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Catholic Encyclopedia (1913)/Edda

Edda, a title applied to two different collections of old Norse literature, the poetical or "Elder Edda" and the prose or "Younger Edda". Properly speaking the title belongs only to the latter work, having been given to the former through a misnomer.

I. "The Younger Edda", the work of the Icelandic historian and statesman Snorri Sturluson (1178-1241), is a treatise on poetics for the guidance of the skalds or Icelandic poets. The title "Edda" is given to this work in the most important manuscript which we possess of it, the "Upsala Codex", dating from about 1300. The meaning of the word Edda is not certain. The older explanation of "great-grandmother" is now generally discarded, the most commonly accepted rendering being "poetics" (from óthr, "spirit", "reason"). Some scholars derive the word from Oddi, the name of a place in southern Iceland, where Snorri received his earliest training. The work itself was intended to supply to the skald all the necessary information concerning mythology, poetic diction, and versification. Besides a formàli (preface) of later origin it contains three parts. (I) "Gylfaginning" (Gylfi's Deception), an abstract of old Scandinavian mythology in the form of a dialogue between King Gylfi and three gods. Appended to this are the "Bragaroedhur" (Bragi's Sayings), stories about Odhin and Thor, related by Bragi, the god of poetry, to the sea-god Aegir. (2) "Skaldskaparmàl" (Diction of Poetry) is a collection of poetic paraphrases (kenningar) and synonyms (ókend heiti), interspersed with mythological and legendary stories. (3) "Hàttatal", a panegyric on the Norwegian King Hàkon Hàkonarson and Jarl Skúli, containing one hundred and two strophes, each of which is composed in a different meter. This is followed by a prose commentary written, however, after Snorri's death by an unknown author. The work was unfinished when Snorri died and was subsequently revised and amplified by other writers. The best edition of the Snorra Edda is that published in three volumes by the Arna-Magnaean Society (Copenhagen, 1848-1887). Selections were edited by E. Wilken (Paderborn, 1877; glossary to this edition, Paderborn, 1883). Parts were translated into German by Gering (Leipzig, 1892), into English by Dasent (1842), by Blackwell in Mallet's "Northern Antiquities" (London, 1770), and R. B. Anderson (Chicago, 1880).

II. "The Elder Edda", a collection of mythological and heroic songs in the ancient Icelandic language. Altogether there are thirty-three such songs, twenty-nine of which are contained in the famous "Codex Regius", the most important of the Eddie manuscripts. This codex was found in Iceland in 1643 by Bishop Brynjólf Sveinsson. It had no title, and, since it contained poems, portions of which are cited in the Snorra Edda, the bishop concluded that this was Snorri's source and so he called the collection "Edda". He furthermore assumed that the priest Saemund (1056-1133), whose reputation for learning had become proverbial, was the author, or at least the collector of these songs, and he therefore wrote on a copy which he caused to be made the title "Edda Saemundi multiscii" (Edda of Saemund the wise), and the title "Edda" has since then remained in general use to designate the kind of poems found in the "Codex Regius". Such poems differ both in content and form from the so-called skaldic poems. There is no doubt that these songs were collected and written down in Iceland from oral tradition; but nothing certain is known concerning their age, original home, and authorship. All this has to be inferred from internal evidence, and hence opinions differ widely. It is agreed, however, that these poems are not common Scandinavian, but purely Norwegian; they were composed either in Norway or in Norwegian settlements like Iceland and Greenland. As to their age, it is conceded that none dates earlier than the middle of the ninth, and that some were written as late as the thirteenth century. The subject-matter of the songs is taken either from mythology or heroic saga. Among the mythological poems the most famous is the "Völuspà" (the prophecy of the volva or sibyl), the most important source for our knowledge of Norse cosmogony. Important also in this respect are the "Vafthrúdhnismàl" and "Grímnismàl", where Odhin's superior wisdom is set forth.

