TS 
 
 637 
 T5 
 
 UC-NRLF 
 
 SB 31 
 
 The Theory of Drying and its Application to the Hew 
 Humid ity-Heg Plated and Reeirculating Dry Kilns 
 
aui 
 
 UNITED STATES DEPARTMENT OF AGRICULTURE 
 
 BULLETIN No. 509 
 
 Contribution from the Forest Service 
 HENRY S. GRAVES, Forester 
 
 Washington, D. C. 
 
 PROFESSIONAL PAPER 
 
 March 17, 1917 
 
 THE THEORY OF DRYING AND ITS APPLICATION 
 TO THE NEW HUMIDITY-REGULATED AND RE- 
 CIRCULATING DRY KILN. 
 
 By HABRY D. TIEMANN, In Charge, Section of Timber Physics, Forest Products 
 ' ' Laboratory. 
 
 CONTENTS. 
 
 Introduction 
 
 Elementary principles of drying 
 
 Elementary principles of hygrometry. 
 
 Types of kilns 
 
 Drying by superheated steam 
 
 Page. 
 1 
 2 
 5 
 7 
 8 
 
 Page. 
 
 Importance of proper piling of lumber 9 
 
 Theory and description of the Forest Service 
 kirn 10 
 
 Theoretical discussion of evaporation 13 
 
 Theoretical analysis of heat quantities 18 
 
 INTRODUCTION. 
 
 The problem of satisfactorily drying lumber without checking, 
 honeycombing, or warping is one of very wide interest. Although 
 an old problem, it has not yet reached an entirely satisfactory solu- 
 tion, especially with hardwood lumber. Even air drying, which is 
 the slowest and what might be called the most conservative method 
 of removing the moisture, is far from satisfactory for some species of 
 wood. The drying of softwoods, or wood from coniferous trees, 
 on the other hand, may be considered as having reached a fairly sat- 
 isfactory solution. With few exceptions, the softwoods present no 
 special difficulty to the lumber drier. The great trouble with the 
 hardwoods lies in their relatively excessive and very unequal shrink- 
 age. This is due largely to the structure of the wood. In soft- 
 woods the vertical elements are all of the same kind, regularly ar- 
 ranged and of approximately the same width (tangentially). The 
 medullary rays also are very fine and regular. In hardwoods, on the 
 other hand, the elements are very complex, varying in diameter in 
 some species in the same section 20 to 30 times, and are often very 
 crooked. Many woods, such as the oak, have large medullary rays, as 
 
 70253 Bull. 50917 1 
 
 437650 
 
3-7 
 
 2 :BtrLLETOjF:5p9; ii.-s. DEPARTMENT OF AGRICULTURE. 
 
 ^iS yej-r mffftones v irfegularly arranged. Consequently, strains 
 are ; pro<ftrcecf when : thfc' wbbcl dries, which cause warping and check- 
 ing. While air drying is undoubtedly the safest method, the process 
 is ordinarily so slow, requiring a year or longer according to species 
 and size, that forced "artificial" drying becomes a business neces- 
 sity. Moreover, air drying is by no means always to be preferred to 
 kiln drying from the standpoint of the quality of the product. 
 
 A correct understanding of the principles of drying is rare, and 
 opinions in regard to the subject are very diverse. The same lack of 
 knowledge exists in regard to dry kilns. The physical properties 
 of the wood which complicate the drying operation and render it 
 distinct from that of merely evaporating free water from some sub- 
 stance like a piece of cloth must be studied experimentally. It can 
 not well be worked out theoretically. 
 
 The thermal process of the drying operation, however, is capable 
 of exact theoretical analysis. It is the purpose of this article to 
 interpret the conditions which exist in the various stages of the dry- 
 ing operation with respect to the heat quantities and the changes 
 which occur in the drying medium, from a theoretical standpoint. 
 The object of this analysis is to show the limiting conditions which 
 may be approached, but can not be exceeded. 
 
 ELEMENTARY PRINCIPLES OF DRYING. 
 
 Before taking up the theoretical discussion, a few remarks upon the 
 elementary principles of drying will be of assistance. 
 
 EVAPORATION REQUIRES HEAT. 
 
 In the 'first place, it should be borne in mind that it is the heat 
 which produces evaporation and not the air nor any mysterious 
 property assigned to a " vacuum." For every pound of water evapo- 
 rated at ordinary temperatures approximately 1,000 British thermal 
 units of heat are used up, or " become latent," as it is called. This 
 is true whether the evaporation takes place in a vacuum or under a 
 moderate air pressure. If this heat is not supplied from an outside 
 source it must be supplied by the water itself (or the body being 
 dried), the temperature of which will consequently fall until the sur- 
 rounding space becomes saturated with vapor at a pressure cor- 
 responding to the temperature which the water has reached ; evapora- 
 tion will then cease. The pressure of the vapor in a space saturated 
 with water vapor increases rapidly with increase of temperature. 
 At a so-called vacuum of 28 inches, which is about the limit in com- 
 mercial operations, and in reality signifies an actual pressure of 2 
 inches of mercury column, the space will be saturated with vapor 
 at about 101 F. Consequently, no evaporation will take place in 
 such a vacuum unless the water be warmer than 101 F., provided 
 
HUMIDITY-REGULATED AND RECIRCULATING DRY KILN. 3 
 
 there is no air leakage. The qualification in regard to air is neces- 
 sary, for the sake of exactness, for the following reason : In any given 
 space the total actual pressure is made up of the combined pressures 
 of all the gases present. If the total pressure ("vacuum") is 2 
 inches, and there is no air present, it is all produced by the water 
 vapor (which saturates the space at 101 F.) ; but if some air is pres- 
 ent and the total pressure is still maintained at 2 inches, then there 
 must be less vapor present, since the air is producing part of the 
 pressure and the space is no longer saturated at the given tempera- 
 ture. Consequently further evaporation may occur, with a cor- 
 responding lowering of the temperature of the water, until a balance 
 is again reached. Without further explanation it is easy to see that 
 but little water can be evaporated by a vacuum alone without addi- 
 tion of heat and that the prevalent idea that a vacuum can of itself 
 produce evaporation is a fallacy. If heat be supplied to the water, 
 however, either by conduction or radiation, evaporation will take 
 place in direct proportion to the amount of heat supplied, so long as 
 the pressure is kept down by the pump. 
 
 At 30 inches of mercury pressure (one atmosphere) the space be- 
 comes saturated with vapor and equilibrium is established at 212 F. 
 If heat be now supplied to the water, however, evaporation will take 
 place in proportion to the amount of heat supplied, so long as the 
 pressure remains that of one atmosphere, just as in the case of the 
 vacuum. Evaporation in this condition, where the vapor pressure 
 at the temperature of the water is equal to the gas pressure on the 
 water, is what is commonly called " boiling," and the saturated vapor 
 entirely displaces the air under continuous operation. Whenever 
 the space is not saturated with vapor, whether air is present or not, 
 evaporation will take place, by boiling if no air be present or by 
 diffusion under the presence of air, until an equlibrium between 
 temperature and vapor pressure is resumed. 
 
 Relative humidity is simply the ratio of the actual vapor pres- 
 sure present in a given space to the vapor pressure when the space 
 is saturated with vapor at the given temperature. It matters not 
 whether air be present or not. One hundred per cent humidity 
 means that the space contains all the vapor which it can hold at the 
 given temperature it is saturated. Thus at 100 per cent humidity 
 and 212 F. the space is saturated, and since the pressure of satu- 
 rated vapor at this temperature is one atmosphere, no air can be 
 present under these conditions. If, however, the total pressure at 
 this temperature were 20 pounds (5 pounds gauge), then it would 
 mean that there was 5 pounds air pressure present in addition to the 
 vapor, yet the space would still be saturated at the given tempera- 
 ture. Again, if the temperature were 101 F., the pressure of satu- 
 rated vapor would be only 1 pound, and the additional pressure of 
 
4 BULLETIN 509, U. S. DEPARTMENT OF AGRICULTURE. 
 
 14 pounds, if the total pressure were atmospheric, would be made up 
 of air. In order to have no air present and the space still satu- 
 rated at 101 F., the total pressure must be reduced to 1 pound by a 
 vacuum pump. 'Fifty per cent relative humidity, therefore, signifies 
 that only half the amount of vapor required to saturate the space at 
 the given temperature is present. Thus at 212 F. temperature the 
 vapor pressure would only be 7J pounds (vacuum of 15 inches gauge). 
 If the total pressure were atmospheric, then the additional TJ pounds 
 is simply air. " Live steam " is simply saturated water vapor at a 
 pressure usually above atmospheric. We may just as truly have live 
 steam at pressures less than atmospheric, at a vacuum of 28 inches for 
 instance. Only in the latter case its temperature would be lower, 
 viz, 101 F. Superheated steam is nothing more than water vapor 
 at a relative humidity less than saturation, but is usually considered 
 at pressures above atmospheric, and in the absence of air. The 
 atmosphere at, say, 50 per cent relative humidity really contains 
 superheated steam or vapor, the only difference being that it is at 
 a lower pressure and temperature than we are accustomed to think 
 of in speaking of superheated steam, and it has air mixed with it to 
 make up the deficiency in pressure below the atmosphere. 
 
 Two things should now be clear : That evaporation is produced by 
 heat and that the presence or absence of air does not influence the 
 amount of evaporation. It does, however, influence the rate of 
 evaporation, which is retarded by the presence of air. The main 
 things influencing evaporation are, first, the quantity of heat sup- 
 plied and, second, the relative humidity of the immediately sur- 
 rounding space. 
 
 IMPORTANCE OF CIRCULATION. 
 
