About a year ago Professor Barbour furnished me some diatomaceous earth from various deposits in Nebraska, and the results of my study on them were brought before this Academy at its last meeting. These deposits were located in Wheeler county, Greeley county, at Thedford, and at Mullen. From the same source I recently obtained material from a deposit at St. Joseph, Mo., and one at Denver, Colo.
   The diatoms from the two latter deposits show a striking similarity to each other, and all of the species in both are represented in Nebraska deposits.
   The deposit at St. Joseph differs from any Nebraska deposit in being made up of comparatively few species. In all of the material examined only fifteen species were found; and of these, three composed the bulk of the deposit, the others being of infrequent occurrence. These three species are Cymbella cymbiformis (Kuetz.) Breb., Cystopleura turgida (Ehr.) Kuntze, and Cymbella gastroides Kuetz.
   The following is a list of the species found:

   Cocconeis placentula Ehr. Rather common, but not forming any considerable part of the deposit. Occurs about as frequently as in Nebraska deposits.
   Cymatopleura elliptica (Breb.) W. Sm. Rare; only one specimen found. Also very rare in Nebraska deposits, being found only at Mullen, and only a single fragment there.
   Cymbella cymbiformis (Kuetz.) Breb. Forms a considerable por-

tion of the deposit, though not so abundant as Cymbella gastroides Kuetz., or Cystopleura turgida (Ehr.) Kuntze. Also common in Nebraska deposits.
   Cymbella gastroides Kuetz. Very common, and next to Cystopleura turgida (Ehr.) Kuntze, the most important species in the deposit. Common in the Nebraska deposits at Mullen, Thedford, and Greeley county.
   Cymbella levis Naeg. Very rare. Occurs only rarely in the deposit at Mullen.
   Cystopleura occellata (Ehr.) Kuntze. Rare. Rather common in the top layer of the Mullen deposit.
   Cystopleura turgida (Ehr.) Kuntze. The most abundant species in the deposit. Varies greatly. A very common species in the Nebraska deposits.
   Cystopleura zebra (Ehr.) Kuntze. Rather common. About as common in Nebraska deposits.
   Encyonema caespitosum Kuetz. Rare. Found in Nebraska only in the Mullen deposit.
   Gomphonema intricatum Kuetz. Rare. Common in the Greeley county deposit.
   Gomphonema montanum Schum. The form called var. subclavatum Grun. is rather common. Found in Nebraska only in the Wheeler county deposit.
   Navicula cuspidata Kuetz. Rare. Not very common in Nebraska deposits.
   Navicula oblonga Kuetz. Rare. Rather common in deposits at Thedford and in Wheeler county.
   Stauroneis phoenicenteron Kuetz. Only one specimen was found. Rather common in Nebraska deposits.
   Synedra sp. Only a fragment was found, and this was too small to identify.

   The material from the Denver deposit was taken from a rail road cut. The leading species in this deposit are the same as

those in the St. Joseph deposit, but there are differences in the less frequent species.
   The following species were found in it:

   Cocconeis placentula Ehr. Common, but forming a very small portion of the deposit. About equally common in Nebraska deposits.
   Cymbella cuspidata Kuetz. Rare. Rather common in Nebraska deposits.
   Cymbella gastroides Kuetz. Common.
   Cystopleura gibba (Ehr.) Kuntze. Rather common, as is also, the form called var. ventricosa (Ehr.) Grun.
   Cystopleura turgida (Ehr.) Kuntze. Very common.
   Cystopleura zebra (Ehr.) Kuntze. Rather more common than in Nebraska deposits.
   Eneyonema caespitosm Kuetz. More common than in Nebraska deposits.
   Fragilaria construens (Ehr.) Grun. The form called var. venter Grun. is more common that the type forming a considerable portion of the deposit.
   Fragilaria elliptica Schum. Common, but less abundant than in some Nebraska deposits.
   Gomphonema acuminatum Ehr. Rare.
   Gomphonema constrictum Ehr. Less common than in Nebraska deposits.
   Gomphonema herculeanum Ehr. Rare. Also rare in Nebraska deposits.
   Melosira distans (Ehr.) Kuetz. Common, but not so abundant as in Nebraska deposits.
   Navicula radiosa Kuetz. Rare. Not very common in Nebraska deposits.
   Synedra capitata Ehr. Not very common. About equally common in Nebraska deposits.
   Synedra ulna (Nitz.) Ehr. Not very common.

