390 MONTHLY WEATHER REVIEW SEPTEMBER, 1927 20 22 The bureau of the section is authorized and requested to draw Shaw; oceanography, Martin Icnudson; geodesy, Bulloni and Norland; vulcanology, Tanakadate; magnetism, Chapman; and hydrology, Wallen. I n view of the increased importance of the application of meteoro- logical stat,istics of the weather to the problems of agriculture, dublic he:tlt,h, and other aspect,s of public economics, t.he bureau of the section is authorized to ask the International Conference of Directors of h,Ieteorological RBseaus to receive a deputation of t.he section a t a meeting of the directors in 1929 (which may be regarded as a jubilee celebration of the Internat,ional Meteoro- logical Congress a t Rome) in order to urge t.he consideration of a more scientific grouping of met,eorological st,at.ist,ics than the cus- tomary one by calendar months of arbitrary and unequal length. And, further, upon receipt of a favorable reply, the directors of the burenu are aut,liorized to arrange the deput,ation on behalf of up a report on the various practices of the different sciences com- prised within the International Geodetic and Geophysical Union with regard to units of measurement and to invite the cooperation of the bureaus of the other sections of the union, with the ult.imate object of a common unitary syst,em for all the sciences comprised within the union. 21 The section approves the appointment of a commission to consider the question of the use of geopotential in the geophysical sciences as the vert,ical coordinate in the represent,ation of t.he position of a point with reference to the earth for the purposes of geodynamic problems. The commission representing the different sections of t.he union is constituted as follows: Seismology, Oddone; meteorology, the secbion. PERFORMANCE IN LONG-RANGE WEATHER FORECASTING By CHARLES F. BROOKS [Clark University, Worcester, Mass., August 1% 19271 SFNOPSTS Long-range forecasts are SO much desired t.hat any number of 01 powef engineers (6) especially value advance indica- unqualified persons issue them without regard for criteria of per- tions of seasonal eve,n when of a general char- formance. Among what might be called “fake” forecast:, are the almanac, astrological, pseudosolar, and mathematical sorts, act’er. “ In l l l a n ~ lines of W O ~S ,” says D o d a s , “ the many of them calamity howls. The “prediction” of clililntic ge,nernl character of the weather has a definite and direct normals, forecasts from phenomena on certain c1at.es and from the influence on sales; in others the effect is present but behavior or aspects of certain aniluals or plants also belong in this indirect,; therefore,, category. T~ be of value a forecast must be specific, lilllitecl as to place: act,er of the weather months in Rdvance are of decided and time, and it must have a probability of more than chance value to the business man. Without predictions the verification. Furthermore, the economic consequences of failures, weat,her fac,tor bec,omes guessworl<.” (4) (( Waste of both in the long run and in a small sequence of years, must be water could be reduced,,i sass R ~~~, ‘‘thus making it reckoned. A forecast that will not hit the mark four times out of five, or a t least Once out of every three in s,lc,cessioll, can not possible to increase the area of agricultural land culti- be of much value, though some claim that a forecast verified only vated.” (6) In other words, reasonably dependable long- three times out of five would be useful. The uncertaillties of range weablier forecasts would reduce the cost of living. meteorolo@Cal relationships on which any long-range forecasts Can -f o ~e c ~,,~t q ~ ; a,l,na,nac, a,,qtrologica,z, and others.-me now be based are generally too great to permit reputable meteor- ologists to forecast on espectations of less than 75 or 80 per cent .fight agginst tAe,n.