Chapter 28 The Climate of the Pacific Slope The western portion of the United States exhibits very interesting climatic features. In California for example, there may be found every degree of temperature between tropic heat and Arctic cold. In the deserts of the southeastern portion of the state, the air is extremely dry, while in the northwest it rains nearly every month in the year. Upon the borders of Puget Sound the thermometer seldom falls below the freezing point, while southern Newfoundland, in the same latitude, is marked by cold and snowy weather for at least six months of every year. Southern California has the same latitude as central Georgia, but its average temperature near the coast is but little higher than that of Puget Sound, while it is warmer in winter and cooler in summer than Georgia. The deserts of Southern California and Arizona are so hot that for four months of the year work in the sun is almost impossible, yet the higher portions of the Sierra Nevada Mountains, but a short distance away, have an Arctic climate. The whole Pacific Coast region has, with the exception of the mountains, a much milder climate than one would expect for a mere knowledge of its latitude. It will be instructive to search out the reasons for the remarkable contrast in climate, presented by different portions of the slope. The imaginary lines passing through points of equal temperature upon the earth are called isotherms. These lines rarely accord in direction with the parallels of latitude, but curve far to the north or south. The irregular course of the isotherms is due to many causes. Among these are the distribution of the land and water, the direction of the prevailing wind, the position of the mountain ranges, and the elevation above sea level. In winter the isotherms curve far to the north over the North Pacific and North Atlantic Oceans, but over the intervening land they curve as much to the south. In summer the isotherms are almost reversed in position, at least as far as the land is concerned, for they bend to the north in the heart of the continent. There are important reasons for the slight variation of the isothermal lines upon the western borders of North America and Europe, and their great change of position in the interior from winter to summer, but these reasons are not at all difficult to understand. The temperature of large bodies of water changes but little throughout the year, for water warms and cools slowly. The surface of the land, on the contrary, heats rapidly, and then as quickly loses its heat with the changing season. The air over the ocean is cooler in summer and warmer in winter because of the influence of the water, but over the land, in districts far from a large body of water, the changes in temperature between day and night, summer and winter, are very great. It was formerly thought that the warm Japan current, which flows against the western shore of North America, was responsible for the exceptionally mild climate there, and that the Gulf Stream produced a similar climate upon the coast of western Europe. More careful study, however, has shown that not the warm ocean currents, but rather the winds blowing from the water are the cause of the mild climate in those lands across which they blow. In temperate latitudes there is a slow movement of the air in an easterly direction, and in consequence the climate of the western coast of North America is not marked by such extremes in winter and summer, as are the interior and the eastern sections. It is also surprising to find how nearly alike the average winter and summer temperature is at San Francisco. It is also surprising to note that the average temperature of Seattle differs so little from that of San Diego, although these two places are separated by sixteen degrees of latitude. In some places the climatic conditions which we should naturally expect seem to be reversed. Oranges are grown in the Great Valley of California, as far north as Red Bluff, and actually ripen a month sooner than they do near Los Angeles, five hundred miles farther south. The early ripening of fruits in the Great Valley may be explained by the presence of the enclosing mountain ranges. The Sierra Nevada mountains upon the northeast shut off the cold winds of winter, while the coast ranges upon the west break the cool summer winds which come from off the Pacific. Another interesting fact, connected with the climate of the west, is the influence exerted by the direction of the mountain ranges. As these ranges usually lie across the path of the prevailing winds, their tempering influence is lost much more quickly than it otherwise would be. West of the coast ranges the summers are cool and the winters are warm. On the eastern side of these mountains the winters are somewhat cooler and the summers very much warmer. In the dry, clear air of the desert valleys, far from the ocean, the daily range in temperature is sometimes as great as fifty degrees, while the winters are cool and the summers unbearably hot.  Where the mountains rise abruptly to a great height, as for example does the San Bernardino range of southern California, one can stand among stunted plants of an arctic climate and look down upon orange orchards where frost rarely forms. Mount Tamalpays, a peak of the coast range north of San Francisco, has an elevation of nearly three thousand feet. The summer temperature upon this mountain forms an exception to the general rule, for while the lowlands are buried in chilling fog, the air upon the summit is warm and pleasant. The north and south mountain ranges not only make the interior hotter than it would otherwise be, but rob it of much of the moisture which it should receive. The winter storms coming in from the ocean find the cool mountains lying across their path and quickly part with a large portion of their moisture. Where the coast mountains are low, as is the case with a great part of California and of Oregon, more of the moisture passes on to the next line of mountains, the Sierra Nevada Cascade Range, the western slope of which is well watered. In the region of the Columbia the Cascade Range is also low, and the storms, which often follow one another in quick succession, sweep across the Columbia Plateau and over the Rocky Mountains. Farther south not only are the storms fewer in number, but the mountains are very much higher, so that the desert basins of the lower Colorado and Death Valley region are extremely dry. One can in imagination stand upon the summit of the Sierra Nevada Mountains, and upon one hand look down upon Barren Valleys of vast extent, broken by mountains almost as barren, where nothing can be grown except by means of irrigation. And upon the other side, toward the coast, see a country plentifully visited by rain, and either covered with forest or given over to farming and fruit raising. The Rocky Mountains form the eastern barrier which the storms encounter. Their summits are very high and are covered with deep snow during the winter. East of these mountains lie the Great Plains, where the precipitation is light until we go far enough toward the Mississippi Valley to reach the influence of the moist air currents from the Gulf of Mexico. Many storms originate over the region of the Gulf of California, particularly in the late summer, and supplement to some extent the light winter storms of Arizona and New Mexico. The storms of which we have been speaking are known as cyclones. This term does not refer to the local storms which occur in the Mississippi Valley and are frequently so destructive, but to great disturbances of the air. Sometimes the column of whirling air is more than a thousand miles in diameter. The air in a cyclone is circling and at the same time rising so that the motion is spiral. If you will study an eddy in a stream of water, you will get an idea of the nature of the motion, except that in the case of the water eddy, the movement is downward. The motion of the particles in the dust whirls, which all have been seen moving across the fields near noon on warm summer days, illustrate the movement of the air in one of these great storms. The direction of the air in a cyclone is opposite to that of the hands of a clock. When the winds come up from a southerly point, when high, thin clouds, gradually growing, thicken, spread over the sky and the barometer begins to fall, then it is known that a storm is coming. If one will learn to watch the clouds and the winds carefully, he may become able to predict a storm with almost as much certainty as if he had a barometer. This instrument registers the pressure of the air, which is always less within the area of a storm, because then the air is rising, so when the barometer falls, we may always know that a storm is approaching. The great number of the storms which occur in the central and northern United States come in from the Pacific Ocean in the latitude of Washington. Continuing east or southeast, they reach the Mississippi Valley and then turn northeastward toward the St. Lawrence Valley. In the summer months, there are a few storms and they very rarely reach as far south as California. As winter approaches, the storms become more frequent and severe and move farther and farther south until the whole land as far as Mexico receives a wedding. Upon the Pacific Coast, there is often very little warning of the coming of a storm, but in the middle and eastern states, they may frequently be predicted several days in advance. With the passing of one of these storms, the temperature falls rapidly and this lowering of temperature, together with the fierce wind, gives rise upon the great plains to blizzards or northers. These storms endanger the lives of both men and animals. At different times in the year, particularly in winter, spring, and early summer, warm, dry winds occur. Those winds which sweep down from the heights of the Rocky Mountains and quickly melt the snows are known as chinooks. The hot north and east winds of California often do great damage to growing crops. Now let us sum up briefly the factors which have together produced the climatic features of the Pacific slope. One, ordinarily the factor of the greatest importance is latitude. We should expect that Seattle would have a much colder climate than San Diego because it receives the sun's raves more slantingly. Two, the influence of latitude is greatly modified by the temperate winds blowing from the Pacific so that places far separated in latitude differ but little in average temperature, their summers being cooler and their winters warmer than we should expect them to be. Three, the storms pass over the land with the general easterly movement of the air. The largest number pass east across the northern portion of the United States. The farther south we go the fewer are the storms and the less the rainfall. Along the coast of Washington the annual rainfall is nearly 100 inches. At San Diego it is only about 10 inches. Four, the position of the mountain ranges causes the influence of the ocean on the air to be lost within a short distance toward the interior of the continent so that the extremes of temperature rapidly become greater. The position of the mountains also affects the rainfall of the interior. Since a large portion of the moisture is condensed upon their ocean slopes the climate of each succeeding range toward the interior becomes more dry and desert like. While in some of the lowlands thus cut off from the ocean the climate is extremely arid. Yet the country is relieved from utter barrenness through the presence of mountain peaks and ranges which often condense considerable moisture. Five, the higher a region is above the sea the colder the climate. The summit of a high mountain and the valley at its base may be in the same latitude and yet one may possess an arctic climate while the other has a subtropical one. The heavy rainfall in western Washington, Oregon and northern California results in dense forests. To the south the rainfall upon the lowlands is not sufficient to produce forests. But as it is greater upon the mountains trees thrive upon their sides. The elevation at which trees will grow becomes higher and higher as we go into the more desert regions. Until in northern Arizona it is found to be above six thousand feet. The high plateaus are generally treeless but are covered with such shrubs as grease wood and sagebrush. We see now that our climate is the product of many factors. It frequently varies greatly in places only a few miles distant from each other. Consequently there may be a great variety