Of the songs dealing with Thor the best known is the "Thrymskvidha" (the song of Thrym), relating Thor's quest of his hammer. The sententious wisdom of the Northmen is represented by the "Hàvamàl" (sayings of the High One, i.e., Odhin). Among the heroic poems the chief interest attaches to the lays of Sigurd and the Niflungs. Unfortunately this cycle of poems is incomplete, owing to a great gap of about eight leaves in the "Codex Regius"; but an idea of the contents of the lost poems may be gained from the prose version of the "Volsungasaga", the author of which still had before him the complete collection. The first complete edition of the "Elder Edda", with Latin translation, was issued by the Arna-Magnaean Society (Copenhagen, 1787-1828). The first critical edition, on which all subsequent ones were based, was given by Sophus Bugge (Christiania, 1867). A lithographic facsimile edition of the "Codex Regius", with a diplomatic text, was given by Wimmer and Jónsson (Copenhagen, 1891). Other editions are those of Sijmons and Gering (Halle, Vol. I, text, 1888-1901; Vol. II, glossary, 1903); F. Jónsson (Halle, 1888-90, 2 vols.); Hildebrand-Gering (Paderborn, 1904v; F. better and R. Heinzel (Leipzig, 1903, 2 vols.). The poems of this kind not found in the "Codex Regius" were edited by Heusler and Ranisch, "Eddica Minora" (Dortmund, 1903). The best translation into German is the metrical version of Hugo Gering (Leipzig, 1892). The first English version (of the mythological songs only) was made by A. S. Cottle (Bristol, 1797). A complete English version is that of Benj. Thorpe (London, 1865-66). The songs are also translated in Vigfusson and Powell's "Corpus poeticum boreale" (Oxford, 1883), and some songs are also rendered in Magnusson and Morris's "Translation of the Volsungasaga" (London, 1870). A new translation by W. H. Carpenter is in preparation (1908).

ARTHUR F. J. REMY

title: Catholic Encyclopedia (1913)/Edda


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Catholic Encyclopedia (1913)/Edelinck

Edelinck, the family name of four engravers.—GERARD, b. in Antwerp c. 1640; d. in Paris, April 2, 1707. Galle instructed him in the rudiments of his art, and from him, in Antwerp, the youth imbibed that vigor and energy characterizing Rubens' school of engravers, which was later to transform the art in France and impart to it Northern freshness and simplicity. In 1665 Gerard came to Paris, studied with de Poilly, quickly surpassed him, and almost immediately reached the height of his powers, which remained undiminished until his death. Le Brun and Colbert called Louis XIV's attention to Edelinck, who received commissions, a pension, the title of engraver to the king, apartments in the Gobelins, and the position of professor in the Gobelins Academy from the monarch whose features he depicted in fourteen engravings. In 1675 he was naturalized; in 1677 he became a Royal Academician; and soon thereafter the order of Chevalier of Saint-Michel was conferred upon him. Edelinck was one of the greatest masters of pure engraving. He never used etching or dry-point on his plates, and of the four hundred that he produced there is not one that is poor or second-rate. Edelinck's work was epoch-making: he revolutionized engraving, abandoning lines that crossed to form squares for lozenge forms. Further, he massed his lines and changed their direction, thus avoiding the monotony that had marked all previous work in France. Edelinck had all the merits of his predecessors and, besides, rendered texture, color, and light and shade as they never before had been rendered. His strokes were clear and bold, and the results beautifully finished, harmonious, and silvery. His proofs were the first to possess the quality called technically by engravers "color". Sometimes they were slightly "metallic". Reproductions on steel by Edelinck frequently suggested more color and quality in the originals than the latter possessed. He worked with marvellous facility and concealed his consummate science under an unobtrusive technic. While he did not confine his burin to portraits, it was these which gave him his great fame, for he so depicted all the notable men of his time, in the Church and the Court, and in literature and art, that we, today, gain an insight into their very character. The greater part of his work was reproductive, but he sometimes engraved from his own drawings, for he was a superb draughtsman. Edelinck was chosen to engrave Raphael's "Holy Family", Le Brun's "Magdalen", and "Alexander Visiting the Family of Darius", the first-named bringing him instant fame. Only two impressions before letters of the "Holy Family" exist. Edelinck's life was one of piety, contentment, and tireless labor; it was made up of teaching engraving to his son and his two brothers and working on his own plates. Death found him engraving the "Alexander Entering the Tent of Darius", a superb plate finished by Pierre Drevet. To his family he left a fortune. Plates wholly his own were signed "Gerard Edelinck", or "Edelinck eques"; but when his compatriot Pitau or Gaspard Edelinck assisted him the signature was "Edelinck". Among his pupils were Gaspard, Jean, and Nicolas Edelinck, Lombard, and Trouvain. His principal works are: "Portrait of Louis XIV", after Le Brun; "Portrait of Rigaud", after Rigaud; "Portrait of Mme. Hélyot with a Crucifix", after Galliot; "Portrait of Philippe de Champaigne", which the artist thought his best work, after Champaigne; "Combat of the Four Horsemen", after da Vinci.