--There is no use discussing in detail verification. A critical study of the methods now used in the here those “forecasts” of the almanac kind, detailing or attempts at scientific long-range weather forecasting and an generalizing, on soIile worthless scheme, the weather usual evaluation of their relative merits for different parts of the world for e,ach Inont,ll (7). ((poor Rohin?i (8) and D~~~ Swiftis satire on Partridge two centuries ago (9) were the opening is much needed. Nature O f long-range foreca*~ti’W.-what is long-range shots of the long campaign against quack forecasters. weather forecasting? This question at once raises Nor need we fe,el conc,erned when given “w&rnin,os” of thoughts of forecasting now what the weather for nest weather disasters “impending” fortnight to a year 01 month, next summer, next fall and winter Will be. The more in advance. Howlers of such c.alaniities have been long-range forecast is beyond the realm of storms already roundly attac1ie.d by scientists time and again. In 1875 in existence and which by their niovement may be likely C. bf. Woodward’s dramatic expose of one planetary to affect us some time next week. Long-range fore- scheme led the way for other scientific attacks in this casting, dealing with the weather abnormalities of par- c,ountry (1 0). Weather Bureau officials and others, ticular months and seasons, therefore, has but little in rlotably Cleveland Abbe (I I ), and Garriott (121, Moore common with day-to-day forecasting or with its exten- alone (IS), and with several other officials (14), Wren (IS), the forecasting on Saturday what the general char- Walz (I 6), Marvin (I 7), Carpenter (I 8), editors (19) and acter of the weather during the coming week will be. (I ) other wite,rs have been unsparing of their criticism of Value of and demand for long-range jorecasts.--Fariliers, the fake or inadequate syste.ms in use in the United city people, merchants, manufacturers, politicians, states- States. Here during the past 10 years well over 50 long- men, engineers, all would find many uses for general rangers of greater or lesser repute have been publishing scientific weather forecasts a month or more in advance. and, in a great inany cases, accepting money for worth- The farmer has good need for them- In the opinion of less or damaging forecasts. European countries also a county farm adviser, for esaniple: support quac.lc forecasters in number, against whom the In general, accurate seasonal forecasting would tend to estab- attacks of scientists have been as strong as in the United lish a more permanent type form of agriculture, insure more profit- States (20). Helllnann lists 96 by name and analyzes and able crops, enable the farmer to replenish and maintain soil fertility c,riticizes their Inethods (20). H~ c,harac,terizes such and reduce somewhat the hazards of agriculture. prophets as “c.onceited, positive,, more or less fanatic, For want of such forecasts, western farmers have paid eager for a fray.” He says they use the same method a “rainmaker” thousands of dollars a t a time (3). Busi- against critics-pic,king out the best hits and keeping the ness men (4), transportation people (51, and water-supply poor ones silent. They are self-praising; they quote predic,tions of the general (2). 1 Essentially as presented at U. 8. Weather Bureau Staff Meeting, Washington, D. C., May 13, 1926. SEPTEMBER, 1927 MONTHLY WEATHER REVIEW 391 letters from people in high positions, and stigmatize meteorologists and scientific societies. Their friends and protectors belong largely to the sensational daily press, which opens its columns to them and occasionally carries some propaganda in their favor. It is difficult to say whether they are hone,st, says Hellmann, though some surely are (21). Probably no country in the world is free. Walker mentions the hold of astrologers and almanacs in India, for esaniple (22). In view of the harm done by spurious warnings Cleve- land Abbe was moved to write hopefully tha,t- the time must soon come when a general law shall