 A piece of wood may be heated in three ways (1) by convection 
 of the air and vapor or other gases, (2) by conduction through some 
 body in contact therewith, and (3) by radiation. Of these three 
 ways, only the first is ordinarily available for use in heating a pile 
 of lumber, since by either of the other two methods only the outside 
 surface of the pile could be heated; hence the necessity of a large 
 and thorough circulation of air. Drying in a vacuum would be 
 feasible if there were some means of conveying the heat to the wood. 
 A single stick can be readily dried in a vacuum, as it can receive 
 heat on all sides by radiation from the walls of a steam- jacketed 
 cylinder; but this is impracticable when it comes to any quantity of 
 lumber, except in the case of superheated vapor alone, as will be 
 shown later, since only the outer surface or the outside boards would 
 receive the heat in this way and the inside ones would not dry. 
 Even an approach to a perfect vacuum, however, is not reached in 
 commercial apparatus. Moreover, the heat convection in a vacuum 
 
HUMIDITY-REGULATED AND RECIBCULATING DRY KILN. 5 
 
 of 26 inches or less is almost as rapid as under ordinary air pressure. 1 
 The viscosity of the gas is a factor in the convection through small 
 spaces, such as between the layers of lumber, and as this is almost 
 i as great at low pressures as at atmospheric pressure, it follows that 
 the actual circulation would nevertheless be very much cut down. 
 Thus, by drawing a vacuum the means of heating the wood is re- 
 duced. Later on it will be shown, however, that drying at low 
 pressure in absence of air should give the highest theoretical heat 
 efficiency, but the volume of vapor required is excessive. 
 
 RATE OF EVAPORATION CONTROLLED BY HUMIDITY. 
 
 It is essential, therefore, to have an ample supply of heat through 
 the convection currents of the air; but in the case of wood the rate 
 of evaporation must be controlled, else checking will occur. This can 
 be done by means of the relative humidity. It is clear now that 
 when the air or, more properly speaking, the space is completely 
 saturated no evaporation can take place at the given temperature. 
 By- reducing the humidity, evaporation takes place more and more 
 rapidly. 
 
 Another bad feature of an insufficient and nonuniform supply of 
 heat is that each piece of wood will be heated to the evaporating 
 point on the outer surface, the inside remaining cool until consider- 
 able drying has taken place from the surface. Ordinarily in dry 
 kilns high humidity and large circulation of air are antitheses to 
 one another. To obtain the high humidity the circulation is either 
 stopped altogether or greatly reduced, and to reduce the humidity a 
 greater circulation is induced by opening the ventilators or otherwise 
 increasing the draft. This is evidently not good practice, but as 
 a rule is unavoidable in most kilns. The humidity should be raised 
 to check evaporation without reducing the circulation. 
 
 ELEMENTARY PRINCIPLES OF HYGROMETRY. 
 
 RELATIVE HUMIDITY AND DEW POINT. 
 
 It is necessary to know something of hygrometry in order to under- 
 stand the drying operations. As stated before, at any given tempera- 
 ture the same quantity of water vapor is required to saturate a given 
 
 1 Bottomly gives for radiation of a bright platinum wire to a copper envelope, at differ- 
 ent air pressures, the temperature of the inclosure being 16 C. and the difference in 
 temperature 408 C. expressed in the heat lost in c. g. s. units per square centimeter of 
 inclosure (Smithsonian Table 250) : 
 
 At 740 mm. absolute pressure 0. 8137 
 
 At 42 mm. absolute pressure . 7591 
 
 At 0.44 mm. absolute pressure . 2683 
 
 At 0.01 mm. absolute pressure .0539 
 
 These figures evidently include radiation and convection. They show comparatively 
 small change at pressures above 42 millimeters of mercury, which corresponds to a 
 vacuum of about 28.4 inches. 
 
6 BULLETIN 509, U. S. DEPARTMENT OF AGRICULTURE. 
 
 space, whether any air is present or not; and the pressure of the 
 vapor is the same in both cases. The total pressure (as registered by 
 the gauge) will not be the same, however, since if air is present its 
 pressure is added to that of the vapor. It is really the space and 
 not the air which is saturated. For instance, at 101 F. it takes about 
 20 grains of vapor to saturate a cubic foot of space. If no air be 
 present, there will be a pressure of vapor only, which will be about 
 1 pound, or a vacuum of 28 inches. If this is open to the atmosphere 
 the air will rush into the space until the total pressure will be one 
 atmosphere, or about 15 pounds. There will then be 1 pound of pres- 
 sure produced by the vapor, as before, and 14 pounds of air pressure. 
 The space will still be saturated, if the temperature is kept at 101 F. 
 If this is now heated to 160 F. and open to the atmosphere so that 
 the total pressure is kept constant, the ratio of the pressures of vapor 
 and air will also remain the same ; there will still be 1 pound due to 
 vapor and 14 pounds due to the air. (The weights in the cubic foot 
 of space of both will decrease, due to expansion by heat.) At 160 F t , 
 however, it requires 91 grains of vapor to saturate a cubic foot of 
 space, and its pressure is nearly 5 pounds (absolute). Consequently, 
 the relative humidity at 160 F. of this space will be one-fifth, or 20 
 per cent. Conversely, if this air and vapor at 20 per cent relative 
 humidity and 160 F., temperature is cooled to 101 F., all at the same 
 atmospheric pressure, the space will again become saturated, and any 
 further cooling will cause precipitation or condensation. This is 
 called the dew point; that is, 101 F. is the dew point of air with 20 
 per cent humidity at 160 F. In Forest Service Bulletin 104, " Prin- 
 ciples of Drying Lumber at Atmospheric Pressure and Humidity 
 Diagram," a humidity diagram is given for solving all problems of 
 this nature. The concave curves on this diagram are simply curves 
 of constant vapor pressure with change of temperature and relative 
 humidity, and the grains of vapor per cubic foot, at saturation or -the 
 dew point, are given in numerical figures. From this it is seen that 
 the dew point determines the relative humidity when the temperature 
 is raised, or vice versa. If we take saturated air at known tempera- 
 ture and heat it up any given desired amount, the resulting relative 
 humidity is thereby determined. This is the principle upon which 
 the humidity regulation depends in a new kiln designed by the 
 writer. 1 It is also evident that whenever air is cooled below its dew 
 point condensation takes place. This is the principle of the con- 
 denser. There are a number of kilns which have made use of this 
 principle to dry the air. Pipes are used for the condensers and cold 
 water is circulated through the pipes. The same thing can be accom- 
 plished by a spray of cold water in place of the pipes, provided all 
 the fine mist is subsequently removed from the air, or even by a sur- 
 
 1 For a description of this kiln see page 10. 
 
HUMIDITY-REGULATED AND RECIRCULATING DRY KILN. 7 
 
 face of cold water. In the new kiln a fine spray of water is used in- 
 stead of a condenser. This has the additional advantage that when 
 the water is heated above a certain temperature (the temperature of 
 the wet bulb in a wet-and-dry bulb hygrometer) it will humidify the 
 air. By simply changing the temperature of the spray the air may 
 be supplied at any desired humidity. 
 
 INSTRUMENTS FOR MEASURING HUMIDITY. 
 
 A common instrument used for measuring humidity is the wet- 
 and-dry bulb hygrometer or " psychrometer." This consists of two 
 thermometers mounted side by side, the bulb of one of which is 
 covered by a silk cloth or wick which dips into a vessel of water. 
 This should be placed in a fairly strong draft of air. The evapora- 
 tion from the " wet bulb " reduces its temperature below that of the 
 dry bulb, and the rate of this evaporation, and consequently the 
 temperature of the wet bulb, depends upon the relative humidity in 
 the air. By noting the two temperatures of the dry and the wet 
 bulb thermometers the relative humidity can be determined by tables 
 which have been carefully worked out by the Weather Bureau. 1 
 
 In the humidity diagram in Forest Service Bulletin 104 the values 
 are expressed in curves (the convex series of curves on the diagram) , 
 by means of which the relative humidity may be read off directly 
 without numerical calculations. This instrument is probably the 
 simplest reliable means for determining humidity. There are instru- 
 ments which read directly from a hand on a dial, the motion of the 
 hand being produced by the swelling of vegetable or animal tissues. 
 These are very convenient but fragile and not to be depended upon. 
 The most direct way of determining humidity is, of course, to de- 
 termine the dew point. This may be accomplished by gradually 
 cooling a bright surface, as polished metal, in contact with the mov- 
 ing air, until a mist is precipitated thereon. Special interest attaches 
 to the wet-and-dry bulb hygrometer for the reason that the wet wood 
 in the dry kiln is actually in the same condition as the wet bulb. It 
 is affected in the same way. The actual temperature of the wood, 
 while it is moist, is therefore that of the wet bulb, provided there is 
 sufficient circulation. 
 
 TYPES OF KILNS. 
 
 There are two distinct ways of handling lumber in kilns. One 
 way is to place the load of lumber in a chamber where it remains in 
 the same place throughout the operation, while the conditions of the 
 drying medium are varied as the drying progresses. This is the 
 compartment kiln or stationary method. The other is to run the 
 lumber in one end of the chamber on a wheeled truck and gradually 
 
 1 See Psychrometer Tables by Marvin, Bulletin 235 of United States Weather Bureau. 
 
8 BULLETIN 509, U. S. DEPARTMENT OF AGRICULTURE. 
 
 move it along until the drying process is completed, when it is taken 
 out at the opposite end of the kiln. An attempt is usually made in 
 these kilns to maintain one end moist and the other end dry. This is 
 known as the " progressive " type of kiln, and is the one most com- 
 monly used in large operations. It is the least satisfactory of the two, 
 however, where careful drying is required, since the conditions can 
 not be so well regulated and the temperatures and humidities are apt 
 to change with change of wind. The compartment method can be 
 arranged so that it will not require any more kiln space or any more 
 handling of lumber than the progressive type. It does, however, 
 require more intelligent operation, since the conditions in the kiln 
 must be changed as the drying progresses. With the progressive 
 type the conditions, once established, remain the same. 
 