NICOLAS, son of the preceding, b. in Paris in 1680; d. there in 1730. He studied under his father, Gerard, and to perfect himself subsequently went to Italy. In Venice he produced many plates in the style of his father, whom, however, he never equalled in vigor or quality. He engraved several plates for the Crozat collection. His masterpiece is a "Virgin and Infant" after Correggio.

His works include a "Portrait of his Father", after Tortebat; "Portrait of Cardinal Giulio de' Medici", after Raphael; "Portrait of John Dryden", after Kneller.

JEAN, b. in Antwerp, c. 1643; d. in Paris, 1680. He was a younger brother and pupil of Gerard, with whom he worked and whose style he imitated. Plates wholly his own are much inferior to those of his celebrated brother, though they have considerable merit. "The Deluge", after A.Veronese, is his masterpiece. He made many engravings of the statues in the gardens of Versailles.

GASPARD-FRANCOIS, b. in Antwerp, 1652; d. in Paris, 1722. Gaspard, the youngest brother of Gerard, who was his teacher and co-worker, was inferior in talent to the other members of the Edelinck family, and did not long follow the career of engraver. Because he used a signature similar to that of Gerard and because his master often helped him with his plates, much of his work is difficult to distinguish from Gerard's.

LEIGH HUNT

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title: Catholic Encyclopedia (1913)/Edelinck


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Catholic Encyclopedia (1913)/Edesius and Frumentius

Edesius and Frumentius, Tyrian Greeks of the fourth century, probably brothers, who introduced Christianity into Abyssinia; the latter a saint and first Bishop of Axum, styled the Apostle of Abyssinia, d. about 383. When still mere boys they accompanied their uncle Metropius on a voyage to Abyssinia. When their ship stopped at one of the harbors of the Red Sea, people of the neighborhood massacred the whole crew, with the exception of Edesius and Frumentius, who were taken as slaves to the King of Axum. This occurred about 316. The two boys soon gained the favor of the king, who raised them to positions of trust and shortly before his death gave them their liberty. The widowed queen, however, prevailed upon them to remain at the court and assist her in the education of the young prince Erazanes and in the administration of the kingdom during the prince's minority. They remained and (especially Frumentius) used their influence to spread Christianity. First they encouraged the Christian merchants, who were temporarily in the country, to practice their faith openly by meeting at places of public worship; later they also converted some of the natives. When the prince came of age Edesius returned to his friends and relatives at Tyre and was ordained priest, but did not return to Abyssinia. Frumentius, on the other hand, who was eager for the conversion of Abyssinia, accompanied Edesius as far as Alexandria, where he requested St. Athanasius to send a bishop and some priests to Abyssinia. St. Athanasius considered Frumentius himself the most suitable person for bishop and consecrated him in 328, according to others between 340-46. Frumentius returned to Abyssinia, erected his episcopal see at Axum, baptized King Aeizanas, who had meanwhile succeeded to the throne, built many churches, and spread the Christian Faith throughout Abyssinia. The people called him Abuna (Our Father) or Abba Salama (Father of Peace), titles still given to the head of the Abyssinian Church. In 365 Emperor Constantius addressed a letter to King Aeizanas and his brother Saizanas in which he vainly requested them to substitute the Arian bishop Theophilus for Frumentius (Athanasius, "Apol. ad Constantium" in P.G., XXV, 631). The Latins celebrate the feast of Frumentius on October 27, the Greeks on November 30, and the Copts on December 18. Abyssinian tradition credits him with the first Ethiopian translation of the New Testament.