   Besides the diatoms, both of these deposits contain a large number of sponge spicules of at least two distinct forms. Although all of the region in which these deposits occur was at one time covered by salt water, none of them were made at that time, for all of the diatoms found belong to fresh-water species. So it is evident that these deposits were made, after the land of this region had risen out of the ocean, but when there were still fresh water lakes covering part of the region. These deposits must have been made in lakes rather than in rivers, for river conditions are too changeable to allow the forming of a large deposit. Diatoms live in rivers as well as in lakes and ponds, but the formation of a large deposit requires quiet water and practically constant conditions. So these diatom deposits tell us that during Tertiary times there were lakes in Missouri, Nebraska, and Colorado. They also tell us that the conditions were practically alike in all of these places, for the species in all of the deposits show a great similarity, a large number of them being identical. The most abundant genus is Cystopleura, and this grows attached to some filamentous algae. So we also have evidence that other algae than diatoms lived in these Tertiary lakes.
   The number of diatoms in these deposits is enormous. Ehrenberg calcuated (sic) that there were 41,000,000,000 individuals in a cubic inch of diatomaceous earth. Taking the largest specimen of Stauroneis phoenicenteron that I ever found, and which is larger than any of the fossils in these deposits, we would have only about 230,000,000 individuals per cubic inch. As this number is based on the largest diatoms, it is farther from the truth than Ehrenberg's. But Ehrenberg's estimate allows a cube of only about 7 micromillimeters for each specimen, and this is probably too small for our deposits. But even taking the number obtained in using the largest diatoms, a cubic inch contains enough to give three to every person in the United States.
   The time required for making these deposits is impossible to determine. If the diatoms multiplied at their most rapid rate, it would take an incredibly short time; but practically, such deposits are made rather slowly. If we started with a single dia-

tom, and this diatom should divide every hour for a week, there would be 168 divisions, but for convenience we may take two hours more than a week, making 170 divisions. At the end of this time the number of diatoms would be one doubled 170 times, or about 512,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. Now taking Ehrenberg's estimate, which is based on very small specimens, this number of diatoms would make 12,000,000,000,000,000,000,000,000,000,000,000,000,000 cubic inches of diatomaceous earth, the product of a single diatom in a week's time. Now if on every square inch we had one diatom to start with, so that these cubic inches could be placed one above another, they would make a deposit 1,000,000,000,000,000,000,000,000,000,000,000,000,000 feet deep; or 200,000,000,000,000,000,000,000,000,000,000,000 miles deep; or, to,bring it nearer to our comprehension, 2,000,000,000,000,000,000,000,000,000 times the distance from the earth to the sun. At this rate, the progeny of half a dozen diatoms would in a few days fill all the space occupied by the solar system, with diatomateous earth enough to satisfy fully the most ardent diatom collectors. It is hardly necessary, however, to mention that diatoms do not ordinarily reproduce at this rate. This will serve as a warning to scientists to make mathematics their servant and not their master. It is quite evident that the supposition that diatoms do divide at this rate is entirely hypothetical. The "struggle for existence" kept diatoms within bounds as well in ancient as in modern times, and it is likely that the formation of these deposits occupied several, or even many years.

   The question often arises as to, whether the rings of growth observed in trees are strictly annual rings. The opinion appears to be generally prevalent that they represent rather periods of growth. Even if that be true they will still be in most cases annual, as that is the normal period of growth in temperate climates. It may then be asked whether depredations of insects which defoliate the tree, or periods of drought which check its growth, will cause the formation of another ring for that year.
   In order to throw some possible light on this subject a simple experiment was made in the summer of 1894. On May 19 a piece of bark about one and one-half inch square was removed from the north side of an ash tree about four inches in diameter and from a maple about three inches in diameter. Both trees were in full growth at the time and the bark lifted readily.
   July 10 the leaves were stripped from both these trees, with the exception of a very few which were purposely left. By the end of the month both trees were leaving out again.
   On the 10th of November both trees were cut down. A cross section cut through the points from which the bark was removed showed no evidence of the treatment which the trees had received. The ring of growth for that year was apparently as uniform as for other years.
   This experiment, it should be noted, does not contradict the general opinion that there may be more than one ring formed in one year, but it does seem to indicate that a greater interference with the normal conditions of growth is needed to produce that effect than has often been supposed. It is quite possible, to be sure, that at some other part of the season the effect might have