 To obtain draft or circulation three methods are in use by forced 
 draft or a blower usually placed outside the kiln, by ventilation, and 
 by internal circulation and condensation. A great many patents have 
 been taken out on different methods of ventilation, but in actual 
 operation few work exactly as intended. Frequently the air moves 
 in the reverse direction for which the ventilators were planned. 
 Sometimes a condenser is used in connection with the blower and 
 the air is recirculated. It is also and more satisfactorily used 
 with the gentle internal-gravity currents of air. 
 
 Many patents have been taken out for heating systems. The differ- 
 ences among these, however, have more to do with the mechanical 
 construction than with the process of drying. In general, the heating 
 is either direct or indirect. In the former steam coils are placed in 
 the chamber with the lumber, and in the latter the air is heated by 
 either steam coils or a furnace before it is introduced into the kiln. 
 
 Moisture is sometimes supplied by means of free steam jets in the 
 kiln or in the entering air; but more often the moisture evaporated 
 from the lumber is relied upon to maintain the humidity necessary. 
 In the new humidity-regulated kiln the humidity is controlled di- 
 rectly. The majority of kilns make no attempt whatever to regulate 
 this all-important factor beyond retaining an indeterminate amount 
 at the beginning of the operation and drying the air, either by con- 
 densers or by ventilation at the end. 
 
 Other methods of drying in vacuum and in various gases have been 
 tried from time to time. 
 
 DRYING BY SUPERHEATED STEAM. 
 
 There is still another type of kiln which is not included in the 
 former classification, viz, that using superheated steam. What this 
 term really signifies is simply water vapor in the absence of air in a 
 condition of less than saturation. Such kilns are, properly speak- 
 ing, vapor kilns, and usually operate at atmospheric pressure, but 
 
HUMIDITY-REGULATED AND RECIRCULATING DRY KILN. 9 
 
 may be used at greater pressures or at less pressures. As stated 
 before, the vapor present in the air at any humidity less than satura- 
 tion is really " superheated steam," only at a lower pressure than is 
 ordinarily understood by this term, and mixed with air. The main 
 argument in favor of this process seems to be based on the idea that 
 steam is moist heat. This is true, however, only when the steam is 
 near saturation. When it is superheated it is just as dry as air con- 
 taining the same relative humidity. For instance, steam at atmos- 
 pheric pressure and heated to 248 F. has a relative humidity of 
 only 50 per cent and is just as dry as air containing the same hu- 
 midity. If heated to 306 F., its relative humidity is reduced to 20 
 per cent; that is to say, the ratio of its actual vapor pressure (one 
 atmosphere) to the pressure of saturated vapor at this temperature 
 (five atmospheres) is 1 : 5, or 20 per cent. Superheated vapor in the 
 absence of air, however, parts with its heat with great rapidity and 
 finally becomes saturated when it has lost all of its ability to cause 
 evaporation. In this respect it is more moist than air when it comes 
 in contact with bodies which are at a lower temperature. When sat- 
 urated steam is used to heat the lumber it can raise the temperature 
 of the latter to its own temperature, but can not produce evapora- 
 tion unless, indeed, the pressure is varied. Only by the heat supplied 
 aboA~e the temperature of saturation can evaporation be produced. 
 This subject will be taken up again in the theoretical analysis. 
 
 IMPORTANCE OF PROPER PILING OF LUMBER. 
 
 The efficiency of the drying operation depends a great deal upon 
 the way in which the lumber is piled, especially when the humidity 
 is not regulated. From the theory of drying just discussed it is 
 evident that the rate of evaporation in kilns where the humidity is 
 not regulated depends entirely upon the rate of circulation, other 
 things being equal. Consequently, those portions of the wood which 
 receive the greatest amount of air dry the most rapidly, and vice 
 versa. The only way, therefore, in which anything like uniform 
 drying can take place is where lumber is so piled that each portion 
 of it comes in contact with the same amount of air. 
 
 In the Forest Service kiln, where the degree of relative humidity 
 is used to control the rate of drying, the amount of circulation 
 makes little difference, provided it exceeds a certain amount. It is 
 desirable to pile the lumber so as to offer as little frictional resist- 
 ance as possible and at the same time secure uniform circulation. If 
 circulation is excessive in any place it simply means waste of energy 
 but no injury to the lumber. 
 
 The best method of piling is one which permits the heated air to 
 pass through the pile in a somewhat downward direction. The natu- 
 ral tendency of the cooled air to descend is thus taken advantage of 
 in assisting the circulation in the kiln. This is especially important 
 70253 Bull. 50917 2 
 
10 BULLETIN 509, U. S. DEPARTMENT OF AGRICULTURE. 
 
 when cold or green lumber is first introduced into the kiln. But 
 even when the lumber has become warmed the cooling due to the 
 evaporation increases the density of the mixture of the air and vapor. 
 Table 3 shows analytically that the spontaneous cooling of the mix- 
 ture produced by the evaporation alone increases its density. This 
 fact is of great significance, and the method of piling lumber in the 
 Forest Service kiln takes advantage of this principle. 
 
 THEORY AND DESCRIPTION OF THE FOREST SERVICE KILN. 
 
 The humidities and temperatures in the piles of lumber are largely 
 dependent upon the circulation of air within the kiln. The tempera- 
 ture and humidity within the kiln, taken alone, are no criterion of 
 the conditions of drying within the pile of lumber if the circulation 
 in any portion is deficient. It is possible to have an extremely rapid 
 circulation of the air within the dry kiln itself and yet have stag- 
 nation within the pile, the air passing chiefly through open spaces 
 and channels. Wherever stagnation exists or the movement of air 
 is too sluggish the temperature will drop and humidity increase, 
 perhaps to the point of saturation. 
 
 When in large kilns the forced circulation is in the opposite di- 
 rection from that induced by the cooling of the air by the lumber 
 there is always more or less uncertainty as to the movement of the 
 air through the piles. Even with the boards placed edgewise, with 
 stickers running vertically, and with the heating pipes beneath the 
 lumber, it was found that although the air passed upward through 
 most of the spaces it was actually descending through others, so that 
 very unequal drying resulted. While edge piling would at first 
 thought seem ideal for the freest circulation in an ordinary kiln with 
 steam pipes below, it in fact produces an indeterminate condition; 
 air columns may pass downward through some channels as well as 
 upward through others, and probably stagnate in others. Neverthe- 
 less, edge piling is greatly superior to flat piling where the heating 
 system is below the lumber. 
 
 From experiments and from a study of conditions in commercial 
 kilns the idea was developed of so arranging the parts of the kiln 
 and the pile of lumber that advantage might be taken of this cooling 
 of the air to assist the circulation. That this can be readily accom- 
 plished without doing away with the present features of regulation 
 of humidity by means of a spray of water is clear from figure 1, 
 which shows a cross section of the improved humidity-regulated 
 dry kiln. 
 
 In the form shown in the sketch a chamber or flue B runs through 
 the center near the bottom. This flue is only about 6 or 7 feet in 
 height and, together with the water spray F and the baffle plates D D, 
 constitutes the humidity-control feature of the kiln. This control 
 of humidity is effected by the temperature of the water used in the 
 
HUMIDITY-REGULATED AXD RECIRCULATING DRY KILN. 
 
 11 
 
 spray. This spray completely saturates the air in the flue B at what- 
 ever predetermined temperature is required. The baffle plates D D 
 are to separate all entrained particles of water from the air, so that 
 it is delivered to the heaters in a saturated condition at the required 
 temperature. This temperature is, therefore, the dew point of the 
 air when heated above, and the method of humidity control may 
 therefore be called the dew-point method. It is a very simple matter 
 by means of the humidity diagram, 1 or by a hydrodeik, to determine 
 what dew-point temperature is needed for any desired humidity 
 above the heaters. 
 
 
 FIG. 1. Diagrammatic section of improved dry 'kiln with spray chambers in center. 
 
 Double-truck form. 
 
 Besides regulating the humidity the spray F also acts as an ejector 
 and forces a circulation of air through the flue B. The heating sys- 
 tem H is concentrated near the outer walls, so as to heat the rising 
 column of air. The temperature within the drying chamber is con- 
 trolled by means of any suitable thermostat, actuating a valve on the 
 main steam line. The lumber is piled in such a way that the 
 stickers slope downward toward the center. 
 
 M is an auxiliary steam spray pointing downward for use at very 
 high temperatures. C is a gutter to catch the precipitation and 
 
 1 Forest Service Bulletin 104, " Principles of Drying Lumber at Atmospheric Pressure 
 and Humidity Diagram," Superintendent of Documents, Government Printing Office, 
 Washington, D. C. Price, 5 cents. Lumber World Review, Feb. 10. 1915. 
 
12 
 
 BULLETIN 509, U. S. DEPARTMENT OF AGRICULTURE. 
 
 conduct it back to the pump, the water being recirculated through 
 the sprays. G is a pipe condenser for use toward the end of the 
 drying operation. K is a baffle plate for diverting the heated air and 
 at the same time shielding the under layer of boards from direct 
 radiation of the steam pipes. 
 