of productions and industries in one small area while in other regions the climate and productions are almost unchanged for hundreds of miles. End of Chapter 28 Chapter 29 of the Western United States This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer please visit LibriVox.org. The Western United States a geographical reader by Harold Wellman Fairbanks. Chapter 29 Something about Irrigation Travelers from the eastern states who visit New Mexico for the first time are attracted by many unusual sites. There are the interesting little donkeys, the low adobe houses of the native Mexicans and the water ditches winding through the gardens and fields which are divided into squares by low ridges of earth. If the fields are seen in the wintertime when dry and barren the meaning of their checkered appearance is not at first clear but in the spring and summer one is not long in finding out all about them. When the time comes to sow the seed water is turned into these squares from the ditches which traverse the valleys and one square at a time is filled until the ground in each is thoroughly soaked. Afterward when the ground has dried enough to be easily worked the crop is put in. The seeds soon sprout under the influence of the warm sun and the land becomes green with growing plants. The same method of moistening the ground is used for the orchards and vineyards. What is the use of all this work? Why not wait for the rains to come and wet the earth as the farmer does in the eastern United States? The Mexicans who have tilled these valleys for more than 200 years ought certainly to have learned in all that time how to get the best returns. You may be sure that they would not water the ground in this way if it were not necessary. The fact is that over a large portion of the western half of the United States it does not rain enough to enable the farmer to grow his crops. The climate is generally very different from that of the middle and eastern states. When the Mexicans moved northward into the valley of the Rio Grande River into Arizona and California they found a climate similar in many respects to that at home and soon learned that it was necessary to water the land artificially in order to make it productive. Though in many places sufficient rain fell yet the heaviest rainfall came in the late summer or winter when the plants needed it less while the spring and summer were long and dry. The Mexicans were not the first to practice watering the land if we may judge from the ruins of ancient ditches constructed by the primitive Indian inhabitants. It is evident that they too made use of water in this manner for the growing of their corn and squashes. This turning of water upon the land to make it productive is termed irrigation. The work is performed in different ways as we shall see later. Irrigation is now carried on through all portions of the United States where the rainfall is light and streams of water are available. To one who has lived in a country where there is plenty of rain it seems to involve a great deal of work to prepare the land and to conduct water to it. One may feel pity for the farmer who has to support himself in this manner in so barren a country. I am sure however that if any such person will stop to think he will remember times when in his own fertile home the expected rain did not come and the vegetation wilted and dried up. He may have become discouraged because of a number of dry years but probably never thought that he had the means at hand to make up at least in part for the shortcomings of nature in sending too much rain one year and another year too little. It would doubtless have paid such a farmer many fold to have been prepared at the coming of a dry year to turn the water from the neighboring stream over his lands. This process would have involved a good deal of labor but how the plants would have rejoiced and how abundantly they would have repaid him for the extra trouble. The showers come without regard to the time when growing things need them most but with irrigation the crops are independent of the weather. The farmer may be sure that if he prepares the ground properly and sows the seed the returns will be all that he can wish. In many localities several crops may be raised in a year by this method where otherwise only one would grow. Now let us see how the water is taken from the streams and what are the different. Now let us see how the water is taken from the streams and what are the different methods employed to distribute it over the land. Almost every valley is traversed by a stream great or small. It may be a river with a large volume of water or a creek which completely dries up during the long rainless summers of the west. In rare cases the stream may flow upon a built up channel which is as high as the valley but usually it is sunken below the level of the floor of the valley and enclosed by banks of greater or less height. How is the water to be sent over the land? Where the current is swift you may sometimes see a slowly turning water wheel having at the ends of the spokes little cups which dip up the water as the wheel revolves and pour it into a flume that runs back over the land. At some places engines are used to pump the water from the stream and lift it to the desired height. Generally however another method is employed. The water is taken out of the stream in an artificial channel dug in the earth but in order to get the water at a sufficient height to make it flow over the fields it is necessary to start a ditch or canal at a favorable point some distance of the stream perhaps miles from the garden. The ditch is made with a slope just sufficient for the water to flow the slope must be less than that of the river for which the water is taken so as to carry the stream at last high enough to cover the lands to be irrigated. Visit almost any valley in the west where agriculture or fruit growing is being carried on and you will at once notice the lines of the ditches apparently level as they wind around the hillsides. At convenient distances there are gates to let out the water for the orchards and fields. The ground may be moistened in different ways the first method is that employed by the Mexicans who if we accept the cliff dwellers were the first to introduce irrigation into our country. This consists in dividing the land into squares by embankments allowing the water to flood each in succession. The method is known as irrigation by checks and can be used conveniently only upon nearly level land. In many orchards a series of shallow furrows is plowed between the rows of the trees and the water is allowed to flow down these until the soil is thoroughly soaked. In alfalfa fields the water is often turned upon the upper end and permitted to work its way across until it reaches the lower edge soaking the ground as it goes. The slopes must in every case be so gentle that the current will not be strong enough to carry away the soil. Once in every two or four weeks throughout the spring and summer the exact period depending upon the rapidity with which the ground dries the wetting is repeated. If the soil is light the water must be turned on more often and a larger supply is required. It frequently happens that the stream from which the water is taken so nearly dries up in the summer when the water is most needed that the cultivated land suffers severely. During the winter little if any irrigation is necessary but at that time the streams are so full that they frequently run over their banks and do great damage. How to preserve the water thus going to waste and have it at hand for summer use has been an important problem in regions where every particle of water is valuable. Study of the question has led to the examination of the streams with reference to the building of reservoirs to hold back the flood waters. A reservoir may be formed of a natural lake in the mountains in which the stream rises by placing a dam across its outlet and so making it hold more water. If this cannot be done an area placed in the canyon of the stream is selected above which there is a broad valley.  Ditches lead away from this reservoir and by means of gates the water is supplied when and where it is needed. The streams which furnish the water for irrigation in the arid region rise in mountains with steep rocky slopes and until the water issues from these mountains it is confined to canyons with bottoms of solid rock so that no water is lost except by evaporation. After the streams emerge from the canyons upon the long gentle slopes of gravel and soil which lie all about the basis of the mountains they begin immediately to sink into the porous material. They frequently disappear entirely before they have flowed many miles. Some of this water can be brought to the surface again by digging wells and constructing pumping plants but the greater part is lost to the thirsty land. To prevent the water from sinking into the gravel ditches lined with cement are often made to carry it from the canyons to the points where it is needed. Sometimes iron pipes or wooden flumes are used in places of the ditches. What a transformation irrigation makes in the dry and desert-like valleys of the west. Land which under nature's treatment supports only a scanty growth of sage brush or grease wood and over which a few half starved cattle have roamed becomes when irrigated covered with green fields and neat homes while sleek well-fed herds graze upon the rich alfalfa. Ten acres of irrigated land will in many places support a family where without irrigation a square mile would not have sufficed. One might suppose that the soil of these naturally barren valleys was poor but such is not the case. The ground did not lack plant food but merely the water to make this food available. With plenty of water the most luxuriant vegetation is produced. The soil is indeed frequently richer than in well-watered regions for a lavish supply of water carries away a portion of the plant food. In some places where the land is almost level and the soil is filled with large quantities of soluble materials such as soda and salt. Keeping the ground moist through the irrigation brings these substances to the surface in such quantities as to injure and sometimes kill the vegetation. In order that such lands may be successfully cultivated the salts have to be either neutralized or washed away. Many of the rivers of the west carry large quantities of silt in suspension which fills the ditches and causes a great deal of trouble but when the silt is deposited over the surface it adds continually to the richness of the land. The full development of irrigation will mean a great increase in the population and wealth of all the western states. End of chapter 29. Chapter 30 of the western united states. This is the LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer please visit LibriVox.org. The western united states a geographical reader by Harold Wellman Fairbanks. Chapter 30. The location of the cities of the pacific slope. This old earth has to be consulted upon every occasion. It is a silent partner in all our undertakings. We sometimes think that we come and go as we please but a little thought convinces us that we are not really so free. The traveler must take account of the slopes of the land. It is much easier for him to follow a valley and cross a mountain range through a low spot although his course be very crooked than it is to make a beeline for his destination. The farmer in choosing his home and the kind of produce which he will raise has to consult the soil and climate. He cannot expect to grow grain where the soil is poor and dry or grow apples where the late spring frost kill the buds. The miner knows that he cannot expect to find gold veins in the valleys where the rocks are deeply covered by the soil and so he turns his steps towards the mountains where nature has made his work easy by lifting up the rocks and exposing them to his view. Roots of commerce and trade are governed by geographic and to a certain extent by climatic conditions. Shallow streams with rapids and waterfalls obstruct navigation. The absence of harbors along a given coast makes it difficult for ships to take and discharge cargoes. Railroads cannot be constructed unless long and expensive surveys have first been made to determine the route which nature has made the easiest between the two given points. The character of the climate and geographic features of a given country determine whether it shall become noted for agricultural productions, mining industries, manufacturers