UC-NRLF KBED, Yf ILL I AM GATHER. FROST I TK GIFT F FROST IN THE UNITED STATES By WILLIAM GARDNER REED Meteorologist, U. S. Weather Bureau, Washingtou, D. C. PAPER PRESENTED BEFORE THE SECOND PAN AMERICAN SCIENTIFIC CONGRESS, WASHINGTON, U.S.A. DECEMBER 27, 1915 JANUARY 8, 1916 WASHINGTON GOVERNMENT PRINTING OFFICE 1917 i FROST IN THE UNITED STATES. By WILLIAM GARDNER REED, Meteorologist, U. 8. Weather Bureau, Wastiington, D. C. INTRODUCTION. The period of plant growth in all middle latitude countries, such as the United States, is limited by the occurrence of low temperatures. Of these low temperatures, killing frost, so-called, probably has the greatest bearing upon agriculture. A killing frost may be defined as a low-temperature condition which is so injurious to plant tissues that growth is no longer possible, even when the low temperature has passed. The limitation of plant growth by frost is different from that due to lack of energy sufficient to bring the plant to maturity. The frost limitation results from the definite destruction of plant tissues, and in most cases when the growth for a single year is injured by frost that year's crop is destroyed. THE NATUBE OF FBOST. Frost conditions have been classified under three headings: (1) The com- mon hoar frost; (2) the dry freeze or black frost; (3) the general freeze. The first two are the result of the chilling of the surface air by rapid radiation from the earth to space and are essentially local conditions. They are often the result of widespread controls, but the temperature in each locality is mainly the result of local radiation conditions. The general freeze is a condition when the temperature of the whole mass of air is dangerously low. The general freeze is not the result of local conditions, although the low temperatures during a general freeze are often intensified by the local radiation. 1 Prom the point of view of frost damage and from the effects on vegetation of these low-temperature conditions the Weather Bureau has made the follow- ing classification : Light frost. That which has no destructive effect, although tender plants and vines in exposed places may be injured. Heavy frost. That in itself severer than a light frost ; that is, the deposit i>f frost is heavier and the temperature falls to a lower point, although the staple crops of the locality are not generally destroyed. Killing frost. That which is generally destructive of vegetation and the staple crop of the locality. 2 The character of frost, whether light, heavy, or killing, must sometimes be determined by the phenomenon itself, rather than by its effect on vegetation and 1 Deals, E. A. Forecasting frost in the north Pacific States. U. S. Weather Bureau Bui. 41, Washington, 1912, p. 41. 8 U. S. Weather Bureau, Instrument Div., Circular B and C, ed. 5, Washington, 1915, p. 25. 25807C-2 17 1 544J47 2 PK SE^MOL20GY'. : 3 In practice many of the frost data used of the maps presented with this paper have been determined by the occurrence of freezing temperatures. There is a varying difference in temperature between the ground and the air at the height of the instrument shelter, which depends upon a great variety of condi- tions, among which are the state of the sky, the humidity (perhaps the amount of water vapor is more important than the relative humidity), the air move- ment, and the length of the night. But as the controls are also the controls of frost, Fassig's statement holds in most cases. If an agricultural standard is used for the determination of frost, it will be found that these low temperatures are of the greatest concern to agriculture at times when the crops are in a condition to be damaged. The probable occur- rence of such damaging conditions limits the availability of different portions of the United States as agricultural regions, and a knowledge of these condi- tions will prevent many agricultural failures. The portions of the United States in which freezing temperatures are not of annual occurrence are very limited. These are a part of the peninsula of Florida, the immediate Gulf coast, and a small area in southern California and Arizona. In so far as these con- ditions are regular and not extended beyond the usual time of occurrence, they are not to be feared ; this is a period of plant inactivity, herbaceous plants are not above the ground, and trees are dormant. Except for the regions men- tioned, frost damage during the winter is not important. It is only the rare occurrence of extremely low temperatures which results in winter-killing, and this is an entirely distinct phenomenon, not to be confused with frost damage. FEOST RECORDS. In the United States frost is of agricultural significance in different regions at different times. In the region of the citrus fruits that is, Florida, the Gulf coast, and southern California frost damage will occur whenever the fruit is on the trees, provided the temperature falls a few degrees below freez- ing. Slightly lower temperatures are necessary to damage the trees, but the general statement that any freezing temperature is dangerous in the citrus region is not far from correct. Outside the citrus region winter frosts are of very little importance ; it is the spring and fall frosts which become of interest to agriculture. Deciduous fruit trees are dormant during the winter; low temperatures are to be feared only after growth has commenced. The time of danger from frost to the deciduous fruits is the time between the opening of the buds and the picking of the fruit. Of course, during a great deal of this time the temperature conditions are such that frosts do not occur in regions where fruit is grown. The period of anxiety is, therefore, limited to the begin- ning and the end of the season of plant activity ; that is, from the opening of the buds to the setting of the fruit in the spring and the period just before picking in the autumn. Other crops than fniit are subject to varying amounts of damage by frost. Temperatures not many degrees below freezing are destructive to most crops except the hardy grains, and successful agriculture can not be carried on except in regions where the time between the last killing frost in spring and the first killing frost in autumn is as long or longer than the normal period of growth required by the plants. The agricultural importance of frost data can hardly be overemphasized, since the character of the farming in any region is .dependent upon the time between killing frosts. This does not mean that the time between killing frost is the only consideration, but that the period available for plant growth is limited to this time. There are often other limiting conditions, such as lack of heat in sufficient amounts to permit plants to reach maturity. These other PROCEEDINGS. -SECOND FA-N AMERICAN SCIENTIFIC CONGRESS. conditions may prevent the growth of all the crops which would appear possible from the length of the season between killing frosts, but the length of the season is to be regarded as a very important and very definite limitation. It is, of course, possible to protect crops from frost damage, but this protection can profitably be carried on only within very narrow limits. Protection is always obtained at considerable expense, and unless applied to a high-value crop is seldom justified by the returns. Thus protection from damage by frost is to be regarded as a type of the most intensive methods of cultivation, which can profitably be resorted to only for such crops as fruits and vegetables where the value is concentrated and where the profits from cultivation out of the natural season or out of the natural region are great. As a type of cultivation out of the natural season, various garden vegetables grown particularly in the spring may be noted, and the extension of orange culture into colder regions is a good example of a type of production out of a natural region. Both of these types of extension are apt to enlarge the profits; vegetables reaching the market early command high prices, the best oranges are grown at the very limits of the possible orange regions, 1 but it is only in such conditions as these RECORD KILL! NO FPOSTAFTER MAY I - SZZZS APR.I5- ??75&n APR. ! - E5S3 MAR IS- V/SSS* MAR. I - fX?^1 ALL FROSTEZHD FIG. 1. From U. S. Weather Bureau: Instructions for preparing meteorological forms. that frost protection is at all justified. It must be looked upon as an insurance charge which the crop must carry in addition to its value, and only increased profits can justify this charge. 2 THE OCCURRENCE OF FROST IN THE UNITED STATES. Except in a limited region, frost is an annual phenomenon throughout the United States. The length of the season between the last killing frost in spring and the first killing frost in fall decreases within increasing latitude. Figure 1 shows, in a general way, the conditions of spring frost. This map was prepared by the Weather Bureau as a guide to its officials in" recording frosts in the 1 Colt, J. E. Citrus fruits, N. Y., Macmillan, 1915, p. 25. * See Reed, W. G. : Protection from damage by frost. Geographical Review 1 130-122, New York, 1916. ASTRONOMY, METEOROLOGY, AND SEISMOLOGY. 5 spring. It is intended that the last killing frost in any year shall be recorded by each regular Weather Bureau station. It is not, however, desired to record frost every day during the winter. The map, therefore, represents a compromise between these two ideas. The most significant thing about this map is the fact that it shows clearly that while the last killing frost in spring along the Gulf coast and in California may occur at any time, the date of this last frost becomes later and later until in a considerable portion of the country there is little or no possibility of the last killing frost occurring before May 1. In the fall the problem is simpler, as the dates of light and heavy frosts are recorded, and that of the first killing frost only, after which no frost is recorded. The temperatures dangerous to growing plants that is, temperatures which are recorded as killing frosts are usually those associated with the types known as "hoar frost" and "black frost." The "general freeze," which is a winter weather type, and, although not usually found at the beginning and end of the warmer season, is occasionally destructive to plants in the' spring or fall. The frost conditions of spring and fall are mainly the result of local nocturnal cooling under the clear sky conditions accompanying anticyclones. The weather conditions which precede and accompany frost in the various sections of the United States are closely associated with the progressive movement of these areas of high pressure. East of the Rocky Mountains the general movement of these anticyclones is from the northwest to the southeast. As a rule the area in which frost occurs is southeast and a little in advance of the area of high pressure. It is frequently possible to follow the advance of frost conditions across a large portion of the eastern United States. The frost probability is successively transferred eastward with considerable overlapping of the areas visited by frost from day to day. Generally the eastern portion of the area visited by frost one day will receive a second visitation on the following day. Studies of the occurrence of frost by the forecast officials of the Weather Bureau are grouped about the anticyclone as a unit rather than about any geographical dis- trict, since frost may occur from rather widely varying conditions of the cyclone with respect to any particular district. 1 Frost west of the Rocky Mountains may be regarded as a somewhat simpler problem than that in the eastern United States. Frost forecasting in the Pacific Northwest has been adequately discussed by Beals. 2 In the Pacific Northwest frosts are intimately associated with the existence of an anti- cyclone over the states of Washington, Oregon, and Idaho. The extension of this anticyclone over the Pacific Ocean seems to make very little difference as long as a portion overlies the land. In other words, the transfer of air from the continent toward the ocean seems to be of relatively little importance. This, however, is not the case with the occurrence of frost in California. While there are numerous minor variations of the frost type for California and Nevada, the essential features of this weather type are exceedingly simple. An anticyclone overlies some portion of the Basin Region accompanied by the usual outflowing winds. This gives the State of California easterly and north- easterly winds for 24 to 36 hours before frost occurs. Under these conditions the air is apt to be clear and dry, and often a great deal of cold air has been transferred from the colder continental interior. As long as the wind con- tinues to blow this air will usually be so well mixed that local radiation will 1 The writer is indebted to the forecast officials of the U. S. Weather Bureau for this statement of frost occurrence. 