 The operation of the kiln is simple. The heated air rises above the 
 pipes H H at the sides of the piles of lumber. As it comes in con- 
 tact with the piles portions of it are cooled and pass downward and 
 inward through the layers of boards into the space between the con- 
 
 FIG. 2. Diagrammatic section of improved dry kiln with spray chambers on sides. Double- 
 truck form. 
 
 densers G G. Here the column of cooled air descends into the spray 
 flue B, where its velocity is increased by the force of the water spray. 
 It then passes out from the baffle plates to the heaters and repeats the 
 cycle. 
 
 Various modifications of this arrangement may be made. For 
 instance, a single-track kiln may be used. This form would be repre- 
 sented by simply dividing the diagram vertically into two parts by 
 extending the wall G (on the left side) upward to represent the outer 
 wall, and erasing the part to the left of this line. Or, again, the 
 spray chambers may be kept on the sides as shown in figure 2. The 
 lumber would then slope in the opposite direction with respect to 
 
HUMIDITY-REGULATED AXD RECIRCULATING DRY KILN. 13 
 
 the center of the kiln and the air would rise in the center and 
 descend on the sides. 
 
 One of the greatest advantages of this natural circulation method 
 is that the colder the lumber when placed in the kiln the greater is 
 the movement produced, under the very conditions which call for 
 the greatest circulation just the opposite of the direct-circulation 
 method. This is a feature of the greatest importance in winter, when 
 the lumber is put into the kiln in a frozen condition. One truck 
 load of lumber at 60 per cent moisture may easily contain over 
 7,000 pounds of ice. 
 
 In the matter of circulation the kiln is, in fact, self -regulatory 
 the colder the lumber the greater the circulation produced, with the 
 effect increased toward the cooler and wetter portions of the pile. 
 
 Preliminary steaming may be used in connection with this kiln, 
 but experiments indicate that ordinarily it is not desirable, since 
 the high humidity which can be secured gives as good results, and, 
 being at as low a temperature as desired, much better results in the 
 case of certain difficult woods like oak, eucalyptus, etc. 
 
 This kiln has another advantage in that its operation is entirely 
 independent of outdoor atmospheric conditions, except that baro- 
 metric pressures will affect it slightly. 
 
 THEORETICAL DISCUSSION OF EVAPORATION. 
 
 In considering the drying effect of vapor alone (superheated 
 steam) and of air mixed with the vapor, one very significant fact 
 must be noticed. Saturate vapor alone in cooling and in order to 
 remain saturate must absorb heat. Its specific heat is negative, so 
 that the only way it can heat a body is by condensation. It is, 
 therefore, incapable of producing evaporation. When air is present 
 with the saturate vapor, however, the air can supply some of this 
 heat, according to the pressure of the air present, so there will be less 
 condensation. 
 
 Still more important is the fact that when air is present with the 
 vapor sufficient heat can be supplied to the body being dried by means 
 of the air without greatly superheating the vapor, thus keeping a 
 high relative humidity and at the same time supplying a sufficient 
 amount of heat to carry on the evaporation. With vapor alone 
 (superheated steam) a relatively high degree of superheating, which 
 means a correspondingly low relative humidity, is required in prac- 
 tice in order to supply the necessary heat for evaporation, after the 
 material has become heated through to the temperature of the sat- 
 urated vapor at the pressure used. Remember that the temperature 
 of the wet wood corresponds to that of the wet bulb in the hygrom- 
 eter when air is present, but very nearly to the dew point in the 
 presence of superheated vapor alone. 
 
14 BULLETIN 50$, U. S. DEPARTMENT OF AGRICULTURE. 
 
 EVAPORATION IN THE ABSENCE OF AIR. 
 
 In vapor alone, no air being present, evaporation from a surface 
 of water takes place at the dew point, but when the water is inti- 
 mately contained in other substances the temperature must be higher 
 than the dew point. If air is present it retards the rate of evapora- 
 tion from a free surface of water, so that the surface is warmer than 
 the dew point, depending upon the degree of relative humidity in 
 the air. While the surface of wood is wet its temperature will not 
 rise above that of the wet bulb in the presence of air, nor above the 
 dew point in superheated vapor alone. As it becomes drier, how- 
 ever, its temperature will rise, due to its affinity for retaining mois- 
 ture. In the former condition there is no danger of too rapid drying, 
 but in the latter condition, if the humidity is too low or the superheat 
 too high, the drying from the surface may become more rapid than 
 the rate at which the moisture is transmitted from the center, and 
 casehardening results. 
 
 In considering the manner in which drying takes place in super- 
 heated steam, suppose the pressure is atmospheric and that a wet 
 piece of wood has been heated in saturated steam to 212 F. No 
 evaporation will take place until additional heat is added. Now, 
 suppose steam superheated to 232 F. or 20 of superheat is in- 
 troduced. The portion immediately in contact with the surface of 
 the wet wood will be cooled to 212 F., and in so doing it will 
 vaporize a certain portion of water from the surface. As the specific 
 heat of this steam is, in round terms, one-half, and as it requires 
 about 1,000 thermal units to vaporize one unit of water, to vaporize 
 a single molecule of water at 212 F. will require contact of 100 of 
 the molecules of superheated steam at 232 F. We will then have 101 
 molecules of steam in the saturated condition at 212 F. Evapora- 
 tion must then cease unless this saturated steam is replaced by some 
 fresh superheated steam. Evaporation from a free surface of water 
 in the absence of air (in superheated steam) always takes place at 
 the boiling point (which in this case is the same as the dew point). 
 If, however, there is a deficiency of water in the wood more heat will 
 be required to separate it and to vaporize it, and evaporation will 
 take place at a higher temperature than the dew point. In fact, 
 evaporation may cease altogether in the superheated steam, and a 
 higher degree of superheating be required (which is equivalent to a 
 lower humidity) to get the moisture out of the wood. In the case 
 of a surface of free water the rate of evaporation depends entirely 
 upon the amount of heat transmitted to the water, whether by in- 
 creasing the circulation or by increasing the degrees of superheat. 
 In the latter case, when the moisture is intimately contained in the 
 
HUMIDITY-REGULATED AND RECIRCULATING DRY KILN. 15 
 
 wood, the rate depends largely upon the relative humidity. 1 There 
 is a balance between what might be termed the retentive or attractive 
 property of the wood, " hygroscopicity," and the tendency of the 
 moisture to vaporize. It is the difference between the tension of the 
 vapor at the higher temperature of the wood and the tension actually 
 existing in the space surrounding the wood. This retentive prop- 
 erty increases as the wood becomes drier and decreases as it ap- 
 proaches the wet condition. Experiments indicate that generally 
 it is nearly inversely proportional to the amount of moisture remain- 
 ing in the wood. 
 
 EVAPORATION WHEN AIR IS PRESENT. 
 
 When air is present with the superheated steam or water vapor 
 the conditions are quite different. Vaporization of a particle from 
 the surface of the free water is retarded by the air pressure, so that 
 the temperature of the water may be raised above the dew point. 2 
 
 The air now, as well as the vapor, conducts heat to the water, so that 
 the rate of evaporation at given pressures depends not alone on the 
 quantity of heat supplied (by circulation and degree of superheat- 
 ing) but upon the relative amounts of vapor and air present. That 
 is to say, the lower the relative humidity the greater is the rate of 
 evaporation at a given temperature and pressure. The temperature 
 of the water will correspond to that of the wet bulb, and not to that 
 of the dew point. When the wood becomes partially dried its tem- 
 perature will rise, as in the case of superheated steam, and it may 
 be heated even above the boiling point at the given pressure without 
 giving up all of its moisture, provided there is some vapor in the air. 
 
 CONCLUSIONS AS TO DRYING IN VAPOR ALONE AND IN AIR AND VAPOR. 
 
 Thus it is seen that the rate of drying may be controlled by the 
 relative humidity, provided there be sufficient circulation to supply 
 the heat required. In the case of steam alone, the rate of drying, as 
 just shown, depends upon the quantity of circulation as well as the 
 degree of superheating. Hence the conclusion follows that moist 
 air, with ample circulation, should give more uniform drying 
 throughout than superheated steam, which varies with the rate of 
 circulation in each portion. 
 
 1 In using the term relative humidity as applied to superheated steam it is understood 
 to mean the ratio of the actual vapor pressure to that of the pressure of saturated vapor 
 al the given temperature, as explained before. 
 
 2 In reality what probably happens is that the layer of air in immediate contact with 
 the water becomes saturated and has a higher vapor pressure corresponding to the tem- 
 perature of the surface of the water, and the air retards the diffusion of this vapor. The 
 temperature of the water, however, can not exceed the boiling point for the given pres- 
 sure, at which point the conditions must become the same as those for superheated steam 
 alone, since then the air will become entirely displaced by the water vapor. 
 
16 BULLETIN 509, U. S. DEPARTMENT OF AGRICULTURE. 
 
 But the chief difficulty with superheated steam at or above atmos- 
 pheric pressure is the high temperature to which the material must 
 be subjected, the minimum with very wet wood being 212 F., and 
 increasing as the wood dries. Below atmospheric temperatures, costly 
 apparatus is required for operating at a vacuum, and the heating 
 medium is attenuated, requiring an excessive volume of vapor to be 
 circulated if the danger is to be avoided of the wood, as it becomes 
 dry on the surface, being heated too high. Instead of a vacuum the 
 same result can be obtained by combining air with the vapor, in 
 which case the air makes up the deficiency of pressure. For in- 
 stance, a vacuum of 28 inches, which is about the extreme in mechani- 
 cal operations, will give an absolute vapor pressure of about 1 pound 
 and a temperature of 101 F. for saturated conditions. Precisely 
 the same value for the vapor occurs if saturated air at 101 F. and 
 atmospheric pressure is used instead, in which case the additional 
 heating capacity of the air present is also available. There would 
 then be in a cubic foot of space vapor pressure of 1 pound (nearly) 
 per square inch and 13.7 pounds of dry air pressure. This amount 
 of vapor would weigh 0.0029 pound and the air 1/15.2 or 0.0658 
 pound (15.2 being the volume in cubic feet of 1 pound of dry air at 
 13.7 pounds pressure and 101 F. temperature). 
 