been different. It may also be that if the leaves had been kept from forming for a short time the result would have been different. In general it seems fair to presume that the number of rings found represent with a fair degree of certainty the age of that part of the tree. To get the full age of the tree it should be remembered that the count should be made at a point low enough to get the sapling produced from the seed in the first year of growth.

   Observations on the internal temperature of trees were begun by the writer in the summer of 1894. The object of the work was to determine if possible whether the temperature of trunks and limbs exposed toe the direct rays of the sun does not at times become injuriously high. Observations were made on several apple trees, a maple, and a cottonwood. Some of the apple limbs were shaded by their foliage, some by boards, and some were in direct sunlight. Half inch holes were bored in the limbs, some on the north side, some on the south, and some on the west. Each hole was bored so that a radius of the circle formed by a cross section of the limb was cut at right angles near its peripheral end. Each hole extended a little over half-way through the tree and left approximately one-half inch of new wood between it and the bark. For taking internal temperatures an accurate thermometer was used. Its stem was fitted in a cork which fitted snugly the hole in the limb, so that, when the thermometer was in place the hole was closed tightly. At each reading the thermometer was left in the hole two or three minutes and so indicated fairly accurately the temperature of the wood. Between readings the hole was kept closed with a cork. Readings were taken at the same times every day. In some cases they were taken in the morning, in some at noon, in others at night, in some both morning and noon, in others both morning and night. The temperature of the air was taken at the same times. For this cheap thermometers were used. They were first compared with the better thermometer and their scales corrected. They were hung on the limbs, one on the side in which the hole was bored, the other on the opposite side. Readings were taken continuously from July 4 to September 5, with but few interruptions.

   Now as to results. In the first place the real object of the work, to determine whether the temperature of exposed trunks and limbs does not at times rise injuriously high, can hardly be said to have been accomplished. The highest temperature recorded was 119^o F. Though this is probably above the optimum temperature for growth, it would be difficult to say whether it is particularly injurious or not. Of course the maximum temperature of the wood one-half inch in from the cambium layer may have been much less than that of the cambium itself. A few interesting points came out, however, that lead to a further study of tree temperatures. Some of the things shown by this first summer's work are: (1.) The temperature of the tree trunks follows closely that of the outside air. (2.) One side of a small limb may have a temperature much higher than that of the other side. (3.) The maximum daily temperature of a limb exposed to direct sunlight is often much higher than that of the outside air. (4.) The maximum daily temperature of the shaded limbs is below that of the air. (5.) Limbs exposed to direct sunlight show a greater daily variation in temperature than shaded limbs. As one illustration of the above points, a part of the readings taken from four apple trees on July 26, 1894, are given in the table below. Hole No. 3 was in a limb shaded by a board, No. 4 in a limb shaded by foliage, and Nos. 1, 2, and 5 in limbs exposed to the sun.

   From this summer's work it became apparent that very little could be learned of tree-temperatures by making observations only once or twice daily. Therefore during a number of days in