or commerce. The locations of the cities and towns and the roads connecting them depend upon geographic conditions. There is not an occupation of any importance in which people engage at any particular place that is not dependent in a large degree for its success upon the conditions which nature has imposed upon that place. A city will not grow up at a given point unless the geographic conditions are favorable. There must be some natural reason to induce people to gather in large numbers in one place. At one spot there are facilities for manufacturing such as water power and coal and easy means of communication with other parts of the world. At another the only reason for the growth of a city is the existence of rich mines. A third place may be conveniently located in the midst of a rich agricultural region where it is easy to bring in supplies and ship out the products of the soil. A study of the founding and growth of some of the cities of the west and particularly the pacific slope will bring out many interesting facts. San Francisco is the metropolis of the pacific. Its population will soon reach half a million. If we look back 75 years we find San Francisco an unimportant Mexican military post and the seat of one of the smaller missions. Monterey, the capital of the province of California and one of the two leading towns, Los Angeles being the other, apparently had all the advantages in the race for supremacy. In date of discovery 1603 Monterey Bay has the advantage of more than 150 years over San Francisco Bay. It is difficult to understand while the different navigators who sailed north along the coast failed to discover California's most magnificent bay. Sir Francis Drake went by it, evidently not seeing the narrow opening between the headlands, now known as the Golden Gate. Viscano, after discovering Monterey Bay, also passed by and anchored where Drake had stopped, in a little bay now called Drake's Bay, a few miles north of San Francisco Bay. After the founding of San Diego in 1769 a party started overland for Monterey, but by reason of the peculiar position of the bay they passed it unknowingly and by accident came upon the body of water which has since been of so great importance to the commercial life of California. Monterey Bay, in time, lost its importance, partly because it was not thoroughly protected from the storms and partly from the lack of easy communication with the rest of the state. Immediately after the acquisition of California and the discovery of gold the advantages of San Francisco Bay began to be appreciated and the little Mexican town grew rapidly. The narrow entrance to the bay which had for so long a time delayed its discovery completely protected it from the storms while its long arms opened across the coast mountains directly into the important valleys of the interior. Ocean vessels could go up and down the bay and through the Strait of Carquinas while river boats could be used for many miles farther. After the discovery of gold ships from all parts of the world found ample room and shelter in San Francisco Bay and the incoming miners going by the water routes to Marysville, Sacramento and Stockton easily reached the gold bearing gravels of the Sierra Nevada streams. With the exception of Southern California and a portion of the northern coast almost all the agricultural and mineral resources of California are directly tributary to San Francisco. This place is naturally the center of home trade, a foreign commerce and of population. Nature failed to supply San Francisco with one essential advantage namely cheap power for manufacturing. There is no water power near and but little coal in the state since the coal has to be shipped in from distant points. Its high price has impeded manufacturing but now it appears that San Francisco is not so badly off after all for important deposits of petroleum have been discovered in the central and southern portions of California and besides processes have been invented for transforming the unlimited water power of the mountain streams into electric energy and transmitting this power to all the cities about the bay. The early Spaniards founded the Pueblo of Los Angeles in its present location because at this point the Los Angeles River carried an abundance of pure water which could be let out in ditches to irrigate the fertile bottom lands in the vicinity. Partly because it became a railroad center and partly because it is surrounded by rich valleys. Los Angeles has grown with great rapidity and now stands next to San Francisco in size among California cities. San Diego which has a harbor next in importance to that of San Francisco has grown more slowly because of the greater difficulty in developing water systems for irrigation and because access is not so easy on account of the enclosing mountains. However it must in time become the second commercial city of the state. Mountain barriers make travel from one portion of California to another somewhat difficult. Mountains separate San Francisco and the great valley of California from all other portions of the continent. Nature seems to have planned here a little empire all by itself. The engineering skill in the construction of railroads has overcome the barriers upon the north which separates California from Oregon. The Sierra Nevada Range upon the east has been crossed at Donner Pass and upon the south an outlet has been found through the Tehachapi Pass. In the state of Oregon the city of Portland ranks first in importance. Why did not Astoria or Fort Vancouver develop into the metropolis of the Columbia Basin? Astoria which was founded in the early part of the last century has a spacious and well protected harbor but it has no large tributary agricultural valleys. Moreover the greater number of deep waterships pass it by and go as far up the Columbia as possible to take on their loads of grain. Fort Vancouver on the side of the Old Hudson Bay Trading Post is practically at the head of deep water navigation upon the Columbia but there seems to be no particular reason why trade should center here and this town also has been left behind in the march of progress. The earliest settlements in western Oregon were made upon the Willamette River which drains a large and extremely fertile valley. Near the point at which this river joins the Columbia the city of Portland sprang up. This town occupies an ideal position. It is accessible for deep sea vessels and has communication by riverboats with the Willamette Valley and the Upper Columbia River. In the 18th century when sailors were looking for a passage across the northern portion of the continent an opening was found extending into the land between Vancouver Island and Cape Flattery. It was at first thought that this was the desired waterway but various navigators among them Vancouver explored the body of water into which the Strait of Fuca opened only to find that every branch and inlet terminated in the land. Puget Sound is nearly enclosed by water and is so large as really to form an inland sea. Its long arms reach out in three directions among the most heavily tempered valleys and mountain slopes of the United States. The cities of Puget Sound had a later start than most of the other cities of the Pacific Coast. For this portion of the old Oregon Territory was for a long time claimed by the English and during that period was peopled only by Indians and Travers. In 1846 the present boundary was established and Puget Sound passed into the possession of the United States. Because of the dense forest agriculture could not play an important part in the development of the sound region for some time. Lumbering was naturally the leading occupation. This industry could be carried on all the more adventagiously because of the innumerable inlets penetrating the land. The advantages of Puget Sound for foreign commerce began to be evident, but the Cascade Range stood in the way of railroads from the eastward. Although it was a comparatively easy task to build a railroad north from Portland, yet the sound region did not begin to grow rapidly until, after careful surveys, two railroads finally found passes through the Cascade Range so as to reach Tidewater. As in other places when the necessity for overcoming them arose the obstacles which nature had interposed were not found to be so troublesome as was at first supposed. Now the once formidable range has been tunneled and will no longer form a serious barrier between the interior portion of Washington and the coast. Tacoma, Seattle, and Everett have grown up on the sound as important commercial and manufacturing cities, and will on account of their favorable situation receive their share of the commerce of the Pacific. The cities of the sound are particularly well situated for intercourse and commerce with Alaska and Northeastern Asia. These cities are also well situated for manufacturing because coal and wood are plentiful and consequently cheap, but they have not in their immediate vicinity so extensive agriculture valleys as the Willamette and the Great Valley of California. The lumberman must be supplanted by the farmer and fruit grower before the slopes about the Puget Sound can be fully developed. The natural outlet for the great wheat fields of Central Washington is by way of the Columbia River to the ocean, but the tunneling of the Cascades partly diverts their products to the sound region. The city of Spokane in eastern Washington clearly illustrates the control which physical features exert upon the settlements and industries of men. The Spokane River, soon after issuing from Sea and Oleg or Dulleen Lake, flows out over the volcanic plains of Washington. In the course of a few miles it descends into a shallow canyon by a series of Cascades and waterfalls. The water power furnished by these falls has determined the position and growth of Spokane. The falls brought sawmills and manufacturing plants, and these in turn brought people and railroads. The city has become a great commercial center for all the region round about. The extensive and rich mineral district upon the north, extending even into British Columbia, finds its most convenient source of supplies at Spokane. East of the city is the Sea and Oleg or Dulleen, mining region, while south and west are large areas devoted to the cultivation of fruit and grain. The city of Great Falls, Montana, in the Missouri River basin is destined to become a great industrial center because of the presence of unlimited water power afforded by the Great Falls of the Missouri River. No other reason would lead to the growth of a settlement at this particular spot, for boundless plains extend about in every direction. The mining cities of the west, such as Butte, Virginia City and Leadville, illustrate the growth of important centers of population in the vicinity of large deposits of minerals. In the case of these cities, as well as many others, there are no agricultural resources in the surrounding country to support the people gathered together here. Nearly all their food has to be shipped hundreds of miles. Cities supported by mining are less likely to be permanent than those supported by an agricultural community, by commerce or by manufacturing. END OF CHAPTER XXXI of the western United States. This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer, please visit LibriVox.org. The Western United States A Geographical Reader by Harold Wellman Fairbanks. Chapter 31 The Forest Belt of the Sierra Nevada Mountains. No other coniferous forest in the world can compare with those covering the western slope of the Sierra Nevada and Cascade Ranges. They are remarkable both for the number of species and for the size of the trees. The moderate temperature and the moist winds from the Pacific seem to offer the conditions which are best suited to the growth of cone-bearing trees. As we go northward along the coast or ascend the mountain slopes, we find the climate growing cooler and cooler. With this changing climate, the species of conifers change. For each has become accustomed to certain conditions of temperature and moisture, which it must have in order to thrive. The Sierra Nevada is the most continuous lofty range of mountains in North America. From the great valley at its western base to the crest of the range the distance is about 60 miles. Because of the great height of the mountains there is found within these few miles every variety of climate between the subtropical atmosphere of the valley where oranges ripen to perfection and the arctic cold of the summits where