 HEATING CAPACITIES OF AIR AND VAPOR IN MIXTURE. 
 
 The heating capacity of the vapor in this cubic foot of space, 
 in falling 1 degree, from 102 F. to 101 F., is .0029 X-42 1 ^. 00122 
 B. t. u., as before, while that of the air present is .0658X-237=.0156 
 B. t. u., or more than ten times that of the vapor present. The total 
 heating capacity of 1 cubic foot of the mixture, in falling 1 degree, from 
 102 F. to 101 F., is then the sum of these two, viz, .01682 B. t. u. 
 The latent heat of evaporation at 101 F. being 1044, it will require 
 the heat given up by 1044/.01682=r62.206 cubic feet of the mixed 
 air and vapor falling 1 degree, from 102 F. to saturation at 101 
 F., to evaporate 1 pound. This is very much less than that required 
 for vapor alone, which, as will be shown farther on, is 829,433 cubic 
 feet. In fact, the quantity in volume is less than that of dry air 
 alone at 212 F. and one atmospheric pressure (69,000), as figured 
 farther on. If the vapor is superheated, say, to 112 F., its pres- 
 sure remaining the same as before, this is simply equivalent, so far 
 as the vapor is concerned, to air at atmospheric pressure with a rela- 
 tive humidity of less than saturation. In this case the relative 
 humidity would be the pressure of the actual vapor 0.972 pound 
 per square inch divided by the pressure which the vapor would 
 have if it were saturated at 112 F., viz, .972/1.34=73 per cent 
 humidity. 
 
 1 The specific heat of superheated vapor at this temperature is 0.421 as given by Thiesen. 
 
HUMIDITY-REGULATED AND RECIRCULATING DRY KILN. 17 
 
 It should now be evident that superheated vapor is the same thing 
 as moist air with the air removed. The same effects upon the mate- 
 rial to be dried are produced in both cases, as far as the vapor is 
 concerned ; but in the case of moist air, the effect of the air is added 
 to that of the vapor. The same laws apply to the vapor, whether the 
 air is present or absent. The air conveys heat, but by its presence 
 retards the diffusion of the vapor, and consequently retards the rate 
 of evaporation. 
 
 RELATIVE HEATING CAPACITIES OF AIR AND VAPOR. 
 
 To compare the relative heating capacities of dry air and of super- 
 heated vapor, the following deductions are made : The specific heat of 
 water vapor at a pressure of one atmosphere is 0.475 ; that is to say, 
 1 pound of superheated steam in falling 1 F. gives up 0.475 British 
 thermal unit. To evaporate 1 pound of water at 212 F., therefore, 
 will require the heat given up by 966 (latent heat at 212 F.)-r- 
 .475=2034 pounds of steam falling 1 degree. At 212 F. the volume 
 per pound is 26.78 cubic feet; therefore, 2034X26.78=54,470 cubic 
 feet of superheated steam falling 1 degree are required to evaporate 
 1 pound of water. The specific heat of dry air is 0.237 and the vol- 
 ume of 1 pound is 16.93 (0.05907 pound per cubic foot) at 212 F. 
 and atmospheric pressure. Therefore, to evaporate 1 pound of water 
 at 212 F. (966 B. t, u.) will require the heat given up by 
 
 16 93 
 
 966X -057- 69,000 cubic feet of dry air falling 1 degree. Thus it 
 .Zo i 
 
 is seen that the heating capacity per unit of volume of superheated 
 steam at atmospheric pressure is but little greater than that of dry 
 air at the same temperature and pressure, in the ratio of 69,000 to 
 54.470, or about 5 to 4. At temperatures above 212 F. and the same 
 pressure of one atmosphere a greater volume is necessary to produce 
 the same effect, since the gas and vapor expand with temperature, 
 but the ratio of the heating capacity of superheated steam and dry air 
 remains very nearly the same. The specific heat of vapor increases 
 slightly at higher temperatures. Thus, figuring in a similar man- 
 ner, it will be found that at five atmospheres pressure (59 pounds 
 gauge) the heating ratio of equal volumes of steam and air is 1.42 
 to 1, and at 1 pound absolute pressure or a vacuum of 28 inches, it 
 is 1.104 to 1. The volume of steam at five atmospheres pressure and 
 306 F. in falling 1 degree necessary to evaporate 1 pound of water 
 at this pressure and temperature is 10,336 cubic feet, and at a 
 vacuum of 28 inches at 101 F. it is 829,433 cubic feet. 
 
 Thus it is seen that there is but little advantage, from the point 
 of view of the volume of gas to be moved, in the use of superheated 
 steam over that of dry air. 
 
18 BULLETIN 509, U. S. DEPARTMENT OF AGRICULTURE. 
 
 In this discussion a cubic foot of space has been used as the basis 
 of the calculations. In analyzing the heat quantities in the drying 
 operation it will be easier to use 1 pound of dry air as a basis, with 
 its accompanying moisture, and follow it through its various stages. 
 Its volume will therefore not remain fixed, but will change with 
 every change in temperature, and consequently the degree of satura- 
 tion produced by a definite amount of moisture accompanying it will 
 depend upon the volume which it occupies. 
 
 THEORETICAL ANALYSIS OF HEAT QUANTITIES. 
 
 For this purpose* the simplest way will be to follow a pound of 
 dry air through a drying cycle as a basis for computations. While 
 in reality the vapor does not enter the air like water in a sponge, but 
 occupies the same space whether air is present or not, we may, for 
 convenience, conceive of a pound of air as containing a certain amount 
 of vapor, which, in reality, means that the space occupied by a 
 pound of dry air under given conditions contains a certain amount of 
 vapor. 
 
 VAPOR AND AIR IN MIXTURE. 
 
 As already explained, the total pressure always is the sum of the 
 individual pressures of the air alone plus the vapor alone. Thus 
 we may speak of a pound of air as being wholly or partially satu- 
 rated with vapor, meaning that it is the space occupied by the pound 
 of air which is in this condition of vapor. If a pound of air said in 
 this sense to contain a given weight of vapor is heated a given amount 
 under a pressure of one atmosphere, both air and vapor will expand 
 the same amount, so that at the new temperature both will occupy 
 the same relative amount of space; the pound of air, however, will 
 still contain the same weight of vapor. The amount of vapor con- 
 tained in a pound of air alone, when it is saturated, can not be used 
 as the divisor in obtaining the relative humidity when compared 
 to the amount of vapor actually contained in the pound of air alone, 
 because when the air is saturated the pressure of the air alone will 
 have been reduced, corresponding to the increase in the vapor pres- 
 sure (since the sum of the two make up one atmosphere), so that for 
 a pound of air a much greater space is required, and, consequently, an 
 equivalently greater weight of vapor to occupy this larger space. 
 For relative humidity it is necessary to compare the weights of vapor 
 which occupy the same amount of space when partially or wholly 
 saturated, or, better still, to compare the vapor pressures. 
 
 CYCLE IN DRYING OPERATION OF 1 POUND OF AIR. 
 
 In following the pound of dry air through its cycle of opera- 
 tion, let the air enter the heater either from outside or from the 
 spray chamber at temperature t 15 and let it contain d pounds of 
 
HUMIDITY-REGULATED AXD RECIRCULATING DRY KILN. 
 
 19 
 
 vapor. (See fig. 3.) After passing through the heater both the air 
 and the vapor are raised to the temperature t 2 . Each pound of air 
 still contains d pounds of moisture, since the vapor expands to the 
 same extent as the air if no vapor is added or subtracted during the 
 heating from t x to t 2 . In passing through the lumber, the air and 
 vapor become cooled to t 3 , and an amount of moistnre, w, is added 
 from the evaporation, so that the pound of air at temperatures 
 t 3 now contains d 3 = (c^+w) pounds of moisture. Thence they either 
 escape into the outer air, as in a ventilating kiln, or pass into the 
 spray chamber, where the 
 heat added by the heater 
 and the extra amount of 
 moisture w is removed from 
 the pound of air into the 
 spray water, and is re- 
 turned at the initial tem- 
 perature t x saturated to re- 
 peat the cycle. The changes 
 in total pressure will be so 
 slight that they may be neg- 
 lected, and the whole op- 
 eration considered to take 
 place at a uniform pressure 
 of one atmosphere. Let r 
 equal the specific heat of air 
 at constant pressure, and s 
 that of superheated vapor. 
 These will be taken as 0.237 
 and 0.475, respectively. 
 Then the quantity of heat 
 imparted to the pound 
 of air and its accompany- 
 ing d x pounds of vapor by the heater is (1), (.237+d 1 X-475) (t 2 tj 
 and the amount of heat given up in evaporating the water w is 
 (2), (.237+d 1 X.47o) (t 2 1 3 ). The amount of water evaporated 
 is w=(d 3 di). Now the heat required to evaporate the water w 
 in continual operation will be that required to raise it from its initial 
 temperature to the evaporating point, plus the latent heat of vapori- 
 zation at this point ; also the heat necessary to raise the temperature 
 of the wood alone the same amount. As the latter is small, it will 
 be neglected. Suppose that the initial temperature of the outside air 
 and of the wet wood is 32 F. Then the heat required is simply the 
 total heat H of w pounds of vapor at the temperature t 3 (nearly). 1 
 
 TD 
 
 22 
 
 FIG. 3. Diagrammatic plan of drying cycle. 
 