2 Beals, E. A. : Forecasting frost in the north Pacific States, U. S. Weather Bureau. Bui. 41, Washington, 1912. 6 PROCEEDINGS SECOND PAN AMERICAN SCIENTIFIC CONGRESS. not be able to effect much further cooling, but if the wind falls off, cooling by night becomes of the utmost importance. 1 The fact that frost conditions are generally associated with anticyclones is of great agricultural significance. The anticyclone is characteristically ac- companied by clear weather; in fact, frost conditions are essentially those of clear nights. The same atmospheric conditions which result in clear frosty nights are also those of bright sunny days, so that days somewhat warm for the season frequently occur at the same time as nights with frost. These days encourage the plants to carry on their activities of growth with the result- ing new and tender tissues. With the rapid nocturnal cooling by radiation from the plant and from the lower air, the plant juices are apt to be frozen and the plants, especially the new tissues, are often damaged. 2 FROST DAMAGE. The mechanism of frost damage is complicated and not very well understood. The following general discussion shows the present state of knowledge : Once it was supposed that frost injuries were due directly to the formation of ice in the cells; the expansion of water in freezing was thought to burst the cell walls, just as it bursts the water pipes in our houses in severe weather. This plausible theory was, however, disproved by examination of freezing plant tissues under the microscope. The process that ordinarily occurs is this : Ice forms not in but between the cells, and in so doing gradually extracts the water from the latter through the cell walls. There are two ways in which this loss of water may kill the protoplasm of the cell, and opinions are still divided among plant physiologists as to which is the more important one. The belief that was generally entertained a few years ago was that the desiccation of the cell contents caused a collapse of the protoplasm, and that whether or not this collapse was permanently injurious depended especially upon whether the water was all restored to the cell in the subsequent thaw. If the temperature rose gradually the water would have time to soak back through the cell wall, and the protoplasm would resume its normal condition. In a rapid thaw the cells would not be able to take up the water as fast as it was furnished, much of the water would escape, and the structure of the proto- plasm would be permanently broken down and destroyed. A more recent view is that the injury is purely chemical ; the loss of water causes a concentration of the salt solutions in the cell, and these attack and "precipitate" the proteins a process too complicated to explain here in detail. Suffice it to say that, according to this view, the death or survival of the tissues depends upon the length of time the concentration of the cell sap continues and not upon the rate of subsequent thawing. We have, then, two rival theories of frost injury: According to one the damage is done chiefly after the actual freezing is over, and may be avoided if the temperature rises slowly ; according to the other the injury occurs during the frozen state, and depends upon the duration of that state. Perhaps horticultural writers have generally laid too much emphasis upon the importance of gradual defrosting. Thus it has been commonly stated that wind- 1 See McAdie, A. G. : Frost fighting, U. S. Weather Bureau Bui. 29, Washington, 1900 ; " Frost " in the Climatology of California, U. S. Weather Bureau Bui. L : 227-237, Washington, 1903 ; and elsewhere. 'For more detailed statements of the conditions under which frosts occur see U. S. Weather Bureau : Weather forecasting in the United States, pp. 177-215, Washington, 1916. ASTRONOMY, METEOROLOGY, AND SEISMOLOGY. 7 breaks, covers, and other devices to shield buds or blossoms from the direct rays of the rising sun after a night of frost will, unless the frost has been very severe, save the fruit by preventing a too rapid rise of temperature. A certain amount of evidence recently accumulated throws some doubt upon the necessity for such precautions. For example, during the frost of December 26, 1911, in southern California, when several million dollars' worth of citrus fruit was damaged, it is stated that at one point the temperature rose 24 in two hours without injury to the fruit. The results of experiments made by the Bureau of Plant Industry in a cold-storage warehouse where oranges were allowed to thaw out under various conditions after having been kept at low temperatures are reported as follows : The length of time the fruit remains in a frozen condition has a very material effect upon its condition after thawing out. There is apparently an optimum temperature for thawing the frozen fruit with the least resultant injury. If the thawing is done too slowly the fruit is injured more than where a some- what higher defrosting temperature is used and the thawing accomplished more quickly. On the other hand, it was found that quick defrosting was more injurious than slow defrosting, so that it appears probable that through experiment the defrosting temperature which would be most effective could be determined. In other words, both the duration of the frozen state and the rate of defrosting are important in determining the fate of the fruit; but while slow defrosting is desirable, it should not be too slow. It is assumed here that what applies to the mature fruit of the cold-storage experiments also applies to the earlier stage of bud and blossom, though in the latter case the process is doubtless complicated by the effects of cold upon the fertilization of the ovary and the consequent setting of the fruit. Evidently much more investigation is needed "concerning the nature of frost effects within the plant. However, there appears to be at least one practical corollary to the foregoing information: Even if orchard heating has been delayed until after freezing temperatures have set in there may still be time to save the fruit. The utility of any information that may be gained in regard to the ideal conditions of defrosting is problematical, for it is not easy to see how such knowledge could generally be applied in the orchard. Now, we come to the important subject of frost resistance. Here, also, much work remains to be done, and it is the duty of the practical horticul- turist as well as the scientist to help in the common cause. Comparatively little information has been collected so far as to the tem- peratures that various species and varieties of cultivated plants will endure for an indefinite period without injury. Such information can, at best, be stated only in averages, because in the case of a given variety its ability to withstand cold depends somewhat upon the weather conditions previous to the freeze. Thus, as has been pointed out, a few days of warm weather, together with an ample supply of soil moisture, will cause the newly formed cells of the blossoms and fruits to be filled with a watery protoplasm, or cell sap, which freezes more readily than concentrated cell sap. Moreover, individual plants of the same variety, grown under apparently identical conditions, vary somewhat in their resistance to cold. Nevertheless, average statements on this subject are exceedingly valuable, because the orchardist is chiefly interested in knowing what will happen in the long run, in the orchard as a whole, and need not concern himself with sporadic cases. 8 PROCEEDINGS SECOND PAN AMERICAN SCIENTIFIC CONGRESS. An authority gives the following table showing the temperatures (Fahren- heit) injurious to fruit at various stages. In bud. 1 In i In set- blossom, ting fruit. At other times. Almonds i 28 I 30 30 28 Apples 27 29 j 30 25 Apricots | 30 31 i 31 30 Cherries. 29 30 I 30 29 Peaches 29 30 1 30 28 Pears i 28 29 i 29 28 Plums 30 31 31 29 Prunes 30 31 31 29 The first column refers to buds about ready to open. In their earlier stages buds can, of course, stand far lower temperatures. 1 THE FKOST DATA OF THE UNITED STATES. The records of frost occurrence in the United States are numerous, although not as complete as might be wished. There are records three years or more in length for nearly 5,000 stations; these records have been made under the direction of the Weather Bureau and, taken altogether, are a mass of data of inestimable value. Of these 5,000 or more records, there are about 700 which have been continued for more than 20 years. These data have made possible the compilation of maps of the dates of frost occurrence over the eastern United States. 1 Where the stations at which frost is recorded are located near one another the official data are sufficient to enable isochronal lines to be drawn with con- siderable accuracy, especially if the region is not one of broken topography. This is the condition to be found in much of the eastern United States, and it is probable that the addition of new data will make possible only minor improvements in the lines already drawn for this region. In a mountainous region such as the western United States, however, the condition is quite different. Here stations are widely separated, and there are often high moun- tains or deep canyons between stations relatively near together, so that the conditions at the stations are in many cases only local. A further difficulty arises from the fact that most of the stations in the western United States are located in the more favored places where farming is possible, rather than in places which may be regarded as characteristic of the whole region. It is, therefore, necessary to supplement the recorded dates of frost by other data unfortunately less subject to statistical treatment. These data are topography and records of crops and natural vegetation. The hardiness of many types of vegetation is known rather accurately, and a study of the vegetation which is able to maintain itself in any particular region gives a good idea of the char- acter of the temperature conditions. It is also true that altitude has an impor- tant effect on temperature. The last killing frost in spring becomes later with 1 Frazer, Calvin : The frost problem up to date. Country Gentleman, 79 :360. Phila- delphia. 1914. In this connection see also Chandler, W. H. : The killing of plant tissue by low tempera- ture. Missouri Agr. Exp. Sta. Research Bui. 8, Columbia, 1913. a See Greeley, A. W. : American Weather, New York, Dodd, Mead & Co., 1883, charts 22-23 ; Day, P. C. : Frost data of the U. S., U. S. Weather Bureau Bui. V, Washington, 1911 ; also Reed, W. G., and Feldkamp, C. L. : A selected bibliography of frost in the United States, U. S. Monthly Weather Review, 43 : 512-517, Washington, 1915. A new series of frost maps will appear in the Atlas of American Agriculture now in preparation by the United States Department of Agriculture. ASTRONOMY, METEOROLOGY, AND SEISMOLOGY. 9 increasing elevation, other things being equal, and the first killing frost in fall becomes earlier. Therefore, these data may be used to supplement the official records where ' the stations are far apart or not well situated, but only when they are wisely and conservatively used, especially as slope and the presence of valleys often result in local warm and cool spots not dependent upon the altitude. It should be very clearly noted, moreover, thal^it is exceedingly easy to make inaccurate use of data other than the official record of a well-conducted climatological service. In practice it has been deemed best to map at the proper location the frost da.ta reported by the Weather Bureau and to consider these records as of primary importance. No record has been neglected except those of a few stations reported by the section directors of the Weather Bureau as un- reliable records or stations with extremely local conditions, and in cases of ap- parent conflict between the record and the botanic or topographic data the record has been followed. The exact course of the isograms between stations has, moreover, been determined by all the data available, which include topo- graphical, botanical, and agricultural material, as well as the Weather Bureau records. Frost data for selected stations with longer records are given in Table I. These stations represent a fair sample of the frost conditions in the country. More extended frost data can be found in Bulletin W of the Weather Bureau. 