MICHAEL OTT


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Rh

Gā nū tō setle,symbel-wynne drēoh, wigge weorþad; unc sceal worn fela māþma gemǣnra,siþðan morgen bið.” Gēat wæs glæd-mōd,gēong sōna tō, setles nēosan,swā se snottra heht. Þā wæs eft swā ǣtellen-rōfum flet-sittendumfægere gereorded nīowan stefne.Niht-helm geswearc deorc ofer dryht-gumum.Duguð eal ārās; wolde blonden-feaxbeddes nēosan, gamela Scylding.Gēat ungemetes wel, rōfne rand-wigan,restan lyste; sōna him sele-þegnsīðes wērgum, feorran-cundum,forð wīsade, sē for andrysnumealle beweotecde þegnes þearfe,swylce þȳ dōgore hēaþo-līðendehabban scoldon. Reste hine þā rūm-heort;reced hlīuade gēap ond gold-fāh;gæst inne swæf, oþ þæt hrefn blacaheofones wynne blīð-heort bodode;*ðā cōm beorht scacan [sunne ofer grundas]. Scaþan onetton,

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Catholic Encyclopedia (1913)/Congregation of Saint Edmund

Edmund,, founded in 1843, by Jean-Baptiste Muard, at Pontigny, France, for the work of popular missions. The members also devote themselves to parochial work, to the education of youth in seminaries and colleges, to the direction of pious associations, and to foreign missions. The motherhouse is at Pontigny, but since the expulsion of the religious orders the superior general resides at Hitchin, England. In the United States, the congregation has two houses: a missionary house and apostolic school at Swanton, Vermont, for the training of young men who wish to study for the priesthood and the religious life; and a college at Winooski, Vermont, with 12 fathers, 8 scholastics, and 100 pupils.

E. M. SALMON


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76

 wǣron æþelingaseft tō lōodum fūse tō farenne; wolde feor þanon cuma collen-ferhðcēoles nēosan. Heht þā se heardaHrunting beran sunu Ecglāfes,heht his sweord niman, lēoflīc īren;sægde him þæs lǣnes þanc, cwæð, hē þone gūð-winegōdne tealde, wīg-cræftigne;nales wordiim lōg mēces ecge.Þæt wæs mōdig secg. Ond þā sīð-frome,searwum gearwe, wīgend wǣron,ēode weorð Denum æþeling tō yppan,þǣr se ōþer wæs, hæle hilde-dēorHrōðgār grētte.

Bēowulf maþelode,bearn Ecgþēowes: “Nū wē sǣ-līðendsecgan wyllað feorran-cumene,þæt wē fundiaþ Higelāc sēcan;wǣron hēr tela willum bewenede;þū ūs wel dohtest.

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text: Beowulf (Wyatt)/Beowulf 24

title: Beowulf (Wyatt)/Beowulf 24


text: Beowulf (Wyatt)/Beowulf 25

title: Beowulf (Wyatt)/Beowulf 25


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Page:Bunny Brown at Camp Rest-a-While.djvu/76

certainly seemed to be the matter with Splash. Bunny and Sue had never seen their dog act in such a funny way. He would dash into the water, not going far from shore, though, and then he would jump back, barking all the while.

Once or twice he tried to grab, in his sharp teeth, something that seemed to be swimming in the water. But either Splash could not get it, or he was afraid to come too close to it.

"Oh, Daddy! What is it? What is it?" asked Bunny and Sue.

Mr. Brown, who with Bunker Blue and Uncle Tad, was fastening the last ropes of the tent, hurried down to the shore of the lake.

"What is it? What's the matter. Splash? What is it?" asked Mr. Brown.