forbid the pub- lication of weather predictions and storm warnings, especially those of a sensational character, by others than properly licensed Demons (23). Abbe did not say on what bases licenses could be issued, but it is not unlikely that he had in mind some consid- eration of the following points: (1) The candidate’s training as a meteorologist, (2) his ability to demonstrate the probability of success of forecasts of the sort lie pro- posed to make, and (3) his willingness to present to prospective customers a statement concerning his syst,em of forecasting signed by a c.ommittee of, say, three c.onipetent scientists. Predicting climatic noriria.ls.-Another t,ype of forecast more respectable than the almanac or astrological guesses, but not real forecasts, is the prediction of cli- matic normals (24). Such forecast)s have even been offi- cially made. Our pilot charts, issued by the United States Hydrographic Office with the cooperation of the Weather Bureau, years ago used to c.arry “forecast for the month” where now they say “average conditions.” The Mexican weathe,r service formerly published ‘( Tiem- PO probable durante el a.no ni6teorologico de 19- en la Repliblica Mesicana,” (Svo, S-10 pp.) (25). Rec,ently the Signal Corps meteorologist, Capt. B. J. Sherry, was issuing, toward the end of eac.h month, a statement of the nornial weather for the succeeding month, calling it a forecast. In the low lat,it,ude of Panama the weather is so steady that prediction acc.ording to normals would have a verification of 85 per cent, the hydrographer there once told the writer. Those who predict weather from actual or supposed occurrences on s ecial dates, “c.ritical days,” such as the snowfall, do no better than guesswork (26). Hellniann has traced this type of forecasting, based on January, back a t least to the eighth century (27). Biological forecasts.-We are amuse4 rather than informed or mislead b the usual autumn pronounce- the flight of gee.se, examined the fur of a woodchuck, looked rtt a goosebone, observed the nature of a muskrat house, the abundance of nuts in squirrels’ stores, and what not. (28). Josh Billings in his almanac, in 1870 wrote (29): When yu see 13 geese walking injun file and toeing in yu can deliberately bet yure last surviving dollar on a hard winter, and grate fluktuousness during the next seazon in the price of cowhide boots. Some biological forecasters will seek to tell you whether the winter is. to begin early or late and about when it is to end, by observing the position and relative length of the central brown division between the black ends of fuzzy caterpillars: And don’t look a t more than one caterpillar! Such forecasts are about as dependable as that by a Minnesota Indian a few years ago, who espected a cold winter because he saw Neighbor Whitme hclnn put in a large supply of coal. John Burroughs, howeve,r, on equinoxes, Can d!i emas, St. Swithin’s, or the date of first ments of this or that 01 B farmer or hunter who has noticed observing Arctic birds in the northeastern United States early in December, 1917, gave newspapers a correct fore- cast of an extraordinarily cold winter to come. Cha.racter a.nd dependabWy of forecasts.-To say “there will be a cold winter” does not mean much. People want to know for the.ir own locality about when the cold weather will set in; the extent to which mild periods will mitigate the winter; t,he average degree of cold (30) and the, number of days and their amounts below the freezing point (31), and when spring will c.ome. And they need some proof that the forecast is much better founded than ordinary guesswork. Forecasts must be specific and reasonably accurate if they are to be useful. ‘(Specific ” and (‘reasonably accurate ” are variously interprehd. Some consider a statement of trend up or down, from the prec.eding year sufficiently explicit (32) and 60 to 75 per cent verification a useful degree of accuracy (33). But a forecast based on a relationship