1 While the actual record of the occurrence of frost dangerous to crops is the best guide at a particular station, th-3se data become so numerous that it is not possible to use them for wide areas. For a particular station in a given year it is probably essential to know only the last date in spring and the first date in fall on which killing frosts have occurred in each year. For a series of years and for many stations these data become hopelessly numerous, and some statistical method of reducing the number of dates without destroying the value from the longer periods covered must be devised. The simplest of all such methods is that of averaging the dates. It is perfectly possible to deter- mine the " average date of last killing frost " in spring by simple arithmetical methods. The date thus obtained is that on or before which the last killing frost has occurred in about half the years for which there is a record. 2 The " average date of the first killing frost " in fall may be similarly ob- tained. The average length of the season without killing frost that is, the time available for plant growth, provided the whole season can be used may best be obtained by the difference between the average spring date and the average autumn date. 1 United States Weather Bureau, Summary of the climatological data of the United States, by sections, Washington, 1912. 2 Strictly speaking, the median date is that before which the last killing frost has occurred in half the years. However, a count of 823 cases shows that 404 occurred before the average date, 396 after the average date, and 23 on the average date. The median and the average, therefore, fall on the same date. This is the case when the distribution of the dates follows the normal curve in which the average, the median, and the mode coincide. 10 PROCEEDINGS SECOND PAN AMERICAN SCIENTIFIC CONGRESS. TABLE 1. Summary of frost Station. 1 County. 2 Alti- tude. 3 Last killing frost in spring. Years of rec- ord. 4 Average date. 5 Latest date. 9-10 years. 6 1895-1914. 7 Since be- 8 Alabama: Conecuh 126 125 125 37 23 33 126 27 32 26 26 43 26 30 42 28 121 59 35 25 24 133 121 126 59 23 123 125 36 43 26 40 25 38 28 26 22 22 22 123 140 42 25 129 133 36 26 130 125 42 41 Mar. 22 Mar. 17 May 6 Jan. 20 Mar. 22 ...do Apr. 2 Feb. 25 Feb. 11 Apr. 11 Apr. 3 May 25 Feb. 17 Apr. 13 Apr. 5 May 2 Apr. 1 Mar. 21 Feb. 17 Mar. 31 May 20 May 8 May 22 Apr. 30 May 14 May 6 Mar. 22 Mar. 23 Apr. 14 Apr. 12 May 18 June 4 May 23 Apr. 29 May 19 May 15 May 6 May 11 Apr. 30 May 12 May 5 May 4 May 5 May 2 Apr. 27 May 2 May 1 Mar. 20 Apr. 13 May 20 May 9 June 3 May 2 Apr. 24 May 9 May 6 May 5 May 8 Apr. 23 May 2 Apr. 26,1910 Apr. 17,1905 May 24,1907 Feb. 14,1908 Apr. 26,1910 Apr. 9, 1914 May 10,1905 Apr. 15,1913 Mar. 27,1898 Mar. 18,1898 Apr. 9, 1900 May 15,1896 2 May 4, 1898 2 May 29,1902 2 Apr. 21,1897 May 17,1895 May 12,1913 Mar. 21,1896 Mar. 13,1914 Apr. 21,1914 Apr. 26,1910 June 16,1895 July 1, 1900 May 31,1897 May 7,1906 May 31,1897 May 25,1907 May 14,1895 May 12,1895 May 4,1907 May 27,1907 .....do Mav 15,1907 May 9, 1906 May 4, 1907 May 15,1907 May 14,1895 May 15,1895 Mar. 23,1914 Apr. 26,1910 June 5, 1910 May 17,1913 June 11, 1899 2 May 12,1907 May 10,1906 May 12,1907 May 16,1910 2 May 12,1907 2 May 12,1904 Apr. 21,1897 2 May 12,1907 Apr. 26,1910 Apr. 17,1905 June 11,1892 Mar. 15,1881 Apr. 26,1910 Apr. 9, 1914 May 10,1905 Apr. 28,1894 Apr. 17,1892 Mar. 18,1898 Apr. 9, 1900 June 6, 1893 May 23,1893 2 May 29,1902 May 30,1884 2 May 17,1888 May 12,1913 Apr. 6,1891 Mar. 30,1894 Apr. 21,1914 Apr. 26,1910 June 16,1895 July 1,1900 May 31,1897 May 11,1857 May 31,1897 May 25,1907 May 15,1888 May 31,1889 May 8,1885 May 27,1907 do May 15,1907 May 20,1894 ....do May 15,1907 May 14,1895 May 15,1895 Mar. 27,1894 Apr. 26,1910 June 5, 1910 May 17,1913 2 June 11, 1892 2 May 12,1907 May 10,1906 May 29,1894 May 16,1910 2 May 12,1907 2 May 12,1904 Apr. 29,1874 2 May 12,1907 Uniontown Arizona: Hoi brook Perry Navajo.. 273 5,500 141 158 481 2,650 851 71 130 84 5,272 4,685 900 117 400 20 108 125 600 365 2,739 1,665 678 519 700 620 525 861 614 1,951 2,513 1,188 800 997 1,377 500 930 33 Yuma Yuma Ouachita... Sebastian.. El Dorado.. Riverside.. Sacramento Santa Barbara Yuba Denver Arkansas: Cam den Fort Smith California: Georgetown Riverside Sacramento Santa Barbara Wheatland Colorado: Denver.... Feb. 27 May 4 Apr. 27 May 6 Apr. 17 May 1 Apr. 22 Feb. 11 Feb. 24 Apr. 2 Mar. 20 Apr. 27 May 11 May 5 Apr. 16 May 1 Apr. 27 Apr. 22 Apr. 23 Apr. 15 Apr. 17 Apr. 19 ...do Apr. 14 Apr. 10 ...do Apr. 18 Apr. 17 Feb. 27 Mar. 24 May 2 Apr. 28 May 18 Apr. 15 Apr. 11 Apr. 21 Apr. 18 ..do Apr. 19 Apr. 9 Apr. 17 Pueblo Pueblo Connecticut: Canton. Hartford New Haven. New Haven. . . do Water bury.. Delaware: Millsboro... Sussex Florida: Jacksonville.. Duval. . . Pensacola Escambia Oglethorpe.... Worth Georgia: Point Peter Poulan Idaho: Boise Porthill... Ada Bonner Illinois: Aurora Kane Peoria.... Peoria Philo.... Champaign Cass. . . Indiana: Logansport Vevay Switzerland... Polk Iowa: Des Moines.... Keokuk Lee Kansas: Ashland Clarke Dodge City Horton... . Ford Brown Independence Montgomery.. Shawnee Tope^a... Wichita.... Sedgwick Warren Kentucky: Bowfing Green Mount Sterling Louisiana: Donaldsonville Liberty Hill. Montgomery.. Ascension... Bienville. Maine: Cornish Eastport York Washington .. Franklin Allegany Frederick.. .. Harford Frederick.. .. Montgomery . . Frederick 784 76 450 623 720 450 275 200 5.50 112 392 Farmington Maryland: Cumberland Emmitsburg Fallston Frederick . . . Great Falls New Market Washington, D. C Woodstock. Baltimore 1 Broken record. ASTRONOMY, METEOROLOGY, AND SEISMOLOGY. records for selected stations. 11 First killing frost in autumn. Number of consecutive days without killing frost. Years of record. Average date. Earliest date. Years of record. Aver- age. 81- 100 years. Shortest number of days. 9-10 years. 1895-1914. Since begin- ing of record. 1895-1914. Since be- ginning of record. 9 10 11 12 13 14 15 16 17 18 127 126 124 37 Nov. 6 Nov. 10 Oct. 15 Dec. 21 Oct. 24 Oct. 25 Sept. 29 Nov. 25 Oct. 21,1913 ... do Oct. 21,1913 do 126 25 124 37 229 238 152 335 196 205 127 281 1861910 2031904 1391908 2841908 1861910 2031904 1361894 2761893 Sepfc 22, 1895 2 Nov. 25,1906 Sept. 22, 1895 Nov. 17,1880 122 33 Nov. 3 Nov. 5 Oct. 16 Oct. 23 Oct. 14,1907 Oct. 22,1898 Oct. 14,1907 Oct. 15,1893 22 33 226 226 186 201 1791910 a 2081895 1791910 200-1893 125 124 131 125 26 Nov. 16 Dec. 8 Nov. 27 Oct. 24 Nov. 11 Nov. 2 Dec. 8 Nov. 11 2 Oct. 15,1897 Nov. 12,1904 Nov. 11,1911 Nov. 28, 1910 Nov. 4,1895 Oct. 15,1897 Nov. 12,1904 Oct. 17,1893 Nov. 28, 1910 Nov. 4,1895 125 124 31 125 26 228 286 289 "278" 175 224 226 294 225 a 1671899 2331913 2411898 2981910 2401908 2 1671899 2151894 2121892 2981910 2401908 Dec. 2 42 27 30 42 28 Oct. 6 Oct. 7 Oct. 3 Oct. 21 Oct. 6 Sept. 22 Sept. 26 Sept. 22 Oct. 9 Sept. 22 Sept. 12, 1902 do Sept. 12, 1902 do 42 26 30 42 28 156 163 150 187 158 125 141 123 162 131 1341912 1391902 1251905 a 1751899 1321911 1101875 1321893 1251905 1421884 1131888 Sept. 15, 1913 Oct. 2, 1899 Sept. 14,1911 Sept. 15, 1913 Sept. 30, 1888 Sept. 7,1888 22 Oct. 20 Oct. 9 Oct. 2, 1895 Oct. 2, 1895 121 181 156 1541906 1541905 59 36 Dec. 6 Dec. 9 Nov. 14 Nov. 8 Nov. 13, 1906 Oct. 27,1898 2 Nov. 12, 1892 Oct. 27,1898 59 35 297 288 237 230 2621914 2471898 230-1894 2271894 125 25 Oct. 30 Nov. 7 Oct. 15 Oct. 24 Oct. 11,1906 Oct. 21,1913 Oct. 11,1906 Oct. 21,1913 125 24 211 232 184 195 1821907 1861910 1821907 1861910 136 121 Oct. 14 Sept. 27 Sept. 27 Sept. 14 Sept. 22, 1895 Sept. 13, 1907 Sept. 22, 1895 Sept. 13, 1907 133 121 170 139 132 102 981895 891900 981895 891900 127 59 22 Oct. 7 Oct. 19 Oct. 3 Sept. 22 Oct. 6 Sept. 16 Sept. 20, 1896 Oct. 5, 1901 Sept. 13, 1902 Sept. 17, 1890 Oct. 1, 1856 Sept. 13, 1902 126 59 22 155 188 155 122 160 120 1261895 1521906 1131897 1261895 1521906 1131897 123 27 Oct. 13 Oct. 23 Sept. 27 Oct. 8 Sept. 21, 1897 a Sept. 30,1895 a Sept. 21, 1887 Sept. 30, 1895 123 25 169 184 135 155 1421907 1391895 1421907 1391895 37 43 Oct. 10 Oct. 15 Sept. 25 Sept. 29 Sept. 22,1913 do Sept. 13, 1890 Sept. 18,1875 36 43 170 183 137 152 1411895 1551909 1191889 1391875 26 40 25 38 28 27 Oct. 20 Oct. 18 Oct. 15 Oct. 22 Oct. 15 Oct. 20 Oct. 5 ...do Oct. 1 Oct. 5 Oct. 1 Oct. 4 Sept. 26, 1912 Sept. 23, 1895 Sept. 17, 1901 Sept. 26, 1912 Sept. 29, 1899 Sept. 23, 1895 Sept. 26, 1912 Sept. 23, 1895 Sept. 17, 1901 Sept. 26,1912 Sept. 28, 1888 Sept. 23, 1895 26 40 25 38 28 26 186 182 179 191 188 193 146 153 150 153 152 160 1341907 l<6 1907 a 150-1907 1541906 1641909 1641909 2 1341894 1491891 a U 01907 1411894 1411894 1631892 121 22 22 24 Oct. 18 Oct. 17 Nov. 23 Nov. 4 Oct. 7 Oct. 5 Nov. 3 Oct. 19 Sept. 30, 1899 do Sept. 30, 1899 do 121 22 22 23 182 183 269 225 158 157 228 189 140-1895 1381895 2271899 1851910 1401895 1381895 2271899 1851910 Oct. 27,1898 Oct. 14,1907 Oct. 27,1898 Oct. 14,1907 140 140 25 Oct. 2 Oct. 23 Sept. 20 Sept. 20 Oct. 9 Sept. 7 Sept. 10,1913 Sept. 22, 1904 Sept. 5,1896 Sept. 10,1913 Sept. 22, 1904 Sept. 5,1896 MO 140 25 153 178 125 123 153 96 a 1101910 150-1904 971899 a 110 1910 150-1904 89-1892 129 135 36 26 131 125 43 41 Oct. 21 Oct. 27 Oct. 20 Oct. 24 Oct. 19 Oct. 22 ...do.... Oct. 14 Oct. 6 Oct. 14 Oct. 8 Oct. 9 Oct. 6 Oct. 7 Oct. 8 Oct. 2 Sept. 29,1914 Oct. 7,1899 Oct. 3, 1899 Sept. 23, 1904 Oct. 1.189.) Sept. 22, 1904 Oct. 2,18.9 Sept. 23, 1904 Sept. 6,1892 2 Oct. 7, 1883 Oct. 3,1899 Sept. 23, 1904 Oct. 1.1899 Sept. 22, 1904 Oct. 2. 1899 Sept. 23, 1904 129 133 36 26 130 125 42 41 189 199 182 189 184 186 196 180 157 173 152 156 154 152 168 153 163-1913 1541906 1541906 a 1541904 1541906 1331904 1731904 1541904 133-1892 154-1906 1391894 a 154-1904 154-1906 1331904 161-1888 1531882 2 And also later years. 12 PROCEEDINGS SECOND PAN AMERICAN SCIENTIFIC CONGRESS. TABLE 1. Summary of frost records Station. n 1 County. 2 Alti- tude. 3 Last killing frost in spring. Year^ of rec- ord. 4 Average date. 5 Latest date. 9-10 years. 6 1895-1914. 7 Since be- ginning of record. 8 Massachusetts: Blue Hill Observ'y Concord Norfolk.. 640 139 53 420 88 40 298 711 609 707 955 614 975 1,039 863 935 1,251 1,300 500 126 .982 1,265 864 797 3,041 2,487 27 128 27 27 139 41 40 138 40 129 135 26 35 25 25 34 28 127 122 24 31 27 25 36 132 33 35 128 128 139 43 26 128 27 136 26 27 139 22 23 140 135 25 130 40 27 40 125 132 126 30 27 26 Apr. 29 May 9 May 13 May 14 Apr. 15 Apr. 20 May 7 May 3 May 14 Apr. 26 Apr. 27 May 15 Apr. 27 May 12 Mav 16 May 14 May 16 May 12 Mar. 18 Mar. 19 Apr. 18 Apr. 15 Apr. 18 Apr. 17 May 15 May 16 May 9 May 14 May 13 Mav 3 Apr. 16 May 6 Mav 21 May 14 May 17 May 22 May 23 Apr. 13 May 11 Apr. 12 Apr. 25 May 4 May 19 Apr. 7 Apr. 17 Apr. 13 May 12 May 13 May 27 Apr. 30 Apr. 19 Mav 1 Apr. 17 May 13 May 20 Mav 28 ...d*. ... Mav 21,1906 May 29,1900 June 3, 1908 do Mav 21,1906 Mav 29,1900 June 3, 1908 June 8, 1894 2 May 2,1895 May 30, 1884 June. 14,1912 May 24,1905 June 9, 1897 Mav 28,1894 Mav 24,1910 Mav 29,1894 May 26,1897 Juno 7, 1901 2 June 7,1897 June 8, 1885 June 11,1903 June 1, 1901 Apr. 25,1910 Apr. 26,1910 May 15,1907 Mav 9, 1906 May 16,1890 May 7, 1906 June 21,1892 June 6, 1901 June 9, 1880 June 26,1892 June 1,1906 May 23,1893 May 19,1894 June 21,1902 June 24,1905 June 11,1894 June 22,1908 June 15,1913 June 10,1913 Apr. 30,1874 May 30,1906 May 8,1896 May 18,1878 June 9, 1913 June 16,1898 May 10,1906 Mav 15,1910 May 11,1906 June 7, 1901 June 6, 1910 June 21,1902 May 28,1907 May 12,1913 May 28,1907 May 17,1895 Middlesex Plymouth Hampden Bristol Middleboro New Bedford Apr. 28 May 7 May 24 May 16 Mav 28 May 13 Mav 14 May 27 May 16 Mav 28 June 2 June 1 June 2 May 29 Apr. 10 Apr. 8 May 3 May 1 May 5 Apr. 30 June 2 May 30 May 26 May 30 May 24 May 15 May 1 May 24 June 11 June 5 June 6 June 8 June 6 Apr. 25 May 23 May 3 May 7 May 21 June 4 Apr. 24 May 2 Apr. 30 May 25 May 29 June 14 May 17 May 6 May 19 May 3 2 May 2, 1895 Mav 11,1900 June 14,1912 May 24,1905 June 9, 1897 Mav 20,1895 May 24,1910 May 28,1907 May 26,1897 June 7, 1901 2 June 7, 1897 do Somerset ...do Westboro Williamstown Worcester Berkshire Alpena Michigan: Alpena Grand Rapids . . Kent Kalamazoo Sault Ste. Marie.... Thorn ville Kalamazoo Chippewa Lapeer Minnesota: Bird Island Renville Crookston Moorhead Pine River Dam... Winnibigoshish Mississippi: Hrookhaven Polk Clav Crow Wing.... Itasca June 11,1903 June 8, 1901 Apr. 25,1910 Apr. 26,1910 May 15,1907 May 9, 1906 ....'