 1 Evaporation will actually take place at the temperature of the wet bulb if the air Is 
 not saturated, after which the vapor is superheated to ta. 
 
20 BULLETIN 509, U. S. DEPARTMENT OF AGRICULTURE. 
 
 Hence (3), (.237+d .475) (t 2 -t 3 )=wH=(d.-d 1 ) H or -^"4 = 
 In this equation t 2 is a known quantity, being de- 
 
 . 
 ! .475 
 
 pendent upon the kind and condition of the material being dried. 
 d-L is known, being the weight of moisture of the outside air per 
 pound of dry air, or the weight required to saturate 1 pound of air 
 in the spray kiln at the temperature t^ H is known approximately 
 (but not exactly, since its value varies with t 3 , or more properly with 
 the wet-bulb temperature), and may at first be assumed for some 
 temperature between t 2 and t 15 and afterwards be correctly assigned. 
 t 3 and d 3 are the unknown quantities required. If the air is to be 
 considered saturated at t 3 , then t s and d s are dependent variables, 
 their equation being that of the curve of saturation for water vapor. 
 As the equation is complex, their relative values can be more readily 
 obtained from a table of saturated vapor, and successive values sub- 
 stituted in equation (3) until the equation is fulfilled. Having thus 
 determined t s approximately, the correct value for H may be in- 
 serted and the more exact value of t 3 determined. This has been 
 done by E. Hausbrand in " Drying by Means of Air and Steam " 1 
 for diffrent temperatures of tj. and t 2 , as well as for different humidi- 
 ties and pressures. 
 
 EFFICIENCY OF OPERATION. 
 
 With no air present that is to say, with water vapor alone under 
 a so-called " vacuum," or with " superheated steam'" at pressures of 
 one atmosphere or greater all the heat may be utilized in evaporating 
 the moisture, the leaving and entering temperatures being the same 
 and the pressure constant. With air present, however, and the pres- 
 sure constant, it follows that if the entering air is saturated the 
 leaving air must be at a higher temperature, in order that it may 
 contain the additional vapor at the same pressure. Thus in raising 
 the temperature of the air leaving the lumber a greater amount of 
 heat is required than that utilized in evaporation. 
 
 There is another combination of conditions possible in which the 
 temperature at exit may be the same or even less than that of the 
 entering air or vapor. With air present this is only possible by de- 
 creasing the pressure below that of the entering saturated air. In 
 this case the heat supplied may be even less than the theoretical 
 amount required for vaporization, and the theoretical efficiency as 
 reckoned by temperatures is more than 100 per cent. The advantage 
 gained here is at the expense of the heat energy in the departing air 
 and vapor, being somewhat analogous to the case of the condenser 
 in a steam engine. The gain in heat is from the fact that the enter- 
 
 1 Translation from the German by Wright. Published by Scott Greenwood & Sons, 1901. 
 

 HUMIDITY-REGULATED AND RECIRCULATING DRY KILN. 21 
 
 ing air is at a higher temperature than the leaving air. If the en- 
 tering air is not saturated, a similar condition is possible, since some 
 evaporation may take place without necessitating a higher tempera- 
 ture of the leaving air. 
 
 From the foregoing it might be concluded that the use of a vacuum 
 or of superheated steam would be the most economical way in which 
 to dry materials. In practice, however, the vacuum has certain dis- 
 advantages, as explained heretofore, the chief one being the greater 
 volume of vapor required and the difficulty of producing a uniform 
 circulation of vapor at high attenuation. The other drawback is the 
 expense of the apparatus and difficulty of operation at pressures 
 other than atmospheric. With superheated steam the temperature 
 is too high for most woods. 
 
 CONCRETE EXAMPLES OF RELATIONS OF HEAT QUANTITIES. 
 
 To illustrate the relations of these quantities under the various 
 conditions, let us take a concrete example where the initial tempera- 
 ture of the air is 32 F. and the air is saturated both at the entrance 
 and upon leaving. This is heated to 158 F. and then passed through 
 the material to be dried. The volume of the gas required at the tem- 
 perature of 158 F. and the theoretically least possible expenditure 
 of heat required to evaporate 1 pound of water from an initial tem- 
 perature of 59 F. at various pressures are given below in Table 1. 
 
 TABLE 1. Volume of gas required at a temperature of 158 F. and the theoreti- 
 cally least possible expenditure of heat required to evaporate 1 pound of water 
 from an initial temperature of 59 F. at various pressures. 
 
 Absolute pressures. 
 
 Volume. 
 
 Total heat 
 required. 
 
 1 \ atmospheres 
 
 Cubicfeet. 
 695 
 
 B. t. u. 
 2 010 
 
 llatmospliere 760mm of mercury 
 
 876 
 
 1 692 
 
 500 mm of mercury partial vacuum 
 
 1 247 
 
 1 578 
 
 250 mm. of mercury, partial vacuum . . . 
 
 2 121 
 
 l'346 
 
 Using steam alone superheated from 140 to 158 F. at pressure of 148 mm. of mer- 
 cury, corresponding to saturated conditions at 140 F 
 
 16 821 
 
 1 125 
 
 
 
 
 The minimum theoretical expenditure of heat, as here calculated, 
 has no direct bearing on the efficiency of any method of drying 
 lumber, since the physical requirements of the lumber may, and 
 generally do, demand conditions totally incompatible with the high- 
 est theoretical heat efficiency. They apply directly only to the evapo- 
 ration of a free body of water, irrespective of length of time re- 
 quired and with no radiation losses. The calculations are useful, 
 however, in showing the limiting values of the efficiency which it 
 is possible to attain under the conditions which have otherwise 
 been found most suitable for drying the lumber in question. 
 
 It is instructive to know the highest possible theoretical efficiency 
 in evaporating a pound of water under given conditions, considering 
 no losses by radiation or otherwise. For this purpose Table 2 has 
 
22 
 
 BULLETIN 509, U. S. DEPARTMENT' OF AGRICULTURE. 
 
 been worked out, assuming the water to start with an initial tem- 
 perature of 59 F. and to evaporate at the temperature t 3 , which is 
 the temperature of the leaving air. The efficiency here expressed is 
 the ratio of the total heat of water vapor at t 3 above 59 F. divided 
 by the least possible expenditure of heat necessary to evaporate it 
 under the assumed conditions of the entering and leaving air at 
 atmospheric pressure. When the temperature t of the entering air 
 approaches that of the heated air t 2 that is, when a high humidity 
 is used the calculations become very uncertain, since the quantity of 
 air called for under the assumed conditions approaches infinity, 
 while the temperature differences beUveen t and t s become infini- 
 tesimal. 
 
 The minimum volume of air required to evaporate 1 pound of 
 water is also given in Table 2. 
 
 TABLE 2. Maximum possible theoretical heat efficiency of evaporation under 
 given conditions (ti, t 2 , hi, h 3 ) at atmospheric pressure (760 mm.). 
 
 
 
 
 Heat con- 
 
 Total 
 
 
 
 
 
 
 sumed to 
 
 heat of 
 
 
 
 Entering air. 
 
 After heating. 
 
 Leaving air. 
 
 evaporate 
 1 pound 
 
 1 pound 
 of vapor 
 
 Minimum 
 
 
 
 
 
 of water 
 
 att 3 
 
 volume 
 
 Efficiency 
 
 
 
 
 from 
 
 above 
 
 of air 
 
 H-s-G. 
 
 
 
 
 initial 
 
 initial 
 
 required. 
 
 
 
 
 
 tempera- 
 
 tempera- 
 
 
 
 
 
 
 
 
 
 ture of 
 
 ture of 
 
 
 
 ti 
 
 hi 
 
 ta 
 
 h 2 
 
 ts 
 
 h 3 
 
 59 F. 
 
 59 F. 
 
 
 
 A 
 
 B 
 
 c 
 
 D 
 
 E 
 
 F 
 
 G . 
 
 H 
 
 J 
 
 K 
 
 F. 
 
 Perct. 
 
 o F 
 
 Perct. 
 
 F. 
 
 Perct. 
 
 B.t.u. 
 
 B.t.u. 
 
 Cubic ft. 
 