little or no vegetation can live. Thus by climbing a single mountain range we may experience all kinds of climate and have an opportunity to observe the different forms of plant life such as we would not otherwise obtain without a journey of several thousand miles. Passing through the groves of Valley Oak and beyond the orange orchards at the foot of the mountains we reach the foothills and begin to ascend. Several species of oak are found upon the hillsides and in the valleys while mingled with them in many places appear such shrubs as the California lilac, camisole, and manzanita. Where the soil is too poor or the slopes too steep for the trees these shrubs commonly called chaparral are massed together in almost impenetrable thickets. The first of the coniferous trees which we meet is an odd looking one known as the digger pine. Instead of having a single straight trunk it divides a short distance above the ground into many branches. The large cones are armed with long hooked spines so that they must be handled rather carefully. But when opened they are found to be filled with nutritious nuts. These nuts were an important source of food for the Indians who once inhabited the foothills. Now the Indians are gone but the nuts are not wasted if one may judge by the fragments of the cones with which the squirrels drew the ground. The road climbs the foothills by many turns and windings through the canyons and up and down ridges. At an elevation of about two thousand feet specimens of the yellow pine appear. The trees increase in size and grow more closely together as we ascend. We soon find ourselves in the edge of the forest belt which extends unbroken northward to the Arctic zone and upward to the line of almost perpetual snow. The yellow pine so named from the color of the bark sometimes attains a diameter of six feet but does not form so dense forest as we shall find higher on the mountains. The rays of the warm sun reaching down between the trees to the carpet of needles and bear clover draw out their spicy fragrance. The yellow pine although it does not afford as good a quality of lumber as some of the other pines is one of our most important trees because of its wide distribution through nearly all mountains of the west. It has a much wider range in elevation than most trees. One variety reaching upward nearly to the timber line. After getting well into the yellow pine forest we soon come upon other trees that contend with the pines for a footing upon the slopes and for a bit of the sunshine. Among these the black oaks deserve special mention for in places they form dense groves upon the ridges. The cedars with their rich brown bark and flat dripping branches are easily recognized. As these trees grow old they become gnarled and naughty and very picturesque. We first meet that king of pines the sugar pine upon the more shaded mountain slopes. Although higher up on barren rocky ridges this tree grows to noble size yet it cannot withstand heat and dryness. Our attention may be first called to the sugar pine by the slender cones 10 to 15 inches in length which are scattered over the ground. Then as we look up to see when the cones come our eyes light upon the smooth trunks often over six feet in diameter and reaching up 150 feet before the branches appear. From the ends of the long dripping branches hang slender green cones. The name of this pine is derived from the fact that a white sugar gathers in little bunches at the spots where their trunk has been injured. This sugar is pleasant to the taste and somewhat medicinal. The wood of the sugar pine which is white and fine grained is of greater value commercially than that of any of the other pines. This fact leads the shake maker and lumberman to seek out the noble tree and mark it for destruction. The sugar pine when once destroyed in a given locality rarely replaces itself as it is crowded out by the more vigorous conifers. Scattered through the forest of yellow pine cedar and sugar pine is the Douglas spruce commonly known in the market as the Oregon pine. This is the most important forestry in Oregon and Washington. It often grows to a height of 300 feet and forms dense forest for hundreds of miles along the base of the western slope of the Cascade Range. In Washington it is found growing down to the sea level but in the Sierra Nevada the requisite moisture for its growth is not found much below an elevation of 4,000 feet. As we go upward the pines become fewer and the furs and big trees take their places. The big trees are found in scattered groves at an elevation of 5,000 to 8,000 feet for a distance of 250 miles along the slopes of the Sierra Nevada mountains. The Sequoia as the genus is called which also includes the redwood of the coast ranges is in many respects the most remarkable of all our coniferous trees. After traveling through the forest made up of other trees of great size it is difficult at first to appreciate the magnitude of the big trees. Rising from a swelling base which is sometimes 30 feet in diameter the symmetrical trunk reaches up and up finally terminating in a top 300 to 350 feet above the ground. Their size their reddish brown bark and their small cones clearly distinguish these trees. Great holes have been burned in many of them and in the hollows thus formed men have made for themselves comfortable living rooms. In one of the southern groves a fallen hollow tree has been used as a cabin. The big trees in redwoods are the last surviving species of a genus which was once widely distributed over the earth. The ancestry of the Sequoia can be traced farther back than that of any of the other living conifers. Impressions of cones and small stems with needles attached belonging to the Sequoia have been found in the oldest rocks of the coast ranges of California. These cones and stems were washed into some muddy estuary and they're buried millions of years ago. The mud enclosing them was compressed and hardened and finally changed to slate. This was at last exposed upon the surface through the uplifting of a mountain range and the work of erosion. Some of the groves of the big trees have been included in government parks and reservations but others are being cut as rapidly as possible by the lumbermen. The redwood of the coast ranges is not easily killed for it sprouts from the stump and will in the course of time form forest again but the big trees rarely replace themselves when a grove has been cut down. These trees are so few in number and of such remarkable interest that they should be spared the fate of the common forest tree. It would make you feel sad to visit one of the groves and see as I did a fallen giant fully thirty feet in diameter lying split open upon the ground. This tree was so large that in order that it might be handled at all powder had to be used to blast it in pieces. The tree was naughty and according to the lumbermen of little value and might as well have been left. What excuse is there for the wanton destruction of a noble tree like this one? It must have stood from five thousand to six thousand years. It was a mighty tree at the beginning of the Christian era and was growing a strong tree when our ancestors were the rudest savages of the wilds of Europe. But we must not remain among the big trees for the forest extend much farther up the mountains. The most important tree of the upper forest belt is the fir which is found growing from five thousand to nearly nine thousand feet above sea level. It is one of the most graceful of the conifers. Sometimes these trees reach a height of two hundred and fifty feet and form dense forest with little undergrowth. The branches make the soft fragrant beds which sow rest and delight the tired mountain climber. Here and there about the springs and at the heads of the streamlets the firs appear to stand back making room for green meadows brightened with a perfusion of flowers. The tamarack or lodgepole pine is sometimes found at about the same elevation as the first but seems to prefer the moist lands about the meadows and the bottoms of the narrow valleys. This tree is widely distributed at high altitudes all over our western mountains. Continuing our climb toward the alpine regions we reach an elevation where the trees begin to show the effects of the winter storms. The fact that life is not so easy as it is farther down the slopes is apparent from the gnarled and stunted trunks. Here are the alpine hemlocks dwarf pines and junipers. The juniper somewhat resembles the cedar but has a short thick trunk. Near the timber line this tree grows but a few feet high and becomes exceedingly gnarled. It seems to like the most exposed and rocky places but in truth like many another form of plant life it has become accustomed to such locations because it cannot successfully compete with other trees in happier ones. Most weird and picturesque of all are the dwarf white pines growing upon the extensive mountain shoulders and ridges at a height of 10,000 to 11,500 feet above the sea. Since an arctic climate surrounds them for nine months of the year their growth is very slow. Their short, gnarled trunks and branches are twisted into all sorts of fantastic shapes. When after struggling with the cold and the storms the trees at last die. They do not quickly decay and fall but continue to stand for many years. These trees become smaller and smaller in size until at the extreme timber line they are almost prostrate upon the ground. In many cases they rise only three or four feet and have the appearance of shrubs rather than trees. Still above them however there are rocky slopes and snow banks reaching to an elevation of over 14,000 feet. If we examine these upper slopes carefully we shall find that they are not utterly devoid of life but that certain plants have been able to obtain a foothold upon them. In sheltered nooks there are little shrubs and lichens. In some places among the rocks beneath overhanging snow banks beautiful flowers spring up at the coming of the late summer. Blossom, mature their seeds and die with the return of the winter cold. The magnificent forest through which we have passed in our long climb if destroyed by the lumbermen cannot be replaced for hundreds of years. They contribute much to the glory of the mountains. They hold back the water so that it does not run off rapidly and thus aid in giving rise to innumerable clear cold springs. The springs help feed the streams during the long dry summers when the water is so sorely needed in the hot valleys below. End of Chapter 31 Chapter 32 of the western United States. This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer please visit LibriVox.org. The Western United States A Geographical Reader by Harold Wellman Fairbanks Chapter 32 The National Parks and Forest Reserves The people who first pushed into the unknown country west of the Mississippi in the earlier half of the last century were chiefly hunters and trappers. They did not intend to make permanent homes in the wilds, but rather to stay only so long as they could secure an abundance of fur-bearing animals. Then came the discovery of the precious metals and thousands of gold-seekers crossed the plains and spread out over the mountains of the Cordillian region. They too expected to get rich by making use of the resources of the country and return to their homes in the east. At the present time the destruction of our forest and serious injury to the water supply has been threatened through the organization of large lumber companies. Those interested in lumbering usually live far removed from the scenes of their operations and consequently care little about the condition in which the deforested lands are left. The farmers were the first permanent occupants of the west. Unlike the wandering trappers and miners they established homes and made the land richer instead of poorer. As long as the population was scanty there was not much danger of exterminating the wild animals and the demands for timber were small. Our forefathers who settled the eastern states had to contend with the forest. Nearly every acre of ground had to be laboriously cleared before anything could be planted. It was only natural that they should come to regard the forest as a hindrance rather than a blessing. As the settlers spread westward to the prairies and plains they came upon a region almost destitute of forest. But still farther in the mountains of the continental divide and the pacific slope they again found extensive forest. To them it seemed impossible that these forests could ever be exhausted and