.do May 7, 1906 June 21,1902 June 6, 1901 June 3, 1910 June 6, 1909 'June 1, 1906 May 16, 1912 ' Mav 1, 1903 June 21,1902 June 24,1905 June 7, 1906 June 22,1908 June 15,1913 June 10,1913 2 Apr. 21,1907 May 30,1906 May 8, 1896 May 15,1907 June 9, 1913 June 16,1898 May 10,1906 May 15,1910 May 11,1906 June 7, 1901 June 6, 1910 June 21,1902 May 28,1907 May 12,1913 May 28,1907 May 17,1895 Lincoln Greenville . Washington... Nodaway Laclede Missouri: Conception Lebanon . Liberty Clay Mexico Audrain Montana: Crow Agencv Havre ' Bighorn. . . Hill Helena Lewis and Clark. Sheridan do 4,110 2,020 3,821 2 821 Poplar Nebraska: Hav Springs North Platte Lincoln Omaha Douglas 1 103 Valentine Cherry 2,598 4,720 4,500 4,291 126 500 16 719 3,863 7,013 928 1,038 500 1,186 81 1,674 1,944 789 960 627 1,050 527 Nevada: Carson City Ormsby Reno Washoe Wjnnemucca. Humboldt Rockingham.. Grafton New Hampshire: Newton Plvmouth. New Jersey: Atlantic City Charlotteburg Atlantic Passaic New Mexico: Agricultural College Santa Fe Dona Ana Santa Fe Tompkins. . . SchuyJer New York: It'iaca PerrvCity. ... North Carolina: Chapel Hill Orange Lenoir Caldwell Weldon Halifax North Dakota: Bismarck Burleigh... Williams Pembina Licking Buford Pembina. . Ohio: Gran ville Marietta Washington... Jefferson Scioto New Alexandria.. Portsmouth Broken record. ASTRONOMY, METEOROLOGY, AND SEISMOLOGY, /or selected stations Continued. First killing frost in autumn. Number of consecutive days without killing frost. Earliest date. Shortest number of days. Years of Average Years of Aver- 81- 100 record. date. 9-10 years. 1895-1914. Since begin- ning ol record record age. years 1895-1914. Since be- ginning of record. 9 10 11 12 13 14 15 16 17 18 27 Oct. 12 Sept. 29 Sept. 22 1904 Sept. 17, 1893 27 166 139 1421904 1421904 129 Oct. 2 Sept. 15 Sept. 11,1914 Sept. 2,1886 128 146 118 1191895 1 191895 27 Sept. 29 Sept. 19 Sept. 14.1011 Sept. 14,1911 27 139 114 1141900 1141900 126 Sept. 23 Sept. 9 Sept. 6,1902 Sept. fi, 1902 126 132 104 105-1908 1051008 139 Oct. 27 Oct. 12 Sept. 22. 1904 Sept. 22. 1904 139 195 167 1521904 1 .-,2 1904 41 <>t. 16 Oct. 4 Sept. 23.1904 Sept. 23, 1904 41 179 150 1531904 1331884 40 O-t. 3 Sept. 15 Sept. 14,1911 Sept. 4,1883 40 143 114 1071912 1071912 40 Oct. 9 Sept. 26 .. do Sept. 14,1911 i 38 158 133 123 1913 123 1913 40 Sept. 29 Sept. 13 Sept. 10, 1898 Sept. 6.18S5 40 138 111 1041897 981894 31 Oct. 13 Sept. 23 Sept. 14.1899 Sept. 6,1892 129 170 133 129-1902 1291902 34 Oct. 21 Oct. 2 Sept. 22.1904 Sept. 22,1904 134 177 141 1271907 1271907 27 Sept. 27 Sept. 14 Sept. 14,1913 2 Sept. 5,1888 26 135 110 1121913 1021891 35 Oct. 11 Sept. 24 do Sept. 14,1913 35 167 131 1181897 118-1897 25 Sept. 28 Sept. 11 2 Sept. 9,1898 Sept. 9.1898 25 139 106 96-1910 961910 25 34 Sept. 23 ...do Sept. 7 Sept. 5 do Aug. 28.1893 Aug. 25.1885 25 34 130. 132 97 96 * 1021897 1021897 921893 7818S5 Sept. 8 1S98 28 Sept. 17 Sept. 4 Aug. 29.1911 Aug. 29.1911 28 124 94 831905 83-1905 28 Sept. 27 Sept. 15 Sept. 10,1898 Sept. 10,1898 127 138 109 1041901 1041901 123 Nov. 5 Oct. 22 2 Oct. 22.1895 Oct. 20.1811 122 232 195 1871910 1871910 24 Nov. 8 Oct. 25 Oct. 21,1895 Oct. 21,18 5 24 234 200 1861910 1861910 130 Oct. 19 Oct. 5 Sept. 28.1908 Sept. 28. 190S 130 184 155 1481908 1481908 127 25 Oct. 21 Oct. 10 Oct. 9 Sept. 23 Sept. 30. 1S95 Sept. 13, 1902 Sept. 30, 1895 "Sept. 13.1890 127 25 189 175 Ifil 141 1531906 * 1481902 1531906 1191890 36 Oct. 17 Sept. 30 do Sept. 13, 1902 36 183 153 * 1491902 149-1902 13 Sept. 25 Sept. 5 Aug. 27,1908 Aug. 27,1908 132 133 95 821902 821902 33 Sept. 18 Sept. 3 Aug. 25.1910 Aug. 25,1910 33 125 96 831910 83-1910 35 Sept. 26 Sept. 7 do do 35 140 104 83-1910 831910 129 Sept. 13 Aug. 30 Aug. 22,1908 Aug. 22,1908 128 122 92 921908 71-1892 128 Sept. 19 Sept. 6 Aug. 25.1910 Aug. 25.1910 128 129 105 951910 951910 141 Sept. 29 Sept. 15 Sept. 12. 1902 J Sept. 10. 1876 139 149 123 1341805 1181893 43 Oct. 12 Sept. 24 Sept. 18. 1901 Sept. 18.1901 43 179 146 1531901 1401890 26 Sept. 30 Sept. 15 Sept. 12, 1902 Sept. 12, 1902 26 147 114 831902 83-1902 128 Sept. 21 Sept. 3 Sept. 2.1898 Sept. 2,1898 128 123 84 821897 821897 28 Oct. 3 Sept. 17 Sept. -6 1900 Sept. 6.1900 27 142 104 108 1893 1 931894 136 Sept. 24 Sept. 7 Aug. 22.1899 Aug. 22,1899 136 130 93 93-1908 921894 26 Sept. 23 Sept. 8 Aug. 29.1908 Aue. 29.1908 26 124 02 * 871908 2 871908 126 Sept. 24 Sept. 13 Sept. 10, 1913 Sept. 7,1888 126 124 99 92-1913 921913 MO Oct. 30 Oct. 19 Oct. 1.1899 Oct. 1,1899 139 200 177 1731899 1611888 22 Sept. 26 Sept. 15 Sept. 14,1911 Sept. 14, 1911 22 138 115 108-1902 1081902 23 Oct. 22 Oct. 11 Oct. 10.1909 Oct. 1,1894 23 193 161 1631899 1551894 MO Oct. 19 Oct. 6 Sept. 27, 1908 Sept. 25, 1889 140 177 152 1461908 1431880 136 Oct. 10 Sept. 27 Sept. 14. 1911 Sept. 14.1911 135 159 129 1161895 1161895 25 Sept. 26 Sept. 10 Sept. 5.1906 Sept. 5.1906 25 130 98 84-1906 841906 130 Oct. 28 Oct. 13 2 Oct. 1,1895 Oct. 1, 1895 130 204 172 1531906 1531906. 36 Oct. 18 Oct. 4 .....do Sept. 30, 1888 i 36 184 155 1531906 153 iQ06 26 Oct. 24 Oct. 12 Oct. 10,1895 Oct. 9, 1889 26 194 165 1521906 1521906 40 28 Sept. 19 Sept. 23 Sept. 5 Sept. 9 Aug. 31,1895 Sept. 9, 1910 Aug. 23,1891 Sept. 5, 1881 40 125 130 133 103 103 1021895 951910 981888 951910. 132 Sept. 12 Aug. 27 Sept. 8,1901 Aug. 20,1875 132 108 74 831902 2 701875 125 Oct. 8 Sept. 22 Sept. 15, 1902 S*ept. 15,1902 125 161 128 1301895 1301895 31 Oct. 21 Oct. 8 Oct. 1, 1895 2 Oct. 1, 1895 30 185 155 1531906 1481886. 27 Oct. 11 Sept. 28 Sept. 30, 1908 Sept. 26, 1X87 26 163 132 1251907 1251907 26 Oct. 21 Oct. 4 Oct. 1, .1 <95 Oct. 1, 1895 26 187 154 1361895 1361895, And also later yaars. 14 PROCEEDINGS SECOND PAN AMERICAN SCIENTIFIC CONGRESS. TABLE 1. Summary of frost records Station. 1 County. 2 Alti- tude. 3 Last killing frost in spring. Years of rec- ord. 4 Average date. 5 Latest date. 9-10 years. 6 1895-1914. 7 Since be- ginning of record. 8 Oklahoma: Healdton Carter 900 1,247 1,940 266 1,640 510 112 1,327 455 250 160 51 711 1,352 1,636 1,306 1,788 3,231 3,647 1,028 347 1,738 1,050 720 4,000 4,360 876 700 40 1,450 681 2,135 13 60 1,380 45 1,943 1,000 1,933 435 586 681 974 616 6,088 7,188 21 24 25 25 26 37 39 31 31 25 30 22 21 224 26 33 27 27 25 44 43 29 231 25 25 40 28 234 28 246 240 29 42 226 25 37 33 29 23 23 28 42 235 31 42 24 Apr. 5 Apr. 2 Apr. 17 Apr. 24 Apr. 18 Apr. 15 Apr. 14 May 17 Apr. 16 Apr. 29 Apr. 22 Mar. 26 Mar. 25 Mav 14 May 19 May 12 May 6 ..do May 8 Apr. 3 Mar. 22 ...do Feb. 27 Mar. 4 Apr. 20 Apr. 21 May 16 May 14 Mar. 30 Apr. 28 Apr. 9 Apr. 23 Mar. 25 Apr. 10 Apr. 19 Apr. 22 Apr. 12 Mar. 30 Apr. 25 Apr. 19 May 6 Apr. 27 Apr. 23 May 2 May 21 May 31 Apr. 25 Apr. 22 May 12 ...do May 4 May 10 Apr. 30 June 9 Apr. 28 May 10 May 4 Apr. 13 Apr. 10 May 30 June 5 May 29 May 19 May 18 May 28 Apr. 17 Apr. 10 Apr. 9 Mar. 23 Mar. 20 May 6 May 14 June 6 June 4 Apr. 14 May 14 Apr. 25 May 8 Apr. 12 Apr. 27 May 2 May 17 May 9 Apr. 20 May 10 May 4 May 21 Mav 15 May 6 May 20 June 3 June 20 'May 1,1903 'Apr. 30,1903 May 18,1901 May 10,1908 do i May 1, 1903 !Apr. 30,1903 May 18,1901 May 18,1892 May 10,1908 May 24,1881 May 12,1887 June 14,1912 May 12,1892 May 12,1907 do Oklahoma City Oregon: Ashland Oklahoma Jackson Corvallis Benton ... Jackson Roseburg Douglas do....... May 1, 1905 June 14,1912 May 2, 1903 May 12,1907 .do The Dalles Wasco Pennsylvania: Wellsboro West Chester. . Tioga Chester Rhode Island: Kingston .. Washington... Providence Berkeley Providence South Carolina: Fergusonand Trial 3 Little Mountain South Dakota: Alexandria Apr. 17,1905 do.. June 21,1902 June 22,1902 June 21,1902 May 30,1897 May 21,1908 June 21,1902 Apr. 23,1904 Apr. 25,1910 Apr. 23,1907 Mar. 26,1913 Mar. 27,1913 May 17,1910 June 18,1895 June 12,1906 June 14,1912 Apr. 21,1897 May 17,1895 Apr. 22,1904 May 15,1910 Apr. 21,1897 May 10,1906 May 15,1910 May 31,1908 May 7, 1898 Apr. 28,1907 May 16,1910 do May 21,1895 May 24,1910 May 11,1907 iMay 21,1895 June 1,1903 July 7, 1904 Apr. 17,1905 do June 21,1902 June 22,1902 June 21,1902 May 30,1897 May 21,1908 June 21,1902 Apr. 24,1893 Apr. 25,1910 Apr. 23,1907 Apr. 16,1870 iMar. 27,1894 May 17,1910 June 18,1895 June 12,1906 June 14,1912 Apr. 21,1897 May 26,1886 May 7, 1891 iMay 15,1888 Apr. 26,1888 May 10,1906 May 15,1910 May 31,1908 June 8, 1891 Apr. 28,1907 Mav 16,1910 do May 30,1894 May 24,1910 May 13,1888 May 26,1891 June 11,1889 July 7, 1904 Newberry Hanson Brookin^s Brookings Beadle Huron Kimball Rapid City... . Brule Pennington . . . Lawrence Knox Shelby Spearfish Tennessee: Knoxville Memphis Texas: Abilene Taylor Fort Clark (Brock- etville). New Braunfels Utah: Moab Kinnev. . Comal... . Grand Salt Lake City Vermont: Northfleld Salt Lake Washington... Windsor Woodstock Virginia: Birdsnest . Northampton. Rockingham . . Campbell Dale Enterprise Lynchburg. . . Marion Smvthe Norfolk Norfolk Petersburg Dinwiddie.... Augusta... Staunton... . Washington: Olvmpia Thurston Spokane Spokane Walla Walla Walla Walla.. McDowell Berkeley West Virginia: Elkhorn Martinsburg Wisconsin: Green Bay . Brown La Crosse La Crosse Dane Manitowoc Laramie Madison Manitowoc Wyoming: Che venue.. . . Laramie Albany i And also later years. 2 Broken record. ASTRONOMY, METEOROLOGY, AND SEISMOLOGY. for selected stations Continued. 15 First killing frost in autumn. Number of consecutive days without killing frost. Years of record. Average date. Earliest date. Years of record. Aver- age. 81- 100 years. Shortest number of days. 9-10 years. 1895-1914. Since begin- ning of record. 1895-1914. Since be- ginning of record. 9 10 11 12 13 14 15 16 17 18 21 24 Oct. 29 Nov. 1 Oct. 18 Oct. 17 Oct. 10,1908 Oct. 20,1905 Oct. 10,1908 Oct. 7, 1891 21 24 207 213 176 178 1631908 1961907 1631908 1831892 26 25 26 37 238 Oct. 21 Oct. 16 Oct. 29 Nov. 12 Oct. 23 Sept. 28 Sept. 25 Oct. 7 Oct. 17 Oct. 7 Sept. 13. 1896 Sept. 21, 1895 do Sept. 13, 1896 Sept. 21, 1895 do 225 25 26 37 238 187 175 194 211 192 139 136 156 160 160 1261896 1351895 1381908 1371908 1701905 1261896 1351895 1381908 1371908 1641883 Sept. 24, 1908 Sept. 25, 1908 Sept. 24, 1908 Sept. 25,1908 32 31 Sept. 25 Oct. 23 Sept. 11 Oct. 10 Sept. 6,1909 Oct. 3, 1899 Aug. 25,1884 Oct. 3, 1899 31 31 131 190 94 165 921913 1711906 921913 1681888 25 229 Oct. 13 Oct. 18 Sept. 27 Sept. 29 Sept. 14, 1911 Sept. 23, 1904 Sept. 14, 1911 Sept. 23, 1904 25 229 167 179 140 148 1331911 1511907 1331911 1501888 21 22 Nov. 5 Nov. 11 Oct. 22 Oct. 27 Oct. 19,1901 Oct. 25,1903 Oct. 19,1901 Oct. 25,1903 221 21 224 231 192 200 1971907 1971907 1971907 1971907 225 27 34 27 226 225 Sept. 26 Sept. 22 Sept. 21 Oct. 1 Sept. 27 Sept. 28 Sept. 8 Sept. 5 ...do Sept. 18 Sept. 14 Sept. 13 Sept. 12, 1902 Sept. 3,1896 Sept. 10, 1898 Sept. 12, 1902 Sept. 13, 1902 Sept. 11, 1898 Aug. 23,1891 do 224 26 33 27 226 225 135 126 132 148 144 143 101 92 99 122 119 108 831902 821902 831902 1281901 1231904 831902 831902 821902 831902 1271890 1231904 831902 do Sept. 12, 1902 i Sept. 13, 1890 Sept. 11, 1898 44 43 Oct. 27 Nov. 1 Oct. 10 Oct. 16 Oct. 1, 1895 Oct. 11,1895 Oct. 1, 1895 Oct. 2, 1876 44 43 207 224 176 189 1801895 1871910 i 1801876 1841893 29 225 Nov. 10 Nov. 25 Oct. 25 Nov. 7 Oct. 22,1911 i Nov. 2,1899 Oct. 22,1911 i Nov. 2, 1899 29 225 233 271 199 229 2091899 2441906 2091899 2391876 26 ...do Nov. 9 Nov. 3,1899 Nov. 3,1899 25 266 234 2401897 2381894 25 40 Oct. 5 Oct. 19 Sept. 17 Oct. 2 Sept. 12, 1898 Sept. 22, 1895 Sept. 8,1890 Sept. 22, 1895 25 40 168 181 134 141 1431912 961895 1431912 961895 28 232 Sept. 19 Sept. 27 Sept. 3 Sept. 12 Aug. 31,1909 Sept. 10, 1913 Aug. 27,1894 Sept. 4,1883 28 232 126 136 89 100 971909 921913 971909 921913 226 2 46 42 29 42 28 25 Nov. 18 Oct. 9 Oct. 27 Oct. 11 Nov. 16 Oct. 25 Oct. 15 Nov. 6 Sept. 23 Oct. 11 Sept. 26 Nov. 1 Oct. 9 Oct. 2 Nov. 11,1901 Sept. 22, 1897 Oct. 2, 1899 Sept. 16, 1902 Oct. 28,1903 Oct. 1, 1895 i do Nov. 1, 1893 Sept. 15, 1873 Oct. 2, 1899 Sept. 16, 1902 Oct. 15,1876 Oct. 1, 1895 i do 226 46 240 29 42 226 25 233 164 201 165 236 198 179 206 132 169 141 203 165 153 2071897 1341907 1751899 1481903 2051903 1541906 1651895 2021875 1281886 1621888 1381888 2041879 1541906 1651895 37 33 29 Oct. 28 Oct. 12 Nov. 7 Sept. 28 Sept. 20 Oct. 18 Sept. 21, 1895 Sept. 10, 1895 Oct. 19,1905 Sept. 11,1889 Sept. 10, 18P5 Sept. 28, 1886 37 33 29 189 183 222 134 134 181 1141908 1421895 1911905 1141908 1151891 1761886 23 24 Oct. 12 Oct. 17 Sept. 27 Oct. 4 Sept. 14, 1902 Sept. 23, 1913 Sept. 14, 1902 Sept. 23, 1913 23 23 170 181 140 153 1341913 1341913 1341913 1341913 28 42 37 31 Oct. 9 Oct. 11 Oct. 18 Oct. 13 Sept. 23 Sept. 29 Oct. 3 Sept. 29 Sept. 23, 1899 Sept. 29,1908 do Sept. 16, 1887 Sept. 21,1889 Sept. 29, 1908 Sept. 27, 1912 28 42 235 31 156 167 178 164 125 137 160 132 1311895 147_1895 1501908 1411895 1161894 1221889 1501908 1331891 Sept. 27, 1912 42 24 Sept. 17 Sept. 10 Aug. 31 Aug. 29 Aug. 25,1910 Aug 22,1904 Aug. 25,1900 Aug. 16, 1 893 42 24 119 102 89 70 941910 451904 851889 451904 8 Trial, elevation 85 feet, 1893-1910 (18 years); Ferguson, elevation 51 feet, 1911-1914 (4 years). 