no closer than this may be no forecast a t all. Thus, Wallrer, in discussing “Some sources of error” (34), reminds us of the strong temptation to think there is a relationship if two curve.s run markedly parallel. The use of changes from year to year instead of the actual values results in a curious paradox. For example, he inadz a c.1ianc.e drawing of 28 trends, plotted them and then made an inverted plot and moved it one value to the right of the original. The two curves showed a 64 pe.r cent trend d a t i o n , while that between the actual values was only 15 per cent, an amount quite useless for forecasting. Anot,her drawing would probably have shown smaller percentages, while the average for a large number of such samplings would be 50 and 0. On low average verifications, one must be willing to take some risk and have sufficient resources and faith to carry on t,hrough the many successive failures likely to occm. Obviously, as is shown by Walker’s statement, one t8rouble wit>li a verificabion of only 60 per cent is the chance t,hat, unrelated variations or errors in the data used may have been responsible for 10 or 20 per cent of the correspondence and that the apparent relationship on which the forecasts may be based is not real. Fur- thermore, it has been found that a correlation continuing for years may suddenly cease or become opposite (35). Expe.rien,ce in Jam.aica.-Most meteorologists, before they will forecast for general issue, must see indications that may be stated quantitatively, a probable vertifica- t,ion, as shown by 50 or 100 years of record, of not less than 75 or SO per cent, and an extreme unlikelihood of two bad failures in succession. An experience of the late Maxwell Hall, in Jamaica, illustrates this last point: Forecasts for montbly rainfall were commenced in 1885 and dis- continued in 1866; of these 80 per cent were correct, but the sub- ject required more attention than I could give it, and when a large rainfall was forecast for May, 1SS6, which proved unusually dry and when with an average forecast for June, 1886, heavy rains fed June 5 and 6, and floods did great damage, i t was clearly time to stop this mode of forecasting (36). If the rains had occurred only a week earlier, his fore- cast would have been a marked success. Later, another forec,ast failed, though based on an apparently close rela- tionship between droughts and maximum sun spots published in Nature (49: 339): In 1893 I gave out that that year and the next few years would probably be drier than usual-the sun-spot maximum was then approaching, and 1S91 had been unusually wet-but 1893 proved to be still wetter, and it was not until two or three gears after the iiiasiniuiii in 1893 that drought was severely felt in certain parts of the island, and the connection preserved (36). Apparently Hall made no further long-range forecasts. His record was too short. Pickering lat,er, with a much 392 MONTHLY WEATHER REVIEW SEPTEMBER, 1927 longer series of years, confirmed Hall's experience that droughts followed rather than attended sun spot maxima (and minima), and successfully forecast the onset of the severe drought beginning in 1919 (37). Ezperience with India's monsoon forecasts.-After early failure to achieve sufficient success in long-range fore- casting in India, says Walker (38)- A preliminary examination (in 1908) led to a formula for fore- casting the monsoon rainfall of the whole of India, and a relation- ship 2 of 58 per cent with the actual rainfall was indicated; and during the 16 years 1909-1924, the formula was fully answered by expectations. So small a relationship as 0.58 does not justify a forecast unless the abnormalities are fairly marked; but this con- dition has been satisfied in nine years out of the 16, and in 8 years out of the 9 the rains were in excess or defect when this was given by the formula. [Improved formuls for northwest India and Peninsular rainfall with 0.76 correlation coefficient are now used.] Aa