therefore little care was taken for their preservation. As the population increased more and more lumber was needed for building purposes. Before the sawmill came split lumber was used and the shaker maker did not hesitate to cut down the largest and most valuable pines on the mere's possibility that fifteen or twenty feet of the butt would split well enough to make shakes. It made no difference to him that the whole trunk rotted upon the ground. When the sawmills were built and there came a demand from abroad for lumber the forest were attacked upon a much larger scale. The need of the moment was all that concerned the lumbermen and they took no care for the preservation of the young trees which in time would have renewed the supply. The litter of the trunks and branches which they left upon the ground furnished fuel for the fires which frequently swept over these areas and killed their remaining growth. As a result of these fires the few animals that have escaped the hunters have been killed or driven from their homes and the forest cover which would retain much of the moisture and preserve it for the supply of the streams in summer has been destroyed. The removal of the forest cover leads also to the washing away of the soil the shoaling of the streams floods in spring and low water in summer. In fact all the people and industries of the region are affected by its loss. It may take hundreds of years for the country to recover. Indeed if the rainfall is light the forest may never grow again without artificial aid. Seeking to enlarge his pastures by burning the underbrush sets fires which often destroy hundreds of square miles of forest. The summer camper and the prospector also frequently go on their way without extinguishing the campfire though a great forest fire may be the result. Ours is a fertile and productive earth capable of supporting a multitude of living things. For ages the lower animals as well as savage man lived under the protection of nature making the best use of her products of which they were capable. But they never brought about the unnecessary and often wanton destruction of which we are guilty. We who call ourselves civilized. In killing the wild animals we cannot make the plea of necessity as can savages who have no other means of support. Likewise there is no necessity for killing the beautiful singing birds merely for their plumage. The forest are cut away without any thought of the retribution which nature is sure to bring upon us. They are a vast importance to the well-being of the country and are the natural possession of all its people. We ought not to permit them to be destroyed indiscriminately for the benefit of a few. We need lumber for many purposes but a careful treatment of the forest with an eye to their continuance, the plan of cutting large trees and preserving the small ones, is a very different thing from our present wasteful methods.  Books of travel, written fifty years ago, tell of animal life in such abundance in many portions of the West that we can hardly believe their stories. A description of California written in 1848 mentions elk, antelope and deer as abundant in the Great Valley. How many of us living at the present time have ever seen one of these animals in its native haunts. There is hope now that this wasteful use of nature's gift will soon be stopped. Large areas of the mountainous portions of the public domain are being set aside as parks and forest reserves. The parks contain some of the finest scenery and most wonderful natural curiosities to be found upon the face of the whole earth. This wild scenery, together with the forest and plants of every kind, as well as the animals and birds that inhabit these areas, are to remain just as they were when the first white man looked upon them. The parks form asylums for the wild creatures which have been hard pressed for so many years. In the Yellowstone National Park, where they have been protected the longest, the animals have lost their fear of man and act as if they knew that they are safe within its limits. In the Yellowstone you may see great herds of elk feeding in the rich meadows, deer stand by the roadside in what you pass, while the bears have become so tame about the hotels that they make themselves a nuisance. Sixteen bears at a time have been seen feeding at the garbage pile near the Grand Canyon Hotel. The forest reserves differ from the parks in that they are established for utility rather than for pleasure. The forests now existing are to be cared for by the government and to be wisely used when lumber is needed. Fires are to be avoided so far as possible and burned areas are to be replanted with trees. Another object to be accomplished is the restitution of the forest about the heads of the streams so as to preserve the summer water supply. Another object to be accomplished is the retention of the forest about the heads of the streams so as to preserve the summer water supply. The water runs off more slowly from a slope covered with vegetation than from a barren one and therefore has more time to soak into the ground. This is a very important matter in all mountainous districts, particularly where the rainfall is light. The Yellowstone National Park is situated upon the Continental Divide in northwestern Wyoming. It is largely a plateau with an elevation of 7,000 to 8,000 feet above the level of the sea. The surface of the plateau is covered with forest, meadows, and lakes, but the region is particularly remarkable for the geysers and hot springs, and the Grand Canyon and falls of the Yellowstone River. Springs dot the surface of many parts of the park. The hot water is continually bringing mineral substances, the chief of which is silica, from the depths of the earth and depositing them about the orifices of the springs. In this manner wonderful basins, terraces, and cones have been built up, while the rocks have been either reddened or bleached out and softened into a form of clay. The park region must have been for a long period the seat of volcanic action, for nearly all of the rocks are cooled lavas. While the heat has disappeared from the surface it must still be very great below, if we may judge by the quantities of hot water continually issuing from the springs. In many a subterranean cavern steam accumulates until its pressure becomes too great for the column of water occupying the channel that leads to the surface. Then the water is suddenly and forcibly expelled giving rise to a geyser eruption. When the pressure of the steam has been exhausted the water sinks back into the earth leaving the basin of the geyser nearly or quite empty until the steam has again collected. Each geyser has its own period of eruption and is generally very regular. One little geyser known as the economic because it throws out but little water spouts regularly about every five minutes. Other geysers are active at intervals of several hours while some take several years to get ready for a new eruption and then spout whole rivers of boiling water. In the upper geyser basin the effect is very impressive particularly upon a cool morning. The clouds of steam and the throbbing or roaring geysers lend to the region a weird and unearthly aspect. The Yellowstone Lake is a large body of water situated almost upon the continental divide. Before the canyon or Great Falls or even the Yellowstone River itself existed the lake stood about one hundred and fifty feet higher than at present and its water emptied into the Pacific Ocean instead of the Gulf of Mexico. The drainage was changed by the work of a small stream having its source in the volcanic plateau north of the lake. It deepened its channel and extended its head waters back until they tapped the lake at a point where the rim of the basin was lowest and so drew away its waters in the opposite direction. The Yellowstone River with its deep, wondrously colored canyon and grand waterfalls is the result of this change. To the south of Yellowstone Park but included in one of the forest reserves are Jackson Lake and the Teaton Range. The three Teatons one of which reaches a height of over thirteen thousand feet were evidently noted landmarks for the hunters and trappers in the early days for you will find them mentioned in many of the narratives of those times. The precipitous range with its crown of jagged peaks and the beautiful lake nestling at its base presents a picture never to be forgotten. Very different from the region which we have been studying is that embracing the Crater Lake National Park which is situated upon the summit of the Cascade Range in Southern Oregon. Here occurred not many thousand years ago one of the strangest catastrophes which so far as we know has ever overtaken any portion of our earth. Towering over the present basin of Crater Lake was a great volcano reaching probably nearly three miles toward the sky. During the glacial period it stood there. It slopes white with snow, apparently as strong and firm as Shasta or Hood or Rainier. But for some reason the volcanic forces within this mountain which has been called Mazama awoke to renewed action. The interior of the mountain was melted and the whole mass unable to stand longer fell in and was engulfed in the fiery seething lava. This lava instead of welling up and filling the crater and perhaps flowing out was drawn down through the throat of the volcano into the earth and left an enormous pit or crater where once the mountain stood. After the floor of the crater cooled and hardened small eruptions occurred within it and a new volcano grew up. But though nearly three thousand feet high it does not reach to the top of the encircling walls of the old crater which are on an average nearly four thousand feet high. Then the rains and melting snows formed a body of water in the crater and the wonderful lake came into existence. No such site is to be found elsewhere upon the earth. Within a circling rim of cliffs from eight hundred to two thousand feet high and nearly vertical lies the lake. Rivaling the sky in the depth of its blue coloring. The height of its encircling cliffs and its five mile expanse of blue water helped to make the lake a spectacle grand beyond description. At the present time the volcanic fires appear to be entirely extinct. Forest of fur and tamarack have spread over the once barren slopes of lava and humus which extend back from the cliffs. In the hollows after the lingering winter snows have melted there are grassy meadows dotted with flowers. It is many miles from the lake to any human habitation and all the region about remains just as nature left it. It was a happy thought to make another national park here. We have already learned something of the grandeur of the Yosemite Valley and have seen how it came into existence. The valley is owned and cared for as a public park by the state of California. But with Hetch Hetchy Valley it is included in a larger park under the control of the general government. Within the boundaries of this national park as in the case of the others described the natural features of the landscape, the forest, and the animals are to be left forever undisturbed. The Yosemite Valley, although situated in the heart of the rugged Sierras, is reached by several good wagon roads and many more people visit it than go to Crater Lake, though the latter is fully as interesting. About a hundred miles south of the Yosemite is the general Grant National Park. This park is of comparatively small size but contains a group of some of the largest and finest big trees in the country. Still farther south there is a reserve called the Sequoia Park which contains the largest remaining groves of the big trees. There are also many state parks scattered over different parts of the union. The establishment of these parks is intended to preserve either the forest or natural scenery. The retention by the state or general government of large tracts of mountain and timberland and of those areas which are particularly interesting on account of their natural scenery is of the greatest importance. The timber and water are preserved for the general good instead of being squandered for the enrichment of individuals. The preservation of scenic features in their original wild state is just and right because such things add to the pleasure of out of door life, elevate men's feelings and cultivate a love for the beautiful. The protection afforded the plant and animal life by these reserves gives a better opportunity for studying them and tends to foster a general interest in the welfare of living things.