16 PROCEEDINGS SECOND PAN AMERICAN SCIENTIFIC CONGRESS. In the determination of these averages a number of interesting mathematical and meteorological problems arose, all of which required working solutions, although the correct solution has not yet necessarily been found. For example, when the average dates were determined there w r as usually a fraction of a date to be disposed of. The date is a discrete thing, not subject to division, hence the whole fraction must be thrown in one direction or the other. At first the fraction was disposed of according to the usual rule; that is, when less than 0.5 the fraction was dropped, and when more than 0.5 the date was increased by a whole day. Later the average dates were checked by charting for the spring the date of last killing frost for a number of stations (see fig. 2). The dates STATIONS DAYS BEFORE AVERAGE AVERAGE DAYS AFTER AVERAGE 40 30 20 10 DATE IO 2O 3O 4O DALE ENTERPRISE. VA GRAND RAPIDS. MICH. BISMARCK. N.DAK. ROSALIA. WASH. MEMPHIS. TENN. ....::. : .11:. .:.::. : :..: . . . . : . h:: .. H:: . : . \ . .. : .. : .. FIG. 2. Occurrences of last killing frost in spring with reference to the average date at selected stations. before and after the average for the whole period of years were then counted and the exact meaning of a fraction of a date in this connection was carefully considered. The same procedure was followed for the dates of first killing frost in fall (see fig. 3). After a careful consideration the conclusion was reached that a more nearly correct method of disposing of the fractions of dates in the case of killing frost averages consists of increasing the average date of the last killing frost in spring by one day, whenever there is a fraction, no matter how small, and dropping all fractions of dates for the average date of first killing frost in fall, no matter how much the fraction may be. This practice also has the advantage that if there is an error it is on the side of safety, although here a matter of a day is not of importance. The method of determining the average length of the season without killing frost has been to count the time between the average date of last killing frost in STATIONS DAYS BEFORE AVERAGE AVERAGE DAYS AFTER AVERAGE. 40 30 20 10 DATE |O 20 3O 4O DALE ENTERPRISE. VA. GRAND RAPIDS. MICH. BISMARCK. N.DAK. ROSALIA. WASH. MEMPHIS. TENN. . :.: : : . : .: . . . . : : :..: ::... :.:!.::.* .. - .: . . - . . . .: . i.:. : ".. .. : . . FIG. 3. Occurrences of first killing frost in fall with reference to the average date at selected stations. spring and the average date of first killing frost in fall. This method has the advantage of avoiding questions of fractions of days and also permits the use of the whole available record for spring and for fall in those cases where one or both are incomplete. Although the "average dates of last killing frost in spring" and of "first killing frost in fall" and the "average length of the season without killing frost" are terms which have been widely used, there is still considerable doubt as to the significance of these terms and of the figures representing them. The average date of last killing frost in spring is that date after which n ASTRONOMY, METEOROLOGY, AND SEISMOLOGY. 17 o a: o z O X LJ 00 ID Q " ii u i iiimiiinimiHiiiimii iiiiiiiHifimiiiiMiiiiiiiu 'im i iiiiiiiiiiiitriiviiiiiiiiiiiiiiiiiii iiiiiHimiiiMiiiiiiiu 'im i MI iiiiiiiiiiiitriiviiiiiiiiiiiiiiiiiiistiiiM IIIIIJIIIIIIIIMIIItimillllHIIIIIUlllll " 1/ ""'"JiSiiiiE iiiiii UJ< is:::::!::::!!:. 1 ::!:::::::::!::: 1 .: 1 .::::: iiiiiiiiiiiiiiiiiiiiiiiimiiiiimiiiii IIIIIIIIIIIIIIIIIIIIIIIIUIIIIIIIIIIIIII Illllitllllllltmillllllllllinilllllll killing frost will occur in approximately half the years. On the average date there is an even chance that the last killing frost has occurred. In other words, one crop out of every two will be destroyed by frost if it is susceptible to frost in- jury on the average date. This is a higher proportion than even the most productive agri- culture can stand, and con- sequently the average date of last killing frost has little significance for the farmer; this also applies to the average date of first killing frost in fall Some date earlier than the average date of first kill- ing frost is the date before which the crop must be har- vested or there will be loss from frost damage in too many years. There are similar con- siderations to be met with in the average length of the sea- son without killing frost. To take advantage of the whole of this season it is necessary for it to begin on the day of the last killing frost in spring and to continue until the date of the first killing frost in fall. If crops are planted so that they become susceptible to frost damage on the average date of last killing frost in spring, the crop in half the years will be destroyed in the spring. This leaves only one crop out of two to continue until fall. Then, if the fall frosts occur at random with reference to the spring frost that is, if there is no casual relation between them one crop out of every two carried through the summer will be destroyed by a killing frost in fall before it can be har- vested. These relations may perhaps be shown to better advantage by figure 4. which shows by bars the total length of the growing season for the following stations selected from the whole United States: Dale Enterprise, Va.; Memphis, Tenn. ; and Bis- 25807C-2 17 2 Lu Z2 iiiiiiiiiiiniiiii ii niiiiiiniiiiiitiiM iniiiiiiiiiniiii iiiiiiiiiiiiMiiiiiiiiii IIIIIIIMIIIIIIIII IIIIIIIMIIIIIIIMIIIIII IIIIIIUIIIIIUIIIIIIIIIIIIIIIIIIIIIIHIIK UJ oo^oo OOOOO>O)O) 18 PROCEEDINGS SECOND PAN AMERICAN SCIENTIFIC CONGRESS. ruarck, N. Dak. If it were possible to determine the latest date of last killing frost in spring for a period covering a hundred years or more and the earliest date of first killing frost in fall for a similar period, we should probably have the season of safe plant growth. The nearest approach possible to this available is the latest date in spring and the earliest date in fall which has been observed since the beginning of the record. In very few cases this is more than 40 years, and in most cases is a great deal shorter than this. These extreme dates of killing frosts represent different things at different places because of the varying length of the records. The longer the record the more probable it is that these extreme dates will not be exceeded, but as extreme dates rest on single occurrences, they can not be considered as absolute limits. The shortest recorded season without killing frost is usually somewhat longer than the period between the latest date of last killing frost in spring and the earliest date of first killing frost in fall, because in most cases these extreme dates did not occur in the same year. THE PROBABILITY OF FBOST. . The date of the last killing frost in 1 year in 20 established the extreme limit for killing frost in spring in that 20-year period; in each of the other 19 years the date of the last killing frost is earlier than that. If the 20-year period has the exact average frost distribution the prob- able occurrence of the last killing frost in 1 year in 20 can be predicted on that o . . FIG. 5. Frequency polygon and most probable normal fre- Under similar average quency curve of the date of last killing frost in spring for conditions the latest date the combined records 61 33 stations, comprising 823 obser- Qf lagt kming frogt during vations. any 10 years will give the date on or after which frost may be expected once in 10 years. How- ever, it is hardly possible that any given 20 or 10 year period will give the . exact average frost distribution, especially in the cases which occur but once or twice during the period. It is desirable to determine as far as possible the risk from frost damage after any particular date. This has been attempted by various methods, the most notable of which is perhaps the table prepared by Wilson 1 for New York State. This method, however, has the disadvantage that the curve of frost occurrence used by him is not smooth, which results from the fact that all the records are too short. To obtain a smooth curve of the distribution of last killing frost in spring in the neighborhood of 1,000 observations are required. However, by grouping a great many cases, it is possible to determine the type of distribution of these recorded dates of last killing frost in spring. Table I shows for a few stations the dates on or after which the last killing frost may be expected to occur in 1 year in 10, provided the period from which the date was calculated was one with average frost conditions. Figure 5 is a frequency polygon which has been constructed for 823 observa- tions, representing the combined records of 33 stations for last killing frost in spring. An attempt was made to fit this frequency polygon to various curves of distribution, both normal and skew curves, by the use of methods suggested i Wilson, Wilford M. : Frosts In New York, N. T. Cornell Agr. Fjxp. Sta. bul. 316 : 536- 543, Ithaca, 1912. ASTRONOMY, METEOROLOGY, AND SEISMOLOGY. 19 by Pearson. 1 From this frequency polygon it appeared that the curve which most nearly fits the conditions is the " normal curve " of distribution. 2 It can be shown that the probability of occurrence of any phenomenon which follows the normal distribution may be determined when the "standard devi- ation" is known. By the use of the standard deviation a much more certain measure of occasional occurrences is determined than is possible by a count of the two or three extreme occurrences in a comparatively short record. Figure 6 shows the normal frequency curves of the distributions of the dates of last killing frost in spring for five stations and of first killing frost in fall for three stations. These stations were selected to show the usual dispersions of the normal frequency curves. Each curve has been shaded to show the region within which 9/10 of these dates fall; that is, the shaded area is-9/10 of the total area under the curve. The normal concentration of last (or first) occurrence of killing frost at any given number of days after (or before) the average date is shown by the height of the curve above the base line at the place where this number appears on the scale. The place where the border of the shaded area cuts the base line shows the date after (or before) which killing frost will occur only 1 year in 10 on the average. By counting the cases of frosts which fall within the dates shown on the smooth normal curves to include 9/10 of the dates, it has been found that out of 27,838 cases of occurrence of last killing frost in spring or first killing frost in fall, 2,739 occurred later in spring or earlier in fall than the dates included in the shaded area. This is 0.984 in 10, which is a very close agreement. 