we shall need an idea of the values of relationships of this kind for purposes of forecasting, some further consideration is necessary. Taking the simplest case, in which either an excess or defect of rain is predicted, success turns on the condition that the probable error of the estimate of the amount of rain shall be less than the amount of excess (or defect) indicated by the data; and, in fact, smallness in the relationship both diminishes the amount indicated and increases the probable error of the estimate. THE BASIS OF CALCULATION If we decide that it is useless to issue forecasts that will not, 011 the average, be right 4 times out of 5, it follows mathematically that if the relationship be 80 per cent [correlation coefficient 0.81 circumstances will justify a forecast in half the occasion; if 70 per cent there is a 3 to 2 chance against the indication of any one occasion being definite enough; for 50 per cent the odds are 6 to1 against; for 40 per cent 18 to 1; for 30 per cent 130 to 1; and for 20 per cent 25,000 to 1. So unless the relationship is of 50 per cent, occasions for a justifiable prediction will occur too rarely for practical purposes. These figures would be modified if forecasts of ["I normal ["I conditions were also made, but the general result would not be fundamentally different. Later, Sir Gilbert Walker presented a more detailed statement and showed that for successes on the average 4 times out of 5 strong indications a t certain times would justify a forecast on a much smaller correlation coefficient than when the indications were more or less uncertain. Thus while we should have to have a correlation coeffi- cient of about 0.8 before we should be justified in making regular forecasts, a correlation coefficient of 0.5 would justify an occasional forecast having a probable success 4 times out of 5 if the forecasted departure were something over twice that required for forecasting with a correlation coefficient of 0.8 (39). In conclusion, Walker says (40) : It must regretfully be admitted that the majority of the methods employed in seasonal predictions have been falee; and insistence on strict conformity to the rules-in other words the principles of probability is not mere pedantry. The larger variations of seasonal rainfall, pressure, and temperature are in general not isolated phenomena, but are linked up with big variations in other parte of the earth, so that there is every cause for hopefulness regarding the possibility of understanding and predicting them; but man researches needing time and money are first necessary, and if is {ighly desirable in the interest of meteorology that as little as possible should be done by careless work t o diminish public confidence in the possibilities of long-range forecasting. Two or three successive failures in a seasonal forecast on the strength of which farmers and business men were governing their operations would mean financial ruin to many. This could not be remedied by many more successes in subsequent ears, even supposing, as would This is different from the run of the weather. Ruinous be unlikely, the users stil 9 retained faith in the forecaster. 8 In technical language there was a correlation coefficient of +0.58, implying that an average fraction of 58 per cent of the variations of the actual rainfall would be provided by the forecast. strings of years mny occur, but the farmer has to take what comes next. A false prediction of a drought one year followed by even a correctly predicted drought the next would constitute a 50 per cent verification that would, if followed, be much worse than the result of a farmer's expecting and preparing for good rains both years. Beginning with empirical forecasting.