the spring and summer of 1895, hourly observations were taken. This time a box-elder tree was used. Holes were bored about as before. A number of good thermometers were placed in the holes and remained there throughout the test, the holes being sealed by putting wax about the thermometer stems. The thermometers were arranged to study the following points: (1.) The temperature of the air, as indicated by a thermometer in the shade. (2.) The same, as shown by a thermometer in direct sunlight. (3.) The temperature of the northeast side of a live limb. (4.) That of the southwest side of the same limb exposed to direct sunlight. (5.) That of the southwest side of the same limb shaded from the sun. (6.) That of the southwest side of a dead limb exposed to direct sunlight.
   In addition to the points brought out before, the following were noted: (1.) The temperature of tree-limbs rises and falls more slowly than that of the air. (2.) The temperature of a dead limb rises: and falls more quickly than that of a live limb. (3.) The extreme daily variations of temperature are greater in a dead limb than in a live one.
   In July the same thermometers were placed in limbs of an apple tree and the same points compared. The results were identical to those obtained in the box-elder tree.
   In September the thermometers were moved to another apple tree. Results were the same again with one exception. The temperature of the live limb followed that of the air more rapidly than did the temperature of the dead limb, just the opposite of what had occurred in both the previous cases. The dead limbs used before had been alive the previous summer and their wood was sound, while the limb used in the last case had been dead longer and its wood was soft and slightly decayed. It would be difficult, however, to account for the difference observed in the two cases on this ground alone.
   It was this difference in behavior that led to a continuation of the work another year. Up to this time no, accurate measurements of the thickness of wood between the hole and the bark had been made. The limbs, having been left in their original

positions on the trees, received the sun's rays at somewhat different angles. This might have had something to do with the difference between the temperatures of the live and dead limbs.
   In August of this year, 1896, the thermometers were again placed in limbs of an apple tree. The thermometers were the same ones used before. They were compared with a thermometer loaned for that purpose by the meteorological department of the university and were found to be sufficiently accurate. A live limb about 10 centimeters in diameter and with fairly smooth bark was chosen. It leaned slightly to the north. All limbs to the south of it were removed, so that the sun's rays might fall directly upon it through the greater part of the day. A dead limb about the size of the live one, with sound wood and fairly smooth bark, was then obtained and a section of it about a meter and a half long was hung up parallel to the live limb and about a half meter from it. The sawed ends of this limb were covered with wax to prevent, as far as possible a loss or gain of water. Holes sixteen millimeters in diameter, just large enough to admit the thermometer bulbs, were bored in these limbs about two and one-half meters from the ground. They were so bored that the thermometer tubes placed in them were perpendicular to the sun's rays at about 1:30 P. M. One hole in the live limb and one in the dead one were bored as in all cases before. In both cases the wood between the hole and the bark was 10 m.m. thick. The bark on the live limb was 3.5 m.m. thick, on the dead limb 4 m.m. thick. In addition to these tangentially bored holes, another was bored radially in each limb about 30 c.m. below the first. These were bored as near the center of the limb as possible. Each was 40 m.m. from the outside of the bark on the south side of the limb. All the holes were carefully sealed with wax. A heavy cloth screen was made to shade the limb, or protect them from the wind as might be desired.
   With these arrangements for accurate comparison between the dead and live limb, the results of the first two trials made in 1895 were confirmed. The temperature of the dead limb changed more rapidly than that of the live one. It was also noticed that,

(1) the temperature of the center of the limbs changed much more slowly than that of the surface, and (2) the extreme daily variations were less. These points and also. those brought out before are shown in the diagram of observations made September 9. 1896. (Fig. 1.) The limbs were shaded until 1:15 P. M., when the screen was removed. Just before 2 P. M. the sky became cloudy.
   The difference in temperature between the center and the surface of a limb can be explained by the fact that wood is a poor conductor of heat. The difference between the dead and live limbs can be accounted for almost entirely by the fact that the live limb contains much more water than the dead one. Water, having a high specific heat, varies in temperature much less rapidly than wood.
   Thus far nothing has been said of the behavior of dead and live limbs when their temperatures approach the freezing point of water. Many observations were made on this point and all indicate the following conclusions: (1) The, temperature of the air and of both the center and surface of a dead limb passes the freezing point of water without appreciable acceleration or retardation in its rise or fall. (2.) The temperature of the surface and center of a live limb remains near the freezing point for some time, but, having once got above this point, it rises nearly as fast as that of a dead limb. These points are shown in the diagram of readings for December 12, 1896. (Fig. 2.) The limbs were shaded all day.
   This behavior is also to be explained, probably, by the presence of considerable water in a live limb and the comparative absence of it in a dead one. The "latent" heat of fusion must play an important part in retarding the melting of ice.

   (Added since the above was read.)

   Since the reading of the above paper a further study was made of the effect of water in controlling temperature changes in live and dead limbs. The dead limb and a section of the live one, containing the thermometers and corresponding in length to the dead one, were removed from the tree to the university green

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