1 Pearson, K. : Skew variation in homogeneous material. Phil, trans. Roy. Soc., ser. A, 186 : 343-414, London, 1895. * The following explanation of the method of obtaining the date in the spring after which, and that in the autumn before which, frost will occur on the average only 1 year in 10 has been prepared by Mr. H. R. Tolley, who made the preliminary mathe- matical studies upon which this statement of frost risk is based : When the problem of investigating the variability of these dates, and consequently the variability of the length of the growing season, first presented itself, it was seen that if the distribution at any station followed the normal frequency curve (variously known as the probability curve, the curve of error, etc.) it would be possible to determine a spring date for any station after which frost would occur on the average 1 year in 4, 1 year in 5, or 1 year in 100, if so desired, and similar dates for early frosts in the fall. Now, owing to the paucity of years of observations at any one station, the average for all stations being probably less than 20 years, and on account of the fact that in the neighborhood of a thousand observations are necessary to obtain a smooth curve, 33 stations distributed over the whole United States, with records varying from 5 to 43 years in length, and 823 as the aggregate number of years, were selected and combined, a curve was made for the combination (see fig. 5). If these are representative stations, and a single type of curve is to be selected to fit every individual station, it will obviously be that of the curve of best fit for this combination. The criteria developed by Karl Pearson in " Skew Variation in Homogeneous Material " were applied to the observations and they showed that while the curve of best fit was not exactly a normal curve, it was similar in all respects except for a very slight amount of skewness i. e., the mean and the mode, or abscissa of the highest point of the curve, did not coincide. The distance between them, however, was less than one day, and since the unit of measurement is one day and it is impossible to consider in the final results anything less than that, it was finally decided to use the constants of the normal curve in the computations, and the results seem to have justified this selection. -12 The equation of the normal curve is y=ye 2ffZ , the origin being at the mean, and the ordinate at that point being y . a is the square root of the arithmetic mean of the squares of all the deviations from the average date (~) and is commoill y known as the standard deviation. The y (ordinate) of any point represents the number of occurrences of the particular deviation, x, to which it corresponds, and the total number of deviations (or observations) is the area of the curve. It was found by referring to a table of the probability integral, which is the integral of the equation to this curve that nine-tenths of the area lies before the ordinate whose abscissa is 1.28 *. 20 PROCEEDINGS SECOND PAN AMERICAN SCIENTIFIC CONGRESS. FREQUENCY CURVES LAST SPRING FROST-FIRST AUTUMN FROST AUTUMN AV.DATE NO V.I HASKELL.TEX. ff-7.7 AUTUMN AV.DATEOCTI2. LEWISB'JRG.PA. SPRING AV. DATE APR.I5 NEW BEDFORD MASS. ff-IO.O It has also been found that in individual cases there is rarely more than one unit variation. For example, from a station with a record of 36 years there are practically never more than five dates of last killing frost in spring'or five of the first killing frosts in fall which fall beyond the date shown by the smooth curve, and practically never less than two. In a great majority of cases the number for such a record is three or four. This apparently shows that the normal curve is a better indication of the frost probabilities than any count of the actual cases, which is what we should expect from a mathematical consideration of the situation. The counting of a large number of cases shows that these extreme frost dates follow very closely the normal distribution. From that the inference is strong that for any individual station the distribu- tion is normal provided tliere is a long enough record. The normal distribution determined from the actual distribution for the period of the record may be used to show the probability of the occurrence of the last killing frost in spring or the first killing frost in fall. The probable error -of the standard deviation of the date of last killing frost was calculated for several stations from ob- servations covering a period of 20 years or more, and was found to vary from two to five days, de- pending upon the length of record and also upon the range of variation. The probable error of the standard deviation and, hence, of the dates deter- mined, varies directly with the magnitude of the standard deviation and inversely as V where n is the number of observations. 1 Of course, the number of observations for a single station is so small that the standard deviation can not be re- garded as well established, but it is significant that the combination of many records results in a nearly smooth curve with a single mode and that the successive addition of more observations makes the curve smoother and smoother. If the normal curve, or rather the standard de- viation, could be determined for each of the 800 or more stations in the United States having records sufficiently long to justify this procedure, it would be possible to show the risk of frost at any particular date. However, the clerical labor. involved in determining standard deviations for a large number of stations is so great that this has been determined only for 569 selected stations. The standard deviations for these stations are given in Table 2 for both spring and fall frosts, together with the average dates of last killing frost in spring and of first killing frost in fall. This method of determining the probability of frost is subject to limitations because .of the small number of observations in any case. As has been pointed out, there are seldom more than 40 observations and more often 20 to 25. This means that it is not possible to obtain a measure of dispersion which is not subject to considerable error. AUTUMN AV.DATE SEPT. 19. B'SMARCK.N.0. 041.0 v SPRING AV.DATEAPRI3. SPRING AV. DATE FE 8.25 SPRING AV.DATEMAR.20. LLANO.TEX. ff-Si.2 AV.DATE MAY 23. ROSALIA.WASH. G-2S.S DEVIA. 1*5 30 15 15 30 0 22 March 20 4 13 4 Novrmb r r 1 6 10 7 Opelika Lee 917 23 March 20 6 12 4 Novemoer 12 2 15 7 Tuscaloosa Tuscaloosa.. 230 25 March, 28.2 13.2 November 5.4 10 3 TJniontown Perry 273 26 March, 16.4 13.7 November 10 1 12 2 Valley Head.... Dekalb 1,031 26 April, 9.0 13.9 October, 21.6 10.3 Arizona: Bishee Cochise 5 500 22 March 21 6 22.8 November 25 7 12 8 Buckeye Maricopa.. . 980 20 March, 5.9 20.4 November, 25.2 18 3 Dudleyville Pinal 2,300 22 March 30.0 . . 16.6 November 11 3 13 4 Fort Grant Graham... . 4,916 31 March, 16.2 22.6 November, 25.5 17.0 Fort McDowell Maricopa.. 1,450 20 March, 9.7 29.6 November, 21.7 21 4 Fort Mohave Mohave 604 23 February, 6.5 21.5 December 10 6 23 5 Holbrook Navajo 5,500 25 Mav, 5.7 15.1 October, 15.3 . ... 12 5 Jerome Yavapai 4,743 17 March, 15.7 . 22.7 November 26 7 17 1 Oracle Pinal 4 500 21 March 9 4 19 1 December 3 6 12 6 Parker .. Yuma .. 353 18 March, 7.3 19.7 November, 22.1 12 Phoenix Exper- Maricopa 1 092 21 March 7 8 17 7 November 27 6 15 iment Sta- tion. Tucson Pima 2 427 24 March 13 2 19 9 November 24 1 17 2 Yuma Yuma... . 141 37 January 1 (29), 19.7. 25.0 December (29), 21.7 22.8 Arkansas: Camden Ouchita 158 23 March, 22.0... 16.6 November, 3.3 13.6 Con way Faulkner. 309 23 March, 25.6 12 1 November, 1.0 10 3 Corning Clav 293 21 \pril 1 5 10 8 October 17 6 11 7 Fort Smith Sebastian 481 33 March, 21.2...'. 11.4 November, 5.8 10.6 Newport J ad 'son 231 26 March, 25.3 . 11.1 October 25.7 9 9 Helena Phillips 182 23 March, 21.6 14.2 November, 5.5 10.1 Malvern Hot Spring. 277 24 April, 30 : 12.2 October, 29.9 9.6 Rogers Ben ton 1 385 22 \pril 11 6 11 5 October 20 5 9 Stuttgart Arkansas 228 23 March 273 13 1 October 28 5 11 8 Texarkana Miller 332 23 March, 20.6 13.2 November, 8.0 11 i California: Berkeley Alameda 320 27 January 1 (18), 17.8. 28.5 January 1 (17), 3.0. . 23.3 Cedarville Modoc 4 675 20 Mav 23 1 . 18.0 September, 26.0 12.0 Chino San Bernar- 714 21 February 14 22 6 December 13 3 23 Claremont Durham dino. Los Angeles. Bntte 1,200 160 26 20 February, 11.7 March, 13.6 9.3 26.4 December, 20.3 November, 2.3 25.9 17.4 Escondido San Diego 650 20 March, 27.3 27.7 November, 19.8 29.8 Georgetown Eldorado 2 650 26 April 1 5 29 7 November 16.2 17.8 Hollister . San Benito 284 20 March, 14.7 37.9 November, 16.1 15.5 Iowa Hill Placer 2 825 21 March, 26.2 25.0 December, 5.2 19.4 Kennedy Gold A mad or 1 500 21 March 13 7 33 December, 7.5 . 14 7 Mine. Lick Observa- Santa Clara 4 209 25 Mav. 7 1 .. 26.9 November, 16.0 23.5 tory. Lodi. San Joaquin 35 22 March, 4.0 21.0 November, 22.8 19.1 Los Gatos Mammoth Tank Santa Clara. Imperial 600 257 20 20 February (18), 3.6. Februarv,7.1 . 24.8 30 7 December ( 17), 23.4 December, 30.0 23.7 36.2 Nevada City Nevada 2 580 22 Mav 3 4 17 8 October 23 4 16.7 Napa..... ..."."I Oroville Napa Butte ' 60 250 24 21 February, 22.4 February, 9.0 10.4 37.4 December, 16.0 December, 6.8 29.4 13.8 Palermo do 213 23 March, 11.7 26.2 November, 21.7 16.0 Placerville Eldorado 1.820 23 April, 5.3 27.0 November, 3.1 19.2 Reddin" Shasta 552 24 March, 9 8 . 26.7 December, 2.3 18.7 Tlepressa Sacramento 305 22 February ' (18), 20.6 9.8 December ( 19), 13.4 14.0 Riverside Riverside 851 27 February > (26), 24.2 27.7 December K23), 8.2. 21.3 Sacramento Sacramento. 71 32 February (31), 10.5 29.6 November '(30), 27.6 19.8 tSome years are frost free. The number in parentheses is the number of years in which frost occurred. J or example, at Yuma the record covers 37 years, of which 8 were frost free and 29 had frost. For a method < I determining the frost risk under such conditions, see Table 3, p. 621. PROCEEDINGS SECOND PAN AMERICAN SCIENTIFIC CONGRESS, TABLE 2. Frost data for selected stations Continued. woH Station. County. H. Years. iifll nr.Ai. DJinirj . 2 en 12 24 April, 3.5... 13.0 November, 5.4. . . 13.5 Salisbury Rowan 760 22 April 105 12.1 October 24 6 10 7 South port Brunswick 18 20 March, 22.9 16.3 No" 1 ember, 11.5. . . 9.7 Waynesville Havwood 2 792 21 April, 255 11.2 October, 12.1 . 11.4 Weldon.. Halifax.. 81 i 27 April, 12.8..., 13.0 October, 25.8 9.7 26 PROCEEDINGS SECOND PAN AMERICAN SCIENTIFIC CONGRESS. TABLE 2. Frost data for selected stations Continued. Station. County. H. Years.' A.. s. A a . ,.. North Dakota: Bismarck Burleigh.... Bottineau... Williams-.. Stark Sargent McLean Stutsman... Grand Forks Renville Billings Walsh 1,674 1,638 1,944 2,543 1,249 1,901 1,390 1,134 1,640 2,225 820 1,955 2,400 789 1,020 1,857 830 962 1,872 1,471 1,276 803 745 960 975 1,087 627 944 880 1,050 720 1,130 527 900 588 1,575 1,150 900 1,062 1,585 1,247 880 212 1,940 3,471 4,157 100 266 670 435 220 32 575 956 1,950 300 1,640 4,400 2,784 154 195 485 69 1,070 510 120 4,700 4,150 112 75 2,242 1,800 1,368 40 20 28 23 23 20 22 21 21 18 23 26 20 32 24 20 23 22 21 22 21 22 21 26 22 21 31 20 22 27 20 22 26 21 22 21 15 21 17 21 24 21 24 26 25 20 22 25 19 21 23 20 22 22 23 25 26 22 20 26 23 22 22 25 37 22 22 20 39 24 21 25 22 May, 11.1 . . 10.2 9.9 12.4 13.9 17.2 12.3 12.0 8.9 12.1 12.5 11.5 13.1 10.1 14.1 14.6 14.1 13.8 12.4 11.8 12.9 14.8 13.7 14.9 13.1 9.1 16.0 13.1 16.6 12.9 14.0 11.7 15.4 12.5 13.3 14.5 14.9 15.6 15.7 15.4 13.2 15.8 15.6 21.7 19.0 21.1 22.4 19.0 13.8 25.6 18.3 13.0 30.1 22.7 17.6 14.2 14.4 12.5 16.1 14.7 15.1 18. * 18.9 20.3 19.7 19.7 18.4 18.9 22.0 13.1 16.1 18.4 18.8 17.2 September, 19.2.. September, 9.3... September, 23.2.. September, 10.3.. September, 20.0.. September, 23. 2.. September, 17.9.. September, 18.6. September, 5.3.. September, 10.9. September, 16.7. September, 9.1 . . September, 9.9.. September, 11.1. September, 19.6. September. 12.0. September, 20.1 . September, 18.2. September, 21.5. September, 13.0. October, 8.2 11.1 19.1 1018 17.7 17.3 12.4 12.4 13.7 14.6 13.5 10.3 12.2 8.8 12.0 12.8 12.1 12.8 14.1 13.8 8.6 11.7 12.5 10.8 12.2 13.0 11.4 10.6 12.2 13.0 9.8 14.7 11.3 13.2 11.4 14.0 9.7 8.8 8.8 13.4 9.6 11.0 12.8 20.3 18.0 13.2 19.0 16.1 16.8 14.6 21.2 19.1 19.9 20.2 15.9 16.8 18.7 17.0 18.2 18.6 21.9 20.0 23.0 19.6 15.6 19.9 20.6 11.0 16.1 12.5 17.0 13.6 16.5 17. a Bottineau May 199 Buford May, 12.3 Dickinson Forman May, 24 8 May,22.3 Garrison Jamestown Larimore . . . . May 18 3 May,23.0 Mo TTir| fifty May 28.2 Medora May, 20.0 Minto May 26.7 Napoleon Logan May 27 1 New England.. Pembina Hettinger... Pembina Richland... Kidder . May, 19.0 - May,26.2 May,24.5 Power Steele. .. . Mav, 23.0 University Wahpeton Grand Forks Richland... Williams.... Bottineau... Logan . May, 18 2 May, 18.0 Williston May,16.2 May, 16.9 t'g G 1 Mav 1 2 Willow City.... Ohio: Bellefontaine. .. Cambridge Guernsey. . . Ross May, 8.2 October, 2.0 Frankfort . . . April 28.0 October, 12.0 Granville... Licking Butler April, 30.0 October, 8.3 Jacksonboro Killbuck April, 28.6 . . . October, 17.2 Holmes Washington. Medina May 4 8 October, 5 4 Marietta April, 18.7 October, 21.9 Medina May, 13 3 October 9 2 Montpelier Williams.... Jefferson Putnam Clark May, 2.0 October, 6.5 New Alexandria Ottawa April, 30.5 . October, 11.2 . May 3 8 October 7 Plattsburg May, 2.2 October, 5.9 Portsmouth Warren Scioto April 16 8 October 21.0 Trumbull... Sandusky... Ouster May 14 3 October 5 7 Vickery May, 8.1 October, 9.5 Oklahoma: Arapaho April 7 6 October 28 5 Fort Sill Comanche... Carter March, 28 2 November 7.4 Healdton April 4 3 October 29 7 Jefferson Grant April, 12.6 March 24 3 October, 24.5 Mangum Oklahoma Greer Oklahoma.. Payne November 3 6 April, 1.5 Nov. 1.0 Stillwater. . March, 30.3 March, 31.0 ... October 29 5 Oregon: Albany Ashland Baker Burns Linn Jackson Baker Harney Hood River. Benton October, 30.5 April 16 8 October 21 3 Mav, 16.0 September, 26.0.. . September, 16.2.. . November, 11.9.. . October 16 5 May 286 Cascade . April 8 4 Corvallis April,23.5 March 14 7 Eola Polk November, 10.4. . . November, 2.3... . October 16 5 Eugene Forest Grove... Gardiner Lane Washington. Douglas Tillamook... Josephine. .. Morrow Hood River. Jackson Wallowa.... Union .... April 9 1 April 30 7 March 26 4 November, 29.5 October, 2.8 G lenora May, 19.1 . . Grants Pass Heppner . May 15 2 October 1 5 April 29 3 October 12 9 Hood River Jacksonville Joseph . April 15 8 October, 22.7 . April, 17.3 Mav 12 October, 29.7 October 5 5 La Grande... Apri'1,22.9 April, 28.3 October^ 4 McMinnville.... Miramon te Farm. Mount Angel... Newport Pendleton Yamhill Clackamas.. Marion October, 11.7 April, 23 1 . October, 31.7 April 1 7 November, 3.5 November, 29.8 October 2 2 Lincoln Umatilla.... Douglas Marion March, 24.7 May 5 8 Roseburg. Apr.ii 14 8 November, 12.1 Salem April 7 Silver Lake Lake. June 17 September', 1.9 October, 14.6 October 23 3 Sparta Baker May,3.4 Tlie Dalles Toledo Vale Weston Williams >.II Wasco Lincoln Malheur. . .. Umatilla.... Josephine... April' 19.5 May,20.1 November 4.2 September, 11.7 October 6 1 May' 10.4 September, 24.2 1^,8 i! ASTRONOMY, METEOROLOGY, AND SEiSMOLOGY. >oafjt TABLE 2. Frost data for selected stations Continued. 