Every bird has a nest, every crab has a hole, every human being must have a house. As the economy started to grow, we started having the internal migration. As in every country, the city is the glitter, the city is the magnet. People coming down to look for work, have a new middle class. At that time, let's look at what the Senutia society was at the time. A girl would stay at home, at her parents' home, until some gentleman, and I say gentleman, would take her away. You know? Now, the economy is getting modern. The girls who were working aside, they're not waiting for any gentleman. They want their own homes. So, must provide for them. What did we have? We're on castries. Look at castries. You had castries, the area where they used to call the Hollywood. It's not there anymore. There was Brooklyn and Hollywood, some little mother cottages there. That side, you go up to the show say, and you go down to Castries River, and then you meet the sea. That's the totality of castries. Then you have the slums of the Conway, and the slums of Marsha, and the slums of Warsaw. That's the totality of castries. So, you had to get land. And in getting land now, you again closed in by history. You know, history now box you in. You still have, you still find the land even in all the land in the vicinity of Castries, owned by the old families. San Soci was owned by the Barnard family. His clavier owned Antropole, and that area. So, they had the moan owned by the War Department in England, or the moan area, moan and kubari owned by the War Department. So, what do you do? So, we decided, look, we have to acquire. We are going to buy the lands once it becomes, once it comes on the urban pressure we have to acquire. So, we negotiated with the Barnard family, and we bought the Conway and San Soci. We negotiated with the clavier family, and bought Antropole. We negotiated with the British War Department, and bought the lands, bought the moan. We created organizations. We created the Urban Development Corporation, the UDC. And the UDC first, it was first the moan development. Then it was the moan and San Soci development, and as we expanded became the Urban Development Corporation. The first chairman of the moan development was Alan Busque. But when Alan became a minister, I then expanded it, and I brought in Reginald Mitchell to handle the UDC.  He was both engineer. He was architect. Metatoud Fair. And we then, first development was at the San Soci. We sold those houses, and a lot for $17,000 complete. I hear the noise in the market steps now. Don't buy. The place is swamp. It's going to sink, etc. etc. But people who bought at the time now had a sweepstake. Then we went to the moan, the moan development. Because of the access road to the moan, it was difficult. People didn't have cars. They had to get home. So the moan went very slowly, until we started improving the road to the moan, and then more and more people started living there. So we had the Urban Development Corporation. When we were doing the redway, we would speak about the redway. Otherwise, also we used the Urban Development Corporation to buy land at Redway. Redway Orchard, Redway Park, UDC. The people in the eastern area, they wanted lands. What was up at Antropo? A cocoa estate. So we acquired and built, put the Antropo Development and more and more people going. So you had to create the blocks, the building blocks, the organizations. So in agriculture, we had the bank. It's not only agriculture. Agriculture expanded into fishing, to small businesses, etc. Until, of course, it's dismantled now.  So we gave now the middle class, the teachers, the nurses, the civil servants, the persons in the banks, give them an opportunity for the first time to own a piece of solution through the Urban Development Corporation. We also now created the San Lucia Mortgage Finance Company so they can go and borrow money from there. We strengthened the cooperative bank, you know, in order to, because hopefully the bank was, at one time, was the only bank that would lend, do long-term lending.


A warm welcome to the 27th lecture on the subject of wavelets and multirate digital signal processing. In the previous lecture, we had completed or almost completed the proof of the theorem of multiresolution analysis. So, in a certain sense, we are at a cross point, a juncture, where we need to explore more avenues. We have understood a whole approach to building multiresolution analysis. We have talked about orthogonal filter banks in great depth. We have also established the connection between the continuous time functions phi t and psi t and the filter banks. And we have brought out a proof that given the axioms of the multiresolution analysis, we are guaranteed the existence of a wavelet psi t, whose dietic dilates and translates can span the whole of L 2 R. And we did that by essentially considering one peel, we looked at one incremental subspace and we showed that that incremental subspace namely W 0 could be spanned by the translates of a single function psi t. And in fact, the function psi t was a linear combination of the basis elements in V 1 as expected. And we could also characterize the coefficients of the linear combination. So, in that sense, the proof that we had in the previous lecture was constructive. Now, the aim of the lecture today is first to complete a few details in the proof that we attempted the last time and to take further by introducing variance. So, what we intend to do today is first to begin with a few details of completion of the proof and that would in fact lead us to the possibilities of varying the notion of multiresolution analysis in ways that will make our time frequency possibilities richer. So, to take the first task that is to complete a few details of the proof of the theorem of multiresolution analysis. The first thing that we need to complete is to prove that psi t is orthogonal to phi t and its translates. We have already shown psi t belongs to V 1 of course and can be expanded as follows. psi t is summation on all integer n g n phi 2 t minus n, where g n is the impulse response of the analysis high pass filter. That is interesting. Expressing phi t in terms of the basis of V 1 involve the coefficients of the low pass analysis filter and expanding the wavelet in terms of the basis of V 1 involve the impulse response of the analysis high pass filter. In fact, just to complete an example let us look at the Haar case. In the Haar case the high pass impulse response is essentially 1 and minus 1 and as expected the Haar wavelet is indeed 1 times phi 2 t minus 1 times phi 2 t minus 1 as an example. Now, let us make an observation in general here. So, what we are saying in effect is if we take g n essentially to correspond to the inverse z transform of z raise the power minus l minus 1 h of minus z inverse, where h of z is the analysis low pass filter. Then what we wish to do is essentially to analyze the following dot product. The dot product of psi t with phi t minus m for any integer m and this is easy to do. Indeed psi t by itself is summation on n g n phi 2 t minus m phi t minus m is simply summation on n and here again I imply summation on all integer n. So, as so as not to confuse these two indices I shall write n 1 here. So, n 1 h n 1 phi 2 t minus 2 m minus n 1 taking a q from expanding phi t minus m in the basis of the high pass basis of v 1 as we can do where upon this dot product is essentially a summation on n a summation on n 1 g n h n 1 complex conjugate times the following dot product phi 2 t minus n minus 2 m minus n 1. Now, once again without going through the whole derivation again I might observe that this dot product is 0 save for the case when n is equal to 2 m plus n 1 and in fact that means that we can drop one of these two summations. We could if we like drop the summation on n what we are saying essentially is that phi 2 t minus n dot product with phi 2 t minus 2 m minus n 1 is half delta n minus 2 m plus n 1 and therefore, we can drop the summation on n and leave summation on n 1 g. Now, you know this is an impulse a discrete impulse which has a non zero value only when n is equal to 2 m plus n 1. So, in place of n we substitute 2 m plus n 1 of course, h n 1 complex conjugate and a factor of half which is not a terribly serious matter at all. Essentially, this is the cross correlation of the sequences g and h evaluated at 2 m for all integers m looks familiar does not it we have been doing this frequently. Now, one can again evaluate the cross correlation by going into the z domain. So, obviously the z transform of the cross correlation can be seen to be essentially g of z times h of z inverse and we know what g of z is g of z is essentially the system function of the analysis high pass filter which is z raise the power minus l minus 1 h minus z inverse and therefore, we have the cross correlation z transform essentially becomes z raise the power minus l minus 1 h minus z inverse h minus z inverse times h z inverse. Now, for the moment let us simplify matters assume the impulse response is real. We can of course, generalize all these results to when the impulse response is complex, but that is not the critical issue here. Let us not get confused by the complex conjugate every time. Anyway, now all that we need to do is to look at the values of the cross correlation at even locations and we know how to do that. If the z transform of the cross correlation is some function of z, we take the same function of z with z replaced by minus z at the two together and see what happens. That tells us about the values of the sequence at even locations. Let us do it for this cross correlation sequence. After that z raise the power minus l minus 1 h of minus z inverse times h of z inverse plus the same thing with z replaced by minus z is as follows.  