 
 32 
 
 100 
 
 95 
 
 11 
 
 65 
 
 75 
 
 2,353 
 
 1,074 
 
 2,163 
 
 0.457 
 
 59 
 
 100 
 
 95 
 
 31 
 
 76 
 
 75 
 
 2,100 
 
 1,078 
 
 3,426 
 
 .514 
 
 32 
 
 100 
 
 158 
 
 2 
 
 84 
 
 75 
 
 ,911 
 
 1,080 
 
 993 
 
 .565 
 
 59 
 
 100 
 
 158 
 
 6 
 
 92 
 
 75 
 
 ,715 
 
 1,082 
 
 1,126 
 
 .631 
 
 86 
 
 100 
 
 158 
 
 13 
 
 107 
 
 75 
 
 ,556 
 
 1,087 
 
 1,402 
 
 .698 
 
 32 
 
 100 
 
 212 
 
 0+ 
 
 97 
 
 75 
 
 ,758 
 
 1,084 
 
 694 
 
 .617 
 
 59 
 
 100 
 
 212 
 
 2 
 
 103 
 
 75 
 
 ,572 
 
 1,086 
 
 731 
 
 .690 
 
 86 
 
 100 
 
 212 
 
 4 
 
 114 
 
 75 
 
 ,422 
 
 1,089 
 
 796 
 
 .767 
 
 32 
 
 100 
 
 95 
 
 11 
 
 84 
 
 25 
 
 6,136 
 
 1,080 
 
 5,738 
 
 .176 
 
 32 
 
 100 
 
 158 
 
 2 
 
 110 
 
 25 
 
 2,972 
 
 1,088 
 
 1,495 
 
 .366 
 
 86 
 
 100 
 
 158 
 
 13 
 
 141 
 
 25 
 
 4,869 
 
 1,098 
 
 4,385 
 
 .225 
 
 32 
 
 100 
 
 212 
 
 0+ 
 
 126 
 
 25 
 
 2,352 
 
 1,093 
 
 930 
 
 .457 
 
 86 
 
 100 
 
 212 
 
 4 
 
 146 
 
 25 
 
 2,166 
 
 1,099 
 
 1,206 
 
 .507 
 
 32 
 
 100 
 
 95 
 
 11 
 
 60 
 
 100 
 
 1,974 
 
 1,073 
 
 1,836 
 
 .544 
 
 59 
 
 100 
 
 95 
 
 31 
 
 70 
 
 100 
 
 1,679 
 
 1,076 
 
 2,733 
 
 .641 
 
 86 
 
 100 
 
 95 
 
 74 
 
 88 
 
 100 
 
 1,476 
 
 1,081 
 
 9,725 
 
 .733 
 
 32 
 
 100 
 
 158 
 
 2 
 
 79 
 
 100 
 
 1,692 
 
 1,079 
 
 876 
 
 .636 
 
 86 
 
 100 
 
 158 
 
 13 
 
 99.5 
 
 100 
 
 1,390 
 
 1,085 
 
 1,329 
 
 .781 
 
 140 
 
 100 
 
 158 
 
 63 
 
 140.9 
 
 100 
 
 1,119 
 
 1,098 
 
 3,879 
 
 .981 
 
 32 
 
 100 
 
 212 
 
 0+ 
 
 90 
 
 100 
 
 1,582 
 
 1,082 
 
 625 
 
 .684 
 
 86 
 
 100 
 
 212 
 
 4 
 
 106 
 
 100 
 
 1,350 
 
 1,087 
 
 721 
 
 .804 
 
 176 
 
 100 
 
 212 
 
 47 
 
 176.5 
 
 100 
 
 1,130 
 
 1,108 
 
 2,002 
 
 .972 
 
 IN WATER VAPOR ALONE. 
 
 140 
 
 100 
 
 158 
 
 63 
 
 140 
 
 100 
 
 1,097 
 
 1,097 
 
 16, 418 
 
 1.00 
 
 212 
 
 100 
 
 230 
 
 71 
 
 212 
 
 100 
 
 1,119 
 
 1,119 
 
 3,657 
 
 1.00 
 
 212 
 
 100 
 
 320 
 
 16 
 
 212 
 
 100 
 
 1,121 
 
 1,121 
 
 664 
 
 1.00 
 
HUMIDITY-EEGULATED AXD RECIRCULATING DRY KILN. 23 
 
 GENERALIZATION. 
 
 A study of the theoretical heat relations, as shown by Hausbrand's 
 tables, makes possible the following generalizations: 
 
 1. With t 2 constant and entering air saturated, the expenditure of 
 heat is less, the higher the temperature, t , of the entering air. 
 
 2. With t x constant, the expenditure of heat is less, the higher the 
 temperature, t 2 , to which the air is heated. 
 
 3. Other things being the same, the heat expenditure increases 
 rapidly with reduction in humidity of the emergent air. 
 
 4. Other things being the same, the heat expenditure is less, the 
 lower the humidity of the entering air. 
 
 5. Other things being the same, the expenditure of heat increases 
 with increase of pressure. 
 
 6. With water vapor in the absence of air, the theoretical efficiency 
 becomes 100 per cent. 
 
 In regard to the weights and volumes of air required, the following 
 observations are obtained, with entering air saturated : 
 
 With t 2 constant, both the weights and volumes of air required to 
 evaporate 1 pound of water increases with increase of the initial 
 temperature, t 15 of the entering air. 
 
 With t t constant, both weighty and volumes decrease with increased 
 temperature, t 2 , of the heated air. 
 
 With the emergent air only partially saturated, the weights and 
 volumes increase with* decrease of relative humidity in the emergent 
 air. 
 
 CONCLUSIONS AS TO EFFICIENCY OF OPERATION. 
 
 From this analysis of the heat equations the following conclusions 
 as regards the efficiency of the drying may be drawn : 1 
 
 1. The air should be heated to the highest temperature compatible 
 with the nature of the material to be dried. 
 
 2. The air upon leaving the apparatus should be as near saturation 
 as practicable. 
 
 3. The temperature of the entering air should be as high as 
 possible. 
 
 APPLICATION OF ANALYSIS TO THE WATER SPRAY OR CONDENSING KILNS. 
 
 The above deductions apply to any form of moist-air kiln. The fol- 
 lowing have more especially to do with the Forest Service water 
 spray humidity regulated kiln. 
 
 The amount of heat absorbed by the spray water and the con- 
 densed moisture aside from losses through the kiln walls is the 
 
 1 It should be noted, as stated above, that these deductions apply solely to the evapo- 
 rating process alone, from a theoretical standpoint, and do not take into consideration 
 heat losses through the kiln walls or through extraneous conditions ; nor do they signify 
 what is the condition best suited for conducting the drying operation from the stand- 
 point of the physical effect upon the wood. 
 
24 BULLETIN 509, U. S. DEPARTMENT OF AGRICULTURE. 
 
 difference between the total heat in the saturated air as it leaves 
 the lumber at t 3 and the total heat in the air at t x . It is, in fact> 
 the amount of heat given up by the coils, since the air is brought 
 back to its initial state in the cycle and the water evaporated 
 from the wood is added to the spray water. Hence the amount of 
 heat removed in water at a temperature t x is (4) , G(t 2 tj X (c+sd x ) , 
 when G is the weight of dry air in the mixture required to evaporate 
 1 pound of water, c and s are the specific heats of the air and vapor. 
 Of this the amount G(t 3 tj (c+sdj represents the loss not ac- 
 counted for in the latent heat of the pound of water which has been 
 evaporated and is taken up by the spray water. The maximum 
 
 possible thermal efficiency is therefore (5), f . 2 ~,^ if just enough 
 
 air is circulating to give up all its available heat to the evaporation 
 of the water so that it leaves the lumber in a saturated condition. 
 From equation (2) and (3) the value of t 3 is determined for any given 
 values of t and t 2 . These values may be most readily obtained from 
 the tables given by Hausbrand, before referred to. ti and t 2 are 
 arbitrary values determined entirely by the physical conditions of 
 the material to be dried. 
 
 In actual operation, however, the efficiency will be much leSvS than 
 this maximum, since the air leaving will not be saturated, and a 
 much larger quantity of air will need to pass through the material 
 than the 'minimum indicated by the equation. If no evaporation 
 takes place, all the heat will be used in heating and cooling the cir- 
 culating medium. The total heat used per pound of air will then 
 be (t 2 t x ) (c+sd-J, and this will go simply to heating the spray 
 water. 
 
 COMPARISON OF EFFICIENCY. 
 
 Comparing the theoretical efficiency of the condensing with that of 
 the ventilating type of kiln, it will be seen that under identical run- 
 ning conditions its efficiency is much greater, because the initial tem- 
 perature t is very much higher. Let the temperature of the outside 
 air be 32 F., so that the water has to be raised from 32 F. to the tem- 
 perature of evaporation an dthen evaporated. Let the air leaving the 
 lumber be three-fourths saturated, 75 per cent humidity. Also let 
 t 1 =113 and t 2 =140, giving a relative humidity of 48 per 
 cent. Then d for 1 pound of saturated air at 113 is 0.0653 
 pound. Substituting those values in equation (3) it is found that 
 t 3 =125 and d 3 =0.06889. Since w=d 3 d 15 the number of pounds 
 
 1 1 
 
 of air required to evaporate 1 pound of water is G= ~= jriig~ = *"^ 
 
 which contains 279X0.0653=18.2 pounds of vapor. The pressure 
 of the saturated vapor alone at 113 is 71.4 mm. of mercury; hence 
 that of the air alone is 76071.4=688.6 mm. of mercury. The 
 
HUMIDITY-REGULATED AND RECIRCULATING DRY KILN. 25 
 
 volume occupied by 1 pound of dry air at 113 and a pressure of 
 688.6 mm. of mercury is 16 cubic feet (more exactly 15.921), which 
 must be the same as that occupied by the 0.0654 pound of vapor 
 present in the pound of air. As 279 pounds of air are required 
 with its inherent 18.2 pounds of vapor, the volume of air, or com- 
 bined air and vapor, is 15.921X279=4,442 cubic feet at 113. At 
 125 this will occupy 4,535 cubic feet. 
 
 The total heat consumed is 279 (0.237+0.0653X0.475) X (140-113) 
 =2,019 B. t. u., 1 of which the useful work has been the total latent 
 heat of 1 pound of vapor above 32 F. evaporated at 116 F. (the 
 wet-bulb temperature) and superheated to 125 F.= 1,122 B. t. u. 
 This should be the same as the heat given out by the air and 
 superheated vapor in cooling from 140 F. to 125 F., 279 (0.237+ 
 
 0.0653X0.475) X (140125) =1,122. The thermal efficiency is *^*= 
 
 to - ^1 
 
 =55 ' 6 per cent Also =55 - 6 per cent 
 
 Compare this first with a ventilating kiln in which the air enters 
 saturated at 32 F., is heated to 140 F., and leaves at 75 per cent hu- 
 midity, escaping to the outer air. We then have 
 
 ^=32, d!=.00387 pound per pound of air 
 
 t,=140 
 
 t 3 =calculated=80.2, and d 3 at 75 per cent humidity=.01692. 
 The quantity of air required to evaporate 1 pound of water is : 
 
 G= .01692-.00387 = 76 ' 6 P Unds ' 
 
 This air contains 76.6X-00387=0.296 pound of vapor. The total heat 
 consumed is: 
 
 76.6 (.237+.00387X-475) (140-32) =1,969 B. t. u. 
 