27 ^, | Station. ^ A County. H. Years. A s . a t . A a . <* 9 7 October 17 3 10 7 Manitowob Manitowoc.. 616 31 Mav, 1.6...* 11.2 October, K-i.R 10 9 Glnrk 96 22 Mav 17 5 13 2 September 24 2 12 5 PrairiPdu rhien Cra \v ford 628 24 \pri , 27 2 13 1 October 1 1 6 11 6 Valley Junction. Wyoming: Chevenne Fort Larauiie .. Monroe Laramie. . .. Gosben / 930 6. OSS 4,472 22 42 20 May, Mav. Mav, 13.9 20.3 . . . 16.0 14.1 10.0 11.1 September, 19.5 September, 17.2. . September, 18.4 17.8 11.3 11 2 Laramie Albany 7 188 24 MaV, 30.2 16.1 September 10 8 10 8 Lander Fremont 5,367 21 Mav, 2? .5 16.1 September, 11.0 11.9 Lusk iobrara 5.007 22 Mav, 24.1.. 15.2 September 14 7 28 6 Sheridan Sheridan 4 000 19 Mav, 189 8 4 September 17 7 7 Yellow stone 6,200 13 Mav, 24.1.. . 15.8 September, 13.8 17 1 Par;. Explanation of symbols: H is elevation above sea level. As is the arithmetical average of the dates of the last Hlling frost in each year of record. * is the stin larl deviation of the date of last illing frost in spring. A a is the arithmetical average of the dates of the first ] illing frost in each year of record. * a is the standard deviation of the date of first Jailing frost in fall. TABLE 3. Factors for determining the chance of killing frost. Killing frost will occur on the average in In spring after. In fall before. 1 year in 2 As A 8 +0. 431 * s A 8 + .674* 8 A 8 + .842<7 8 A 8 +1.282* g A 8 +1.50l* 8 A 8 +1.645* 8 A 8 + 1.751* 8 A 8 +1.834* 8 A 8 +2.054* 8 -A+2.326* 8 Aa-0. 431 *. A a . 674 * A a - .842* A a - .282* A a - .501* A a - .645* Aa- '884* Aa-2.054* A a- 2. 326* Aa-3.090* 1 year in b. 1 year in 4 1 year in 5 1 year in 10 .. year in 15 year in 20... vear in 25 . . year in 30 year in 50 .. year in 100.. 1 year in 1,000 A a +3. 090 = 0.674-^= ..... Ci is the date after which killing frost will occur in 1 year in on the aver- Co, is the date before which killing frost will occur in 1 year in 10 on the average C a = A a 1 .28 ff a . _ EC is the probable error of C. E e = JEA Z +(1.28 J0 Nt is the calendar date after which killing frost will occur 1 year in 10* No. is the calendar date before whichikilling frost will occur 1 year in 10*. C a = Sept. 5.0. E c = 1.6 Jfc-Sept.5. * The calendar date M is determined from A by increasing the date one whole day whenever A contains a fraction, no matter how small. A~ is determined in a similar manner from C t . Ma is de ermined from A a by dropping any fraction, no matter how large. No, is similarly determined from Co. oa*i o ASTRONOMY, METEOROLOGY, AND SEISMOLOGY. 3 For any place in the United States, then, which has a record covering a period of approximately 20 years, it is possible to determine with very con- siderable accuracy the risk of a killing frost after any particular date in spring or before any particular date in fall. FIG. 7. Dates of last killing frost in spring, 1907, in Kansas. 1391 9ftt , o 9fl o AVERAGE DATES OF LAST KILLING FROST IN SPRING. In order that a proper study may be made of the regional distribution of frost condition, it is desirable to map as far as possible the conditions of U5 IQO 95 9O 85 BO 75 70 65 115 no 1 FIG. 8.-Average dates of last killing frost in spring. t\' )!;'> ' '+i!J rtfloHq'-nX'J lonhil ^197 frost occurrence. Figures 8 to 13 show the frost conditions as far as is prac- ticable on small-scale maps with the data available. Figure 8 is a map of the average date of last killing frost in spring for the United States based on 32 PROCEEDINGS SECOND PAN AMERICAN SCIENTIFIC CONGRESS. the period 1895-1914. In the eastern United States isochronal lines have bcon drawn for the 1st, llth, and 21st of each month from March 1 to June 1. In addition, lines showing the limit of annual frost that is, the line separating 125 12O 115 HO 105 1OO 95 90 85 8O 75 70 65 9O 8l> 8O 75 FIG. 9. A erage date of first killiag frost in fall. the regions where frost occurs at least once in each year from those in which one or more winters passed with no record of killing frost, and the line mark- ing the regions which have more than half the winters without killing frost 125 12O 115 11O 1O5 KXr 90 85 8O 75 115 11O* 1O 85 80' 75 FIG. 10. Average length of the season (number of days) without killing fiost. have been entered on the map. This map shows, in the first place, that with very minor exceptions the whole United States is subject to killing frost each year. It also shows clearly the large area of the United States which is ASTKONOMY, METEOROLOGY, AND SEISMOLOGY. 33 subject to frost after June 1. It should be noted that the isochronal lines on these maps represent the dates which will be exceeded on the average in 125 I2O 115 HO IO5 1OO 95" r>G" if !i-" ; i!O '05 100 95* SO' 85 FIG. 11. Computed dates when the chance of killing irost falls to 1 in 10. After these dates killing frost will occur only 10 years in a century. one year out of two, that is, along the line marked June 1 one year out of every two on the average will have a killing frost after June 1. A striking 125 12O 115 11O IO3 1OO' 95 9O 85 8O . 75 70* 65" us no" 105* 100 FIG. 12. Computed dates when the chance of killing frost rises to 1 in 10. Before these dates killing frost will occur only 10 years in a century. feature of this map is the- large area of the country which has its last spring frost rather late in the season. 25807C-2 17 3 34 PROCEEDINGS SECOND PAN AMERICAN SCIENTIFIC CONGRESS. In the western part of the United States that is, west of the front range of the Rocky Mountains it is possible to draw the isochrones only for the 1st of each month, because of the broken topography and the rapid change in frost conditions in short distances. However, it has been possible to draw these lines with one-month intervals, so that they show the conditions reasonably well. A great portion of the more elevated parts of the country are subject to late spring frosts. Between one-fourth and one-third the total area of the United States is probably subject to June frosts in half the years. In the western portion of the country, except in favored valleys and some parts of the Southwest late frosts are the rule. In the eastern part of the United States the lines of killing frost dates run more or less parallel to the latitude line showing later dates with increased latitude and increased distance away from bodies of water. The topography in the East is not of such marked importance as the topography in the West, although it has been found that even the lower mountains exert a very considerable influence. The average 125 12O' 115 HO 1O5 1OO* 95 90 85 80 75 70' 65' FIG. 13. Computed length of available growing season 4 years in 5. probable error of the average dates of last killing frost shown by the map is of the order of three days, that is about one-third the interval between the isograms. As far as possible the lines have been curved to include all stations and in most cases the areas between the lines actually represent the regions with frost dates indicated by the limiting lines. There is some question as to whether absolutely uniform records will give smooth lines with broad curves and fe\v sharp angles, or whether even the smoothest topography is so rough that local air currents are set up which com- plicate the conditions so that smooth lines do not represent the actual case. There is, of course, one other point to be noted about the isochronal lines of frost occurrence, and that is that these lines do not represent anything which actually takes place. They are statistical lines resulting from the accidental distribution of many conditions, and this accidental distribution tends to smooth out irregularities. The way in which frost actually occurs may be shown by figure 7, which is a map of the conditions in Kansas during the severe spring ASTRONOMY, METEOROLOGY, AND SEISMOLOGY. 35 frosts in 1907. The last killing frost in the spring of 1907 in eastern Kansas occurred on May 4. The area in which this occurred is limited by a rather definite line which is shown on the map. The last killing frost in a strip of varying width from northeastern to south central Kansas in the same year occurred on May 15. In the northeastern half of the State the last killing frost occurred on May 27. There was no gradation between these areas. The region in which the last killing frost occurred on May 4 is separated from that on which the last killing frost occurred on May 15 by a line, and the same is true of the separation between this region and that where the last killing frost occurred May 27. AVERAGE DATES OF FIRST KILLING FROST IN FALL. Figure 9 shows the average date of first killing frost in fall. It is similar to figure 8. The regions which are not subject to annual frosts are, of course, the same on both maps. The area which has autumn frost before September 1 is similar to that having spring frost after June 1, although there are minor differences. Perhaps the most striking thing about the two maps is their great similarity. AVERAGE SEASON WITHOUT KILLING FROST. Figure 10 shows the average number of days between the last killing frost in spring and the first killing frost in fall. This has sometimes been called the " growing season," but it can not be so regarded because it is not possible in practice to make use of the whole time, owing to the risk involved at the beginning. The data for this map were obtained by subtracting the average date of last killing frost in spring from that of first killing frost in fall for all Lhe stations available. Isograms have been drawn for 10-day intervals in the eastern United States, and for 30-day intervals in the western United States. The length of the season varies from 3G5 days at Key West to considerably less than 90 days in the extreme northern portion of the United States and in the higher mountain regions of the West. There is, of course, a similarity between this map and the maps of average date of last killing frost in spring and first killing frost in fall. A striking feature of this map is the large area of the United States in which the season without killing frosts is 90 days or less. This is so shoft that ordinary agriculture is largely out of the question, and only hardy grains and grasses can be cultivated with any degree of assurance. This, of course, does not mean that these areas are waste, because in very many cases this is the region in which the most important forests of the country exist, but these regions are distinctly outside of the strictly agricultural area. DEVIATION FROM THE AVERAGE DATES. Although it has not been possible to show by a map the deviation from average -dates which will occur at varying intervals, maps have been prepared which show the dates beyond which frost is a probability 1 in only 1 year in 10 on the average. Figure 11 shows the date after which the last killing frost in spring will occur in 1 year in 10. This has been determined by multi- plying the standard deviation for 569 stations by the factor 1.28, as shown in 1 The writer wishes to record his obligation to Prof. W. J. Spillman, Chief of the Office of Farm Management, U. S. Department of Agriculture, for the original suggestion of this method for determining frost probability and for advice and assistance at all stages of the study. 