This is very interesting. Remember l is even. We have agreed that our orthogonal filter bank is going to have an even number of samples in the impulse responses. If it does not, then we are going to have a problem in the requirement of orthogonality to even shifts. So, take for example the Doberts series. Obviously, their impulse responses are of even length. In fact, it is not too difficult to show that even if you assume an odd length, you will find the last sample must be 0 for the requirement that the impulse response be orthogonal to its even shifts. Anyway, coming back to this, since l is even, l minus 1 is odd and therefore minus 1 raise the power l minus 1 is minus 1. As you can see, this term and this term are exactly identical if you just interchange the order of the products. Therefore, these two cancel. This is identically 0. Therefore, the cross correlation of g and h is 0 for all 2 m and that amounts to saying that the dot product of psi t and phi t minus m is equal to 0 for all integer m, which is exactly what we had set out to prove. So, we have completed that little detail and in completing that detail, we have also brought out an important issue, namely the intimate connection between the z domain representation of the filters and orthogonality of the functions. We had seen this implicitly in the proof at points. In fact, now to take this discussion a little further and to give you a feel of the connection in a slightly greater depth, let me again take the issue of orthogonality of phi t with its own integer translates. How does that manifest on to the behavior of the autocorrelation of the low pass filter impulse response? So, in fact, if we look at the function phi t and its integer translates, consider the dot product of phi t and phi t minus m. We can see that it can use a similar set of steps as we have just done. So, I would not repeat all the steps that this is equal to summation on n h 2 m plus n h bar n and then of course, you have you know you have a factor of half there. So, it is essentially the cross or the autocorrelation of the impulse response of the low pass filter. Now, once again we are evaluating the impulse response at only even locations. So, let me first write down the z transform of the impulse response. You know you will remember the z transform of the autocorrelation of the impulse response would essentially be h of z times h of z inverse. What we are asking is what is h z h z inverse plus h minus z h minus z inverse. This is essentially what would tell us about the values of the autocorrelation at the even locations. Now, we know the answer to this by the very design of an orthogonal filter bank. This is essentially a constant. So, the design equations for an orthogonal filter bank ensure that this quantity h z h z inverse plus h minus z h minus z inverse is a constant and therefore, the autocorrelation is 0 at all even locations. Let us call them 2 m except for m equal to 0. That is why you get that constant non-zero constant. So, there is a very beautiful observation we have made. The so called power complementary property that is also a consequence of this essentially manifests as the orthogonality of the impulse response to its own even translates and that also becomes a part of establishing the orthogonality of phi t to its own integer translates. So, they are all related. Now, this again brings out the intimate connection between the autocorrelation behavior of the filters in the filter bank and the orthogonality requirements that we insist upon in the underlying continuous functions that are generated on iteration of the filters in the filter bank as we have done before. You know how to iterate the impulse responses, convolution of the impulse responses to go towards phi t and psi t. Now, what are the variants that we can introduce at this point? You see when we look carefully at these equations, I mean we put them all down together like this and when we look at them from these perspectives, we see that there are many things which we have not done to date which can we can probably explore and let us put them down one by one. The first thing we need to explore is must we have essentially the same analysis and synthesis filters. Of course, this leads to an orthogonal filter bank, but then you know remember when we talk when we move from the continuous wavelet transform towards the discrete wavelet transform going through one step where we discretized the scale parameter logarithmically, we had made a remark. We had come to a point where we said there are two options. Either have different wavelets psi and psi till day on the analysis and synthesis side and build different analysis and synthesis filter banks and get perfect reconstruction or use the same wavelet on the analysis and synthesis side, but that so called quote unquote same wavelet would be different from the wavelet from which we started. In case the discretization of the scale parameter was such that the sum of dilated spectra did not come to a constant for all frequencies, but lay between two positive bounds, we could bring in a new wavelet which gave us an orthogonal analysis and synthesis filter bank. The wavelet would be the same psi double till day, but different from the original wavelet psi from where we started. So, there were two options. Now, we must explore the same two options in the context of discrete filter banks. Establishing the connection between the continuous case and the discrete filter bank is an involved exercise, but taking inspiration from the continuous case from the continuous wavelet transform and realizing that there are these possibilities to be more general namely that you could have different analysis and synthesis filters and come up with a variant of the concept of multi resolution analysis is certainly something that we should explore in depth. And in fact that needs to be explore in depth for another reason. One of the most recent data compression standards actually employs a filter bank with that perspective. Let me say a little more about this. You see wavelets have been rather successful in the area of data compression. In fact, the central idea in wavelet based representation is that you can represent both global and local information efficiently with a few number of with a few coefficients. So, you could take transient information or short lived information and represented with few coefficients in the details and long lived information or you know information spread all over the interval over which the signal last and also represented with few coefficients in the approximation part. And therefore, wavelets are an attractive proposition for data compression. Now, using this fact the joint photographic experts group or GPEG as it is called for short came up with what are called the GPEG 2000 standards. 2000 refers roughly to the year around which these standards were finalized. So, GPEG 2000 standards for data compression actually employ what are called bi orthogonal filter banks. And in the lecture today we shall look at these bi orthogonal filter banks in some depth. So, bi orthogonal filter banks are filter banks where the analysis and the synthesis filters are not quite the same. In other words you do not just have one analysis low pass filter from which everything else is derived by small variations of replacing z by minus z or z by z inverse and so on. There are essentially in a in fact in the GPEG 2000 standards. There are essentially two filters and the other two are derived out of them. So, we come to that in slightly greater depth in a few minutes. But before that let us look at some other variants that are possible. Now, so far we have been looking at finite impulse response filters. Do the filters in the filter bank have to be finite impulse response? Well obviously the answer is no. One does not have to have a finite impulse response which one could certainly conceive of an H z or for that matter a G z I mean H 0, H 1, G 0, G 1 where the sequence underlying the z transform is infinite in length as an infinite number of non-zero samples nothing stops us from considering such H z and G z. So, we have to admit that possibility and actually when we look at the 5 3 filter bank as it is called in the JPEG 2000 standards we will see that if I insist on getting an orthogonal filter bank solution for this kind of a paradigm we need to go to an infinite length impulse response filter bank. We shall build that up in a subsequent lecture. So, this is the second variant that we wish to explore must be restrict ourselves to finite impulse response filter banks. The third variant which we need to explore is as follows must we always iterate on the low pass branch and obviously again the answer is no. In principle nothing stops us from putting the whole filter bank back on the high pass branch let me put before you what I am saying graphically. What I am saying is this the discrete wavelet transform looks like this essentially we have a low pass filter and a high pass filter where the finite or infinite length that is not the issue followed by a down sample and we keep iterating here. So, we put the low pass filter here and the high pass filter there and down sample once again and keep doing this.  In fact it is obvious that if you were to take one stage of this namely if I were to do the following I were to take the input I were to subject it to the action of a low pass and high pass filter followed by down sampling as usual followed by iteration here LPF HPF down by 2 and down by 2 there. But also do the same here I could get back here by using the corresponding synthesis filter bank for this and I could get back here by using the corresponding synthesis filter bank for this and once I get back here and here. Now, please remember of course I would get back with a constant multiplier and a delay, but that is not such a serious issue I mean I can always take both the constant and the delay across the down sampler and I could actually absorb it with these filters here and finally, I could in principle reconstruct this once I have got here. So, whatever argument allowed me to decompose on the low pass branch every time can also allow me to decompose on the high pass branch. So, there is a new possibility that has opened up suppose I were to conceive of decomposing the high pass output what does it imply for the underlying functions and that would lead us to the idea of what is called the wave packet transfer. The central idea in the wave packet transform comes from iterating on the high pass branch as well not only the high pass branch, but allowing for iteration on the high pass branch also that would lead us to the idea of the wave packet transform. So, this is a brief introduction to the variance of the idea of multi resolution analysis that we wish to explore one by one. Now, let us begin with the first of the variance namely the filter bank used in JPEG 2000 let us not be too general. Let us consider one particular filter bank which is used in JPEG 2000 where the filters are of different lengths the analysis filters are of different lengths and that would lead us to the idea of what is called a bi orthogonal filter bank or a filter bank where we do not quite have orthogonal scaling functions or scaling functions which are orthogonal to its to their translates. Now, you know how the inspiration for the 5-3 filter bank in the context of JPEG 2000 could be seen to be the following there are various ways to explain the inspiration, but one of the inspirations can be seen to be the following. Let us begin with the Haar case where we have the dilation equation for phi t given as follows phi of t. Now, you know just to ease our notation we shall call the corresponding scaling function for the Haar MRA as phi 0 t we will understand why the 0 in a short while phi 0 t is phi 0 2 t plus phi 0 2 t minus 1 and you will recall that this translates graphically to the following this is phi 0 t this is phi 0 2 t and this is phi 0 2 t minus 1 this explains what we are saying graphically. Now, suppose we convolve this equation with itself. So, we write the equation down twice and convolve it with itself what would happen?  