-The few dy- namic principles of daily and weekly foreca3ting now known (41) are based on experience and investigations involving. records of thousands of days or weeks. Corresponding principles of seasonal forecasting on physical grounds, on the contrary, can hardly be built on the 5, 10,30,60, or even 100 records of months or seasons of the same name, which constitute our available data, and this for only a fraction of the earth's surface. Over enormous areas we do not know what the weather is or has been. How sure could we be of a forecast for to-morrow if our first daily weather records over an area within one day's weather reach had been made only two or three months ago and not yet mapped for the whole region for any day? Though we did not know the immediate causes of the storms whose appearance and approach were reported, we should, nevertheless, be able to make useful predictions for a t least portions of our area, not only from the reports from other places but also from empirically established local sequences, e. g., the normal cyclonic sequence. This appears to be the present status of long-range forecasting. Some fore- casts are made for favored points, but scientific long- range weather forecasts are not yet generally available, probably not only because our records are still of in- sufficient length and world-wide scope to provide ade- quate bases for them. Meteorologists are mostly agreed that the fundamental problem of long-range forecasting is that of the physical bases of world weather, as yet not fully known, nor, indeed, knowable till the earth is far better covered with a network of stations than a t present (42). Nevertheless, some, McEwen, for example (43), are using empirical rules, which, supported by a working hypothesis, can provide useful forecasts and tide us over the learning period. Conclusion.-While the bibliography in this pa er successful, scientific long-range weather forecasting, it does not pretend to cover this field even in part. A much needed investi ation in scientific long-range methods now or formerly emplo ed and an attempt to cability to various parts of the world. includes many references to present-day, more or P ess forecasting is a critica 9 examination of the numerous determine for those found of va 9 ue the probable appli- LITERATURE CITED (1) BIBLIOGRAPHY ON WEEKLY FORECASTINQ: GARRIOTT, E. B., HALL, J. P. 1903. RELATION OF LOW PRESSURE OVER THE (Also favorable comment by J. P. Hall.) Mo. Wea. Rev., 3 I : 479. [Low pressure in the eastern Atlantic leads to stagnation in the western Atlantic and eastern North America.] WEATHER FORECASTS. Ibid. 34: 22. 1906. A NEW DEPARTURE IN FORECASTING. Ibid, 34: 116. [Cryptic announcement of weekly forecasting soon to commence.] BRITISH ISLES TO AMERICAN WEATHER. GARRIOTT, E. B. MOORE, W. L. 1906. POSSIBLE EXTENSIONS OF THE PERIOD6 OB GARRIOTT, E. B. 1908. LONQ-RANQE FORECASTS MADE BY THE WEATHER BUREAU. Ibid. 36: 275. SEPTEMBER, 1927 MONTHLY WEATHER REVIEW BIBLIOGRAPHY ON WEEKLY FORECASTING-COntinUed. GARRIOTT, E. B. BOWIE, EDWARD H. NEWNRAM, E. V. 1908. WEEKLY WEATHER. Ibid. 435. 1915. RESUMPTION OF THE WEEKLY FORECAST. Ibid. 43: 185. [Map and forecast.] DROUGHT. The Met’l. hlag, 56: 153-155. [Noted in Mo. Weather Rev., 49: GSG.] 1926. SEASONAL FORECASTING AND ITS VALUE TO THE 12 of the Scripps Institation of Oceanography, La Jolla, Calif., p. 7l-77; Abstr. in Bull. Ani. Met’l. SOC., 6: 180-181, 1925. 1921. T H E PROBLEM O F FORECASTING PERIODS O F FRANCE, JAMES G. AGRICULTURIST I N SAN DIEGO COUNTY. Bull. 19iO. Bull. Am. Met’l. SOC., 1: 47-48, 80-82. 1921. Ibid. 2:GQ-70. 1920. WHAT CAN BE DONE ABOUT LONG-RANGE FORE- 1921. REPT. OF THE COM. ON BUSINESS MET. Ibid. DUDLEY, P. H. 1920. Bull. Am. Met’l. Sor., I : 67-68. ROWE, EDGAR A. 1926. THE VALUE OF LONG-RANGE RAINFALL FORECASTING DOUGLAS, A. W. CASTING? 2: 11-12. Bull. Am. Met’l. Soc., I : 122-133. TO IRRIGATION AND WATER-SUPPLY PROJECTS I N SOUTHERN CALIFORNIA FROM AN ENGINEERING STANDPOINT. Bull. 12 of the Srripps Institution of Oceanography, La Jolla, Calif., p. 68-73; Abstr. in Bull. Am. hIet’l. SOC., 6: 150, 1925. WILSTAM, A. 1926. FORECASTING WATER-POWER SUPPLY FOR T H E HYDRO-ELECTRIC PLANTd O F T H E SOUTRERN CAIJFORNIA EDISON COhIPANY FROM OCE.4N TEMPERATURES. Ibirl. p. 60-67; Ahstr. in B d l . Am. hlet’l. SOC., 6: 179. ELECTRIC LIGHT ASSN. IN BAN FRANCISCO. hlo. Wea. Rev., 49: 21G213. 