36 PROCEEDINGS SECOND PAN AMERICAN SCIENTIFIC CONGRESS. Table 3, and adding the product to the average date. For example, the date after which a killing frost at Bismarck, N. Dak., in 1 year in 10 on the average is May 25. 1 This date has been entered on the map for Bismarck and similar dates have been entered for each station for which the standard devia- tion has been determined. This map, otherwise, is similar to the map of average date of last killing frost except,- of course, that the number of stations used is much smaller. Figure 12 is similar to figure 11 ; it shows the date before which the first killing frost in fall will occur 1 year in 10. PROBABLE LENGTH OF THE SEASON WITHOUT KILLING FROST. Figure 13 shows the probable length of the season without killing frost in four years in five. This has been determined by obtaining the difference between the date shown by figure 11 and that shown by figure 12. Strictly speaking, this map shows the probable length of the season without killing frost in 81 years in 100, but the probable error is of the order of four days, nnd consequently for practical purposes it is sufficient to assume that the map shows the season for four years in five. If crops are in a condition to be injured by frosts by the date shown in figure 11, 1 crop in 10 will be injured by frost in the spring. If the crops require the full time until the date shown in figure 12 to mature, and are subject to frost damage until this date, 1 crop in every 10 which survive the exceptional spring frost will be destroyed in the fall. This may be stated as follows: If the chances of safety in the spring are 9/10 and the chances of safety in the fall are 9/10, then the chance of a safe growing season is represented by the product of the chances of safety in spring and the chances of safety in fall. Expressed mathematically this is 9/10X9/10=81/100, which is the probability of a frost-free season of the length indicated on the map. INFLUENCE OF TOPOGKAPHY ON FROST DATES. The influence of topography on frost is twofold. In the first place higher altitudes have lower temperatures that result in later killing frost in spring and earlier killing frost in fall. This is clearly shown on the maps of average dates of killing frost. The second influence of topography depends not so much on altitude above sea level as the character of the slope. During quiet nights there is a tendency for the air to rearrange itself under the influence of gravity. This is particularly noticeable in regions of broken topography. While the mechanism by which this rearrangement takes place is complicated and under discussion at the present time,* certain phases may be pointed out. In the first place there is a tendency for cold air to collect in the low places, particularly in inclosed valleys. During the night the cold builds up from the bottom of the valley until this process is checked by the morning warming. There is also a tendency for the chilled air to flow away from the slopes. Whether this chilled air flows down the hills in a manner similar to water, or whether there is a complicated exchange of air from the hillsides to the air over the valley, is still under discussion. It has been noted in many regions that there is a warmer belt along the valley sides the so-called "thermal belt." This belt has frost less often than the valley bottoms and less often than the hilltops in most cases. However, where the hills are of only moderate height it sometimes happens that the hilltops are included within the thermal belt. Practical application of the influence of topography on frost may be 1 See Table 4 for the method by which this date is obtained. * See McAdie, A. G. : Temperature inversions in relation to frost. Harvard College Observatory Annals, 73 : 168-177, Cambridge, 1915 ; and Marvin, C. F. : Air drainage explained, [U. S.] Monthly Weather Review, 42:583-585, Washington, 1915. ASTBONOMY, METEOROLOGY, AND SEISMOLOGY. 37 seen in the occurrence of places which are particularly subject to frost damage or are particularly frost free. The relations of "air drainage" are probably responsible for the well-known spottedness of frost occurrence. Slight dif- ferences of elevation make possible the movement of air under the influence of gravity during the calm of the typical frost night. The .whole problem is one of a very nice adjustment of conditions and can not be dealt with in a general way, although in determining the liability to frost of particular portions of small regions the influence of "air drainage" becomes of enormous im- portance. No careful attempt has yet been made, largely because of lack of available data, to determine just what is the relation between altitude and topography. It has been suggested that a canyon approximately 500 feet deep in central Washington will be colder at the bottom than at the canyon rim. If the depth is greater than 500 feet the altitude effect usually makes the canyon rim more frosty than the bottom of the canyon. In general it may be sufficient to say that very considerable portions of the western United States are subject to early and late frosts because of their altitude above sea level, and that the exact occurrence of frost locally in a broken region is dependent upon the topography, the most frost-free places being the valley sides, especially the slopes of alluvial fans extending into the valleys. There are also areas which are subject to cold air drainage, particularly areas opposite canyon mouths from which a stream of cold air flows, making these subject to frosts when other portions of the valley do not reach such low temperatures. The whole question of topography and frost is one which needs a great deal more study, and work similar to that now being carried on by Cox in North Carolina should be extended to all parts of the country. An example of the commercial value of these studies is to be found in the work done in southern California near Pomona and in the Corona district. 1 THE RELATION BETWEEN DATES OF LAST KILLING FBO8T IN SPEING AND FIRST KILLING FROST IN FALL. In the study of frost dates it appears that the last spring frost and the first full frost could not be regarded as entirely independent of each other. From a theoretical consideration it seems wholly possible, if not probable, that the low temperature conditions resulting in late spring frost might extend through the summer and give earlier fall frosts, or that the higher temperatures re- sulting in an early date of last spring frost might also affect the first fall frost. In the attempt to determine the probable length of the season without killing frost in 9 years in 10 that is, to determine the business risk in the same manner as for the last spring and the first fall frost a slight but constant relation was found. Coefficients of correlation 2 between spring and fall frost were determined for several stations. In nearly all the cases con- sidered there is a coefficient of correlation of between 0.10 and 0.30 with a probable error of something less than half this amount. Correlation is not regarded as well established unless the coefficient of correlation is equal to six times the probable error of the coefficient, but there is here a condition 1 See Carpenter, F. A. : Utilization of frost warnings in the citrus region near Los Angeles, Cal., [U. S.] Monthly Weather Review, 42 : 569-571, Washington, 1914. Garth- waite, J. W. : Letter on frost and frost prevention, [U. S.] Monthly Weather Review, 42 : 571-572, Washington, 1914. Carpenter, F. A., and Garthwaite, J. W. : Memorandum on air drainage in the vicinity of the Corona district, California, [U. S.] Monthly Weather Review, 42 : 572-573, Washington, 1914. * See Yule, G. Udny : An introduction to the theory of statistics ; London, C. Griffin & Co., 1912, pp. 157-253. Davenport, C. B. : Statistical methods; New York, Wiley, ed. 3, 1914, pp. 42-61. [Great Britain] Meteorological Office: The computer's handbook, section 5, London, 1915. 38 PROCEEDINGS SECOND PAN AMERICAN SCIENTIFIC CONGRESS. in which the slight correlation always leans in the same direction. In the very small number of cases in which there is positively correlation, the coeffi- cient of correlation is less than 0.10, and its probable error has practically the same value. This means that zero is as likely as the value of the coefficient as the value determined. Without going into the matter in detail, the indica- tions are that if the last killing frost in spring is late, there is a tendency for the first killing frost in fall to be early, and if the last killing frost in spring is early, there is a tendency for the first killing frost in fall to be late. How- ever, the records are not complete enough, nor is the correlation well enough marked for individual stations to make this more than a probability. This condition, however, opens an interesting field for study which should be pur- sued further. 1 PROTECTION AGAINST DAMAGE BY FROST. Fruits and vegetables are now successfully protected in many parts of the United States, and equipment for frost fighting is regarded as necessary in all the important fruit regions. Protection against frost damage has been accomplished mainly by the use of small fires, which keep the tempera tur* above the dangerous point by supplying heat to the low area to make up for the loss to space by radiation. Usually there is a good deal of smoke together with the heat, so that radiation of heat from the earth is somewhat checked. Various other methods have been used to prevent occurrence of freezing temperatures under the local radiation conditions which result in hoar and black frosts. During the general freeze condition attempts to protect against frost damage have not been so successful. 8 CONCLUSION. The maps presented represent in the first place the average conditions of frost and season without killing frost which exist in the United States. They have been drawn on a basis of all available data, included first and fore- most, the frost dates recorded by the observers of the United States Weather Bureau, and, secondly, topographic and botanic data obtained from various sources. The maps showing probable occurrence of last killing frost in spring and first killing frost in fall in one year in ten are new, and show more clearly than the others the business risk involved in planting and harvesting at particular times. The map of probable length of the season without killing frost in four years out of five shows what time is available for the growth of crops in the different parts of the United States with a loss of only one- fifth of all crops from frost, which may be assumed as a fair business risk. This map and the data upon which it is based show better than any maps previously prepared the existence of killing frost as a limiting factor for crops. It does not, however, show the heat supply upon which the crop depends for its growth. The frost problem for most crops in the United States, from an agricultural point of view, is that of determining the proba- bility of frost and the risk involved in planting at different times. The cost of protection against frost damage is so great that it does not apply to the staple crops of the country. The problem for the farmer is to determine the frost conditions he will have to meet and to arrange his crops and his agri- cultural practice with reference to these frost conditions. 1 See Reed, W. G. : The probable growing season, [U. S.] Monthly Weather Review, 44 : 509-512, Washington, 1916. 8 Protection against damage by frost is discusseg in the [U. S.] Monthly Weather Review, 42:562-592 (October, 1914), and in Better Fruit (Hood River, Oreg.), 5 : no. 4 (October, 1910). See also Reed, W. G. : Protection from damage by frost, Geographical Review, 1 : 110-122, New York, 1916. O 14 DAY USE RETURN TO DESK FROM WHICH BORROWEDj LOAN DEPT. % This book is due on the last date stamped below, or on the date to which renewed. Renewed books are subject to immediate recall. 5Hy'58Jp RECTO ID 281951 LD 21A-50m-8,'57 (C8481slO)476B General Library University of California Berkeley Binder Gaylord Bros. Makers Syracuse, N. Y. PAT. JAN 21, 1908 544147 UNIVERSITY OF CALIFORNIA LIBRAR