In other words we are asking the following general question given h t convolved with g t to be r t what is h t with g a t plus b convolved with g a t plus c please note a the same a is used here b and c can be different, but the same scaling factor is used a of course belongs the set of real numbers same scaling that should be emphasized and a is real. In fact, let us evaluate it indeed h a t plus b convolved with g a t plus c as we desire here is essentially integral h a lambda plus b g a t minus lambda plus c d lambda integrated overall lambda and we use the standard principle of substitution of variable.  Now, there are two possibilities a is of course not equal to 0 and a is real. So, when a is greater than 0 d gamma is of course always a d lambda and lambda going from minus to plus infinity translates to gamma also going from minus to plus infinity on the other hand when a is negative of course, d gamma is as usual a d lambda, but lambda going from minus to plus infinity translates to gamma going from plus infinity to minus infinity. However, if you look back at the limits of the integral here. So, you know when a is positive d lambda is going you are going to have d gamma as a d lambda. So, you know you are going to have a factor of a coming here in general a 1 by a. So, here d lambda is going to be d gamma by a. So, 1 by a is going to be positive if a is positive 1 by a is going to be negative if a is negative when a is negative these limits are reversed when a is positive the limits are where they are. So, all in all we can write down the following we can say in general or rather a lambda let us make it a lambda is equal to 1 by mod a integral minus to plus infinity h gamma g gamma well actually let me let me work this out. So, a t minus a lambda plus c is essentially a t minus gamma now minus gamma means minus a lambda minus b plus b plus c.  So, I am saying essentially it is 1 by mod a integral from minus to plus infinity h gamma g a t plus b plus c minus gamma d gamma and this is obviously the convolution of h and g evaluated at a t plus b plus c. So, we have the answer now h a t plus b convolved with g a t plus c is essentially 1 by mod a h convolved with g evaluated at a t plus b plus c and we can use this in the dilation equation that we had a few minutes ago. Therefore, using this and denoting phi 0 t convolved with phi 0 t as phi 1 t and now I will explain why I am calling it phi 1 t what is phi 0 t convolved with phi 0 t this is phi 0 t when you convolve it with itself it gives you a function that looks like this this is phi 1 t what is 1 about this and 0 about this the degree of the polynomial if you look at it phi 0 t is essentially piecewise polynomial with the polynomial of degree 0 constant phi 1 t is piecewise polynomial with polynomials of degree 1 linear. So, you could similarly conceive piecewise polynomials of higher and higher degree. So, you could have a phi 2 t in fact if you take phi 1 t and convolved with phi 0 t once again you would get a so called phi 2 t a piecewise polynomial with polynomials of degree 2 and if you keep repeating this the degree of the polynomial increases by 1 every time. So, that is the reason why 0 1 2 and so on. Anyway coming back to the dilation equation phi 1 t can easily seem to be half phi 1 t plus 2 phi 1 2 t well phi 1 2 t I am sorry plus 2 times phi 1 2 t minus 1 plus phi 1 2 t minus 2. In fact, what we are saying essentially is that phi 0 t convolved phi 0 2 t convolved with phi 0 2 t minus 1 is the same as phi 0 2 t minus 1 convolved with phi 0 2 t and both of them are equal to half phi 1 2 t minus 1. This is a simple application of the result that we derived a few minutes before and in fact this can be seen graphically. You know if you draw phi 1 t let us draw it large and big it is not very difficult to see that if you were to mark the half points here and draw these triangles this is essentially half phi 1 2 t this is essentially half phi 1 2 t minus 2 and this is essentially phi 1 2 t minus 1 I mean this means this here this means this here and this refers to this here. So, this piecewise linear function plus this piecewise linear function plus this piecewise linear function would obviously give you this solid piecewise linear function it can easily be seen graphically. In fact, linear functions are easy to add you need to add them only at the end points. For example, here the sum is this at this point the sum is essentially this at this point the sum is essentially this. So, you can see that these three dilates and translates of phi 1 t give you back phi 1 t and therefore, phi 1 t obeys a dilation equation in its own right and what are the coefficients of the dilation equation the coefficients in the dilation equation phi 1 t is half phi 1 2 t plus phi 1 2 t minus 1 plus half phi 1 2 t minus 2 are essentially half 1 and half and if you put a filter to represent these coefficients that filter would essentially be the following. This filter is easily seen to be 1 plus z inverse the whole squared, but there is just one short coming here. Unfortunately, phi 1 t is not orthogonal to its integer translates in general. Let me show this to you graphically. If you consider phi 1 t and phi 1 t minus 1 this is phi 1 t and this is phi 1 t minus 1 they are not orthogonal. So, we have a problem although phi 1 t obeys a dyadic dilation equation and in fact, in principle one could also start investigating the basic axioms of a multi resolution analysis. The axiom of orthogonality is not obeyed. So, now we have two options. We can ask whether we can do something similar to what we did in the discretization of scale. If not quite a constant I am talking about the sum of dilated spectra, we said if that sum of dilated spectra is not quite a constant could be allowed to be between two positive constants. So, something similar could possibly be investigated here that is one option. The other option is think out of the box and in fact, we will do that first and come to the JPEG 5-3 filter bank. Why stick to the same analysis and synthesis filters? Can we allow different lengths for the low pass and high pass filter, analysis filter and then therefore, derive the synthesis filters in a slightly different more relaxed way from the analysis filters and establish a perfect reconstruction filter bank and that is what we shall do in the next lecture. Investigate that variant think out of the box, do not insist on orthogonality or do not insist on using the same axioms of an MRA. Build a perfect reconstruction filter bank where you have different length analysis and synthesis filters. I mean different length analysis high pass and low pass filters and therefore, different analysis and synthesis filters and build a different paradigm for multi resolution and this is out of it. So, we shall proceed the next time to derive the JPEG 2005-3 filter bank.


Hamas movement declared war on Israel, swords of iron operation began. The radical Palestinian movement Hamas has declared war on Israel and the Israeli military is fighting the enemy, Israeli Defense Minister Joav Galant said. The Hamas movement made a serious mistake and started a war against the state of Israel. Units of the Israel Defense Forces are fighting the enemy everywhere, the minister said. Galant also ordered the introduction of a special security situation in central Israel and the south of the country amid rocket attacks from the Gaza Strip that began on the morning of the 7th of October. The Israeli army has launched attacks on the Gaza Strip after massive rocket fire from the Palestinian enclave the army press service reported. The name of the Israeli offensive, which saw multiple airstrikes in the Gaza Strip and the call-up of thousands of reserve troops for potential ground operations was given the codename swords of iron. Officers of Palestinian militants fired 5,000 rockets into Israel, al-Arabiya TV reported citing a statement by representatives of the Palestinian movement Hamas. The Hamas has named the terror attack operation al-Aqsa. Hamas deputy leader Salah al-Arouri stated that the objective of the operation is to defend al-Aqsa and release the prisoners. In addition, top Hamas leaders abroad were seen in television images. We thank Allah for this victory, said Hamas leader Ismail Haniyeh. His deputy, the terrorist strategist Salah al-Arouri, was also documented alongside him. Television authorities decided to cancel all public events in the city and close to the city's beaches. The Hamas terrorist organization carried out a combined attack including the firing of rockets and terrorist infiltrations into Israeli territory from the Gaza Strip the Israeli foreign ministry wrote on X. The Israeli will defend Israeli civilians and the Hamas terrorist organization will pay a heavy price for its actions. Civilians are asked to act according to the special instructions posted on the National Emergency Portal and stay adjacent to shelters. Residents in the areas surrounding the Gaza Strip are asked to stay in their homes, the ministry said.