1926. WEATHER PROPHET IS NOW SCIENTIFIC.-METE- N. Y. Times, July BEALS, E. A. 1921. WEATHER-FORECASTING MEETING O F THE NATIONAL TALMAN, c. F. OROLOGISTS HAVE RESCUED PREDICTIONS FROM REALM O F SUPERSTITION-FORECASTERS, LUCKY AND UNLUCKY, OF THE PAST. 25, 1926, p. 13. ALMANAC FOR 1823. Chicago. p. 112-121. XVXI k XIX. Veroff. d. Preuss. Met. Inst. Nr. 315, p. 15-46. 1917. DIE WETTERVORHERSAQE IN AUSGEHENDEN MIT- TELALTER (XII BIS xv JAHRHUNDERT). Bei- triige zur Geschichte der Meteorologie. 3 band. Nr. 8, p. 167-229. Berlin. Verirff. d. I<. Pr. Met. Inst. Nr. 296. TALMAN, C. F. HELLMANN, G. 1922. ALMANAC WEATHER. T H E NORTH AMERICAN 1922. GESCHICHTE DES HUNDERTJXHRIGEN KALENDARS, HELLMANN, G. ICIENAST. HERMAN. 190s‘. WETTERVORAUSSAGE VOR 180 JAHREN. Das Wet- ter, 25: 265273. KITTREDGE, G. L. 1904. THE OLD FARMER AND HIS ALMANACK. Boston. 1903. WEATHER CYCLES AND FARMERS’ ALMANACS. Mo. p. 191-205. ABBE, CLEVELAND. HELLMANN, G. Wea. Rev., 3 I : 139-140. S V UND XVI JAHRHUNDERTS. Neudrucke yon Schriften und Karten uber Met.eorologie und Erdmag. herausg. v. Prof. Dr. G. Hellmann. Nr. 12. Berlin. p. 7-21. 1898. ALMANACS AND THE WEATHER BUREAU. Mo. Wea. Rev., 26: 21-22. 1895. METEOROLOGISCHE VOLKSB~CHER. Sammlung popularer Schriften herausgegeben von der Gesellschaft Urania zu Berlin, Nr. S . 1899. WETTERPROQNOSEN UND WETTERBERICHTE DES ABBE, CLEVELAND. HELLMANN, G. TALMAN, C. F. 1922. Ibid. p. 116. (9) CHAMBERS, R. (editor) 1863. THE BOOK OF DAYS. A MISCELLANY OF POPULAR ETC. London and Edinburgh. vol. 1, p. 10-13. ANTIQUITIES I N CONNECTION WITH THE CALENDAR, (IO) WOODWARD, C. M. 1904. T H E PLANETARY EQUINOXES-AN EXAMINATION O F u. s. Weather Bur. Bull. h,fR. TICE’S THEORY. 35, p. 11-31. Washington. (I 1) ABBE, CLEVELAND. 1901. FAKE FORECASTS. 1904. PLANETARY METEOROLOGY. Ibid.. 32: 180-181. Mo. Wea. Rev., 29: 467. 1904. FAKE FORECASTS. Ibid., 32: 322-323. 1904, AN HONEST LONQ-RANGE FORECASTER. Ibid., 32: 517. (12) GARRIOTT, E.-R.- 1904. LONG-RANGE WEATHER FORECASTS. U. S. Weather Bur. Bull. 35, Washington, p. 7-10, 36-43, 4s-50. (13) hIoonE, W. L. (14) hlOORE, w. L. and others. 1904. Ibid., p. 3-4. 1904. Pnoc. OF THE THIRD CONV. OF WEATHER BUREAU OFFICIALS. Washington, p. 42-46 (general dis- cussion). 1905. LONG-RANQE FORECASTS. Rept. of the Chief of the Weath. Bur. 1903-4. Washington. p. xiii-svii. Also in Mo. Wea. Rev. Ann. S u m . for 1904, 32: 597-599. R ~O O R E , w. L., with GARRIOTT, E. B. and HENRY, A. J. 15) WREN, H. B. 16) WALZ, F. J. 1904. LONG-RANGIE FORECASTS. Mo. Wea. Rev., 32: 1905. FARE WEATHER FORECASTS. Pop. Sci. Mon., 469-470. 67:503-513. 17) hfARVIN, c. F. 1916. WARNING AGAINST WEATHER FORECASTINQ FAL- LACIES. Printed letter, Mar. 24, 1916. Wash- ington. Abbreviated in U. S. Dept. Agric. Weekly Kews Letter, -4pr. 5, 1926. 1921. WEATHER PREPAREDNESS. Calif. Cultivator, Nov. 12, 1921, p. 500-501. 1913. CHIMERICAL WEATHER FORECASTINQ. Sci. Am., 190: 332. 18) CARPENTER, F. A. (19) -- (20) CAVE, C. J. P. 1927. POPULAR LONG-RANGE WEATHER FORECASTS. Nature (London, Jan. 8, 1927), 119: 52-55. Reply by Bulter, R. P., ibid., Jan. 29, 1927, 164-166, 167. [50-day forecasts based on 15 cycles.] WEGNER, R. 1925. RUDOLPHS WETTERKALENDAR 1925. Das Wetter, 42: 29G-295. [Astrological-worthless. VerSca- tion no dilTerent from-chance.] AUF CRUND DER MONDSTELLUNQEN. Natur- wissenschaften, 12:535. [Almanac weather forecaster quoted on him prowess over meteorologists.] 1917. WETTERPROPHETEN DES XIX UND XX JAHR- HUNDERTS. Verbff. d. K. Preuss. Met. Inst. Berlin. Nr. 296. D. 231-314. SCHWALBE 1924. D I E HINSELMANNSCHEN WETTERVORHERSAQEN PEPPLER, W. 1922. WETTERPROPHETEN. Das Wetter, 39: 58-60. HELLMANN, G. KOPPEN, W. 1906. WIE ERKENNT MAN BLINDLINGSPROQNOSEN? Met. Zeitschr. Hann-Band: 347-356. [Compare results with chance.] Mag., 39: 31-32 (Abstr.). I