1274 .1258 ,1242 .1227 ,1212 ,1(98 .1183 .1170 .1156 .1143 .1130 .1)17 .1105 .1093 .1081 .1070 .I05S .1047 .1036 .1026 .1015 .1005 6 .1975 .1938 .1901 .1865 .1832 .1799 ,1767 .1736 .1706 .1678 .1650 .1623 .1597 .1572 .1548 .1524 .1502 .1479 • .1458 .1437 .1416 .(397 • .1377 .1359 .1340 .1323 .1305 .1289 .1272 .1256 .1241 .1225 .1211 .1196 .1182 .1168 .1155 .1142 .1129 .1116 .1104 .1092 .1080 .1068 ,1057 .1046 .1035 .1025 .1014 .1004 7 .1972 .1934 .1898 .1862 .1828 .1795 .1764 .1733 .1704 .1675 ,1647 .1621 .1595 .1570 .1546 .1522 .1499 .1477 .(456 .1435 .1414 .1395 .1375 .1357 .1339 .1321 .1304 .1287 .1271 .1255 .1239 .1224 .1209 .1(95 .1181 .1167 .:1153 .1140 .1127 .1115 .1103 .1091 .1079 .1067 .1055 .1045 .1034 .1024 .1013 .1003 8 .1969 ,1931 .1894 .1859 .1825 .1792 •• .1761 .1730 .1701 .1672 .1545 .1618 .1592 .1567 .1543 .1520 .1497 .1475 .1453 .1433 .1412 .1393 .1374 .1355 .1337 .1319 .1302 .1285 .1269 .1253 .1238 .1222 .1208 .1(93 .1179 .1166 .1152 .1139 .1125 .1114 .1101 .1089 .1078 .1066 .1055 .1044 .1033 .1022 .1012- .1002 9 .1965 .1927 .1890 .1855 .1821 .1789 .1757 .1727 .1698 .1669 .1642 .1616 .1590 .1565 .1541 .1517 .1495 .1473 .1451 .1431 .1410 .1391 .1372 .1353 .1335 .1318 .1300 .1284 .1267 .1252 .1236 .1221 .1206 .((92 .1178 .1164 .1151 .1138 .1125 .1112 .1100 .1088 .1076 .1065 .1054 .1043 .1032 .1021 .1011 .1001 |§ -4 -3 -2 -' ' •Moving the decimal point in either direction in N requires moving it in the opposite direction m body of table (see p. 5). Sec. I] MATHEMATICAL TABLES TABLE 4.—COMMON LOGABITHMS* {special table\.^. B " 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 i.n 1.12 1.13 I.I4 1.15 1.16 1.17 1.18 1.19 1.20 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29 1.30 1.31 1.32 1.33 1.34 1.35 1.36 1.37 1.38 1.39 1.40 1.41 1.42 1.43 1.44 1.45 1.46 .1.47 1.48 1.49 0 0.0000 0043 C086 0128 0170 0212 0253 0294 0334 0374 0.0414 0453 0492 0531 0569 0607 0645 0682 0719 0755 0.0792 ^ 0828 0864 0899 0934 0969 1004 1038 1072 1106 0.1139 1173 1206 1239 1271 1303 1335 1367 1399 1430 0.1451 1492 1523 1553 1584 1614 1644 1673 1703 1732 1 0004 0048 0090 0133 0175 0216 0257 0298 0338 0378 0416 0457 0496 0535 0573 0611 0648 0686 0722 0759 0795 0831 0867 0903 0938 0973 1007 1041 1075 1109 1143 1176 1209 1242 1274 1307 1339 1370 1402 1433 \ 1464 1495 1526 1556 1587 1617 1647 1676 1706 1735 2 0009 0052 0095 0137 BI79, 0220 0251 0302 0342 0382 0422 0451 0500 0538 0577 0615 0652 0689 0726 0763 0799 0835 0871 0905 0941 0975 1011 1045 1079 1113 1146 1179 1212 1245 1278 1310 1342 1374 1405 1436 1467 1498 1529 1559 1590 1620 1649 1679 1708 1738 3 0013 0056 0099 0141 ).0183 0224 0265 0306 0345 0386 0426 0465 0504 0542 0580 0618 0656 0693 0730 0765 0803 0839 0374 0910 0945 0980 1014 1048 1082 1116 1149 1183 1216 1248 1281 1313 1345 1377 1408 1440 1471 1501 1532 1562 1593 1623 1652 1682 1711 1741 4 0017 0060 0103 0145 0187 0228 0269 03)0 0350 0390 0430 0469 0508 0546 0584 0622 0660 0697 0734 0770 0806 0842 0878 0913 0948 0983 1017 1052 1086 1119 1153 1185 1219 1252 1284 1315 1348 1380 1411 1443 , 1474 1504 1535 1565 1596 1626 1655 1585 1714 1744 5 0022 0055 0107 0149 0191 0233 0273 0314 0354 0394 0434 0473 0512 0550 0588 0526 0663 0700 0737 0774 0810 0846 0381 0917 0952 0985 1021 1055 1089 1123 1155 1189 1222 1255 1287 1319 1351 1383 1414 1446 ' 1477 1508 1538 1559 1599 1529 1658 1588 1717 1745 6 0025 0039 0111 0154 0195 0237 0278 0318 0358 0398 0438 0477 0515 0554 0592 0630 0657 0704 0741 0777 0813 0849 0885 0920 0955 0990 1024 1059 1092 1126 '1159 1193 1225 1258 1290 1323 1355 1386 1418 1449 1480 1511 1541 1572 1602 1532 1661 1591 1720 1749 7 0030 0073 0115 0158 0199 0241 0282 0322 0362 0402 0441 0481 0519 0558 0596 0533 0671 0708 0745 0781 0817 0853 0888 0924 0959 0993 1028 1062 1096 1129 1163 1195 1229 1261 1294 1325 1358 1389 1421 1452 1483 1514 1544 1575 1605 1635 1664 1694 1723 1752 8 0035 0077 0120 0162 0204 0245 0285 0326 0365 0405 0445 0484 0523 0561 0599 0537 0574 0711 0748 0785 0821 0855 0892 0927 0962 0997 1031 1065 1099 1133 1165 1199 1232 1255 1297 1329 1361 1392 1424 1455 1485 1517 1547 1578 1608 1538 1667 1697 1726 1755 — 9 — - 0039 0082 0124 0166 0208 0249 0290 0330 0370 0410 0449 0488 0527 0565 0603 0641 0678 0715 0752 0788 0824 0860 0895 0931 0966 1000 1035 1069 1103 1136 1159 1202 1235 1268 1300 1332 1364 1396 1427 1453 1489 1520 1550 1581 1611 1641 1670 1700 1729 1758 i 4 3 Moving the decimal point n places to the right [or left] in the number requires adding + n [or —n] in the body of the table (see p. 9). * From Marks, "Mechanical Engineers' Handbook," 4th ed,, McGraw-Hill, New York, 1941.

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