 The thermal efficiency is ~ =55.6 per cent, which happens to be 
 
 14(J o 
 
 the same as in the condensing kiln, but examination will show at once 
 that the two cases are not analogous. In the condensing kiln the 
 
 1 Another way of arriving at this result is to compare the total heats ; thus, in the 
 vapor at 125 and 75 per cent saturation : 
 Total heat in the air alone at 125=279X 0.237 (125 32) equals ______________ 6, 149 
 
 Total heat in saturate vapor at the dew point of 115 (75 per cent humidity at 
 
 125) =279X0.06889 XI 117 equals _______________________________________ 21, 491 
 
 Superheating this vapor from its dew point of 115 to 125=279 X 0.06889 X 
 
 0.475X10 equals _______________________________________________________ 91 
 
 Total at 125 27,731 
 
 At the initial stage, 113 : 
 
 Total heat in air=279 X 0.237 (113 32) equals 5,356 
 
 Total heat in saturate vapor at 1 13=279X 0.0653 X 1116.4 equals 20, 339 
 
 Total heat at 113 25,695 
 
 The difference, 27,731-25,695=2,036 B. t. u., is the heat added to the air. This 
 should be the same as before, namely, 2,019, the difference being in inaccuracy of the 
 constants used. 
 
26 BULLETIN 509, U. S. DEPARTMENT OF AGRICULTURE. 
 
 humidity after heating to 140 F. was 48 per cent ; in the other kiln 
 it is only 3 per cent, an extremely low amount. 
 
 For a correct comparison, the condition of the air entering the 
 lumber should be the same in both cases, namely, it is necessary to 
 raise the humidity in the ventilating kiln from 3 per cent to 48 per 
 cent. This can be done by allowing live steam to escape into the 
 heated air sufficient to saturate it at 113 F., the dew point for 48 
 per cent humidity. Now, if 1 pound of dry air saturated at 32 F. 
 is heated to 113 F. it will still contain its original weight of vapor, 
 namely, 0.00387 pound; but to saturate a pound of air at 113 F. re- 
 quires 0.0653 pound of vapor; consequently, the difference between 
 this and 0.00387 or 0.06143 pound of vapor must be added for each 
 pound of air at 113 F., in order to make the two cases comparable ; 
 they are then exactly alike, and we shall have for our kiln, to re- 
 capitulate, as before 
 
 ^=113 saturated 
 t 2 =140 humidity 48 per cent 
 t 3 =125 humidity 75 per cent. 
 
 Number of pounds of air required to evaporate 1 pound of water 
 at 115 from initial temperature of 32 =279 
 
 Total heat required=2,019 B. t. u. 
 Heat lost * 2,019 1,122=897 B. t. u. 
 
 In the ventilating kiln, on the other hand, we shall have by com- 
 parison : 
 
 ^=32 saturated. 
 t 2 =140 at 3 per cent humidity. 
 t 3 =125 humidity 75 per cent. 
 h 2 =heat in vapor added to raise the humidity 
 to saturation at 113 F. ; 0.0614 pound are required per pound of 
 air. The total heat in saturate vapor at 113 above 32 =1,117 
 B. t. u. per pound; 1,117X.0614=68.58 B. t. u. required per pound 
 of air. There are 279 pounds of dry air required as in the other 
 case. 68.5X279=19,134 B. t. u., which must be added as vapor. 
 
 K 2 =heat required to raise temperature of the air and vapor from 
 32 to 113=279 (.237+.00387X.475) (113-32) =5,396 B. t. u. 
 
 Therefore, in this case the total heat which must be given to the 
 air to evaporate 1 pound of water is 
 
 B. t. u. 
 
 Heat given by coils to raise the air from 32 to 113 equals 5, 39G 
 
 Heat given by coils to raise saturate air from 113 to 140 as before 
 
 equals 2, 019 
 
 Heat supplied in vapor equals 19, 134 
 
 Total heat required 26, 549 
 
 Heat lost (provided it all escaped to the air) 26,549 minus 1,122 equals. 25,427 
 
 1 In the spray kiln this is not in reality lost, since part is utilized in producing the 
 circulation and all the remainder is recovered in the spray water. It is simply a transfer 
 of heat from lumber to spray water. 
 
HUMIDITY-REGULATED AND RECIRCULATING DRY KILN. 
 
 27 
 
 Compared to the loss in the Forest Service kiln, as just shown, of 
 only 897 B. t. u., this would be enormous. It would mean an effi- 
 
 1122 
 ciency of only 05X27 = 4>41 P er cent - ^he assum ption, however, that 
 
 it all escapes to the outside air is not carried out in practice in moist 
 air kilns, but instead a large proportion of this is returned by inter- 
 nal circulation, and only a small amount escapes into the air. It is 
 not possible in the latter case to calculate the theoretical efficiency, 
 since there is no means of knowing what portion of the heat is re- 
 turned in the recirculation within the kiln. The analysis is instruc- 
 tive, however, in showing what enormous heat losses are possible in 
 a ventilating kiln. In no case can the theoretical efficiency of the 
 ventilating equal that of the Forest Service kiln when operating 
 under identical conditions within the drying chamber. 
 
 INCREASE IN DENSITY PRODUCED BY EVAPORATION. 
 
 TABLE 3. Increase in density of mixture of air and vapor produced ly the 
 spontaneous cooling of the mixture from the evaporation of moisture as it 
 through the lumber. 
 
 Entering air. 
 
 After heating before 
 entering lumber. 
 
 Leaving lumber. 
 
 Weight of 1 c. c. of mix- 
 ture in grams. 
 
 ti. 
 
 hi. 
 
 t. 
 
 h s . 
 
 Dew 
 
 point. 
 
 t 3 . 
 
 ha. 
 
 Entering at 
 
 t*j. 
 
 Leaving at 
 tshs. 
 
 F. 
 
 Percent. 
 
 F. 
 
 P.ct. 
 
 F. 
 
 o p 
 
 Percent. 
 
 
 
 32 
 
 100 
 
 158 
 
 1.8 
 
 32 
 
 78.8 
 
 100 
 
 0.0010264 
 
 0.0011658 
 
 32 
 
 100 
 
 158 
 
 1.8 
 
 32 
 
 110.5 
 
 25 
 
 .0010264 
 
 .0011057 
 
 86 
 
 100 
 
 158 
 
 13 
 
 86 
 
 99.5 
 
 100 
 
 .0010126 
 
 .0011094 
 
 86 
 
 100 
 
 158 
 
 13 
 
 86 
 
 140.5 
 
 25 
 
 .0010126 
 
 . 0010394 
 
 140 
 
 100 
 
 158 
 
 64 
 
 140 
 
 140.9 
 
 100 
 
 .0009525 
 
 .0009779 
 
 140 
 
 100 
 
 158 
 
 64 
 
 140 
 
 151.7 
 
 75 
 
 .0009525 
 
 .0010154 
 
 86 
 
 100 
 
 212 
 
 14 
 
 86 
 
 105.8 
 
 100 
 
 .0009310 
 
 .0010915 
 
 86 
 
 100 
 
 212 
 
 14 
 
 86 
 
 146.3 
 
 25 
 
 .0009310 
 
 .0010255 
 
 176 
 
 100 
 
 212 
 
 47 
 
 176 
 
 176.5 
 
 100 
 
 .0007820 
 
 .0008221 
 
 The weights are given in grams per cubic centimeter of the mix- 
 ture. The independent variables which may be assumed at choice 
 are (1) the temperature of the entering air t ; (2) the relative hu- 
 midity of the entering air h^; (3) the temperature to which the air 
 is heated before it enters the lumber t 2 ; and (4) the degree of satu- 
 ration of the air leaving the lumber, h 3 . From these, h 2 , t 3 , and the 
 volumes and weights of the air and vapor are determined. 
 
 METHOD USED IN CALCULATING TABLE 3. 
 
 1. The temperature, t" 3 , of the air leaving the lumber is determined 
 first, as for Table 1. The dew point must also be determined in 
 order to determine the vapor pressure. 
 
28 BULLETIN 509, U. S. DEPARTMENT OF AGRICULTURE. 
 
 2. The following equation gives the value of the density (grams 
 per c. c. ) of the mixture of air and vapor : 
 j_B 0.3T8.e .00129305 * 
 760 X l+.003670t' 
 
 B= total barometric pressure in millimeters of mercury. 
 e= pressure of the vapor in the mixture. 
 t=temperature Centigrade of the mixture. 
 .00129305 is the weight in grams of 1 c. c. of dry air at 
 C. pressure 760 mm. under gravity at 45 latitude and 
 sea level. The figure .003670 is the coefficient of ther- 
 mal expansion of air at 760 mm. 
 
 The first fractional expression may be explained as follows: 
 Let di=density of dry air at B-e mm. pressure. 
 
 d v = density of vapor at e mm. pressure. 
 Then d=d 1 -fd v . The air pressure alone is B-e and 
 
 , B-e 
 di a 
 
 d v =.622 X d X j. 
 
 when .622 is the density of vapor compared to air at 760 pressure. 
 
 Knowing the values t 2 and t 3 and the vapor pressures at these two 
 points (pressures at the dew points) the values of d 2 and d 3 are 
 obtained from the above equation. 
 
 It will be noted that in every case chosen in Table 3 the density 
 increases due to the evaporation, hence the tendency of the air is to 
 descend as it passes through the pile of lumber. 
 
 1 See Smithsonian Meteorological Tables, Tables 83 to 86. 
 
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