Splash never turned around to look at


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Bunny Brown and His Sister Sue at Camp Rest-a-While daddy. He again rushed into the water, barking and snapping his sharp teeth. Then Mr. Brown, taking up a stick, ran toward the dog.

"Let it alone, Splash! Let it alone!" cried Daddy Brown. "That's a big muskrat, and if it bites you it will make a bad sore. Let it alone!"

Daddy Brown struck at something in the water, and Bunny and Sue, running down to the edge of the lake, saw a large, brown animal, with long hair, swimming out toward the middle. Splash started to follow but Mr. Brown caught the dog by the collar.

"No you don't!" cried Bunny's father, "You let that muskrat alone. Splash. He's so big, and such a good swimmer, that he might pull you under the water and drown you. Let him alone."

Bunker Blue, who had come down to the edge of the lake, threw a stone at the swimming muskrat. The queer animal at once made a dive and went under the water, for muskrats can swim under the water as well as on top, and Bunny and Sue saw it no more.

Splash rushed around, up and down the


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70 shore, barking loudly, but he did not try to swim out. I think he knew Mr. Brown was right in what he said—that it was not good to be bitten by a muskrat.

"Is that what it was, Daddy—a rat?" asked Bunny.

"Yes," answered his father. "Splash must have seen the muskrat swimming in the water, and tried to get it. The muskrat didn't want to be caught, so it fought back. But I'm glad it got away without being hurt, and I'm glad Splash wasn't bitten."

"What's a muskrat?" Sue wanted to know.

"Well, it's a big rat that lives in the water," said Daddy Brown. "It is much larger than the kind of rat that is around houses and barns, and it has fine, soft fur which trappers sell, to make fur-lined overcoats, and cloaks, for men and women. The fur is very good, and some persons say the muskrat is good to eat, but I would not like to try eating it. But this muskrat was a big one, and as they have sharp teeth, and can bite hard when they are angry, it is a good thing we drove it away."

Bunny and Sue looked out over the lake.


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Bunny Brown and His Sister Sue at Camp Rest-a-While They could see the muskrat no longer, though there was a little ripple in the water where it had dived down to get away.

"Now we must finish putting up the tents," said Daddy Brown. "It will be night before we know it, and we want a good place to sleep in at Camp Rest-a-While."

"And are we going to have a fire, where we can cook something?" asked Bunny.

"Yes, we'll have the oil stove set up."

"I thought we would have a campfire," said the little boy.

"So we shall!" exclaimed Uncle Tad. "I'll make a campfire for you, children, and we'll bake some potatoes in it. We'll have them for supper, with whatever else mother cooks on the oil stove."

"I'll get some sticks of wood for the fire!" cried Sue.

"So will I!" added Bunny.

And while the older folk were finishing putting up the tents, and while Mother Brown was getting out the bed clothes, Bunny and Sue made a pile of sticks and twigs for the fire their uncle had promised to make.


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72 Soon the big sleeping tent was put up, and divided into two parts, one for Sue and her mother, and the other for Bunny and the men folk. Cot-beds were put up in the tent, and blankets, sheets and pillows put on them, so the tent was really like a big bedroom.

"It will be nicer sleeping here than on the ground, like we did in the tent at home that night," said Bunny to Sue.

"Yes, I guess it will," she answered. "My dollie won't catch cold in a nice bed."

"Did she catch cold before?" Bunny wanted to know.

"Well, she had the sniffle-snuffles, and that's almost like a cold," Sue answered.

In the second-sized tent the dining table had been set up, and the chairs put around ready for the first meal, which would be supper. Mother Brown got the dishes out of the box, and called:

"Now, Bunny and Sue, let me see you set the table."

She had taught them at home how to put on the plates, knives, forks, spoons, cups, saucers and whatever was needed, and now Bunny


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Bunny Brown and His Sister Sue at Camp Rest-a-While and Sue did this, as their share of the work, while Bunker Blue, and the older folk, were busy doing different things.

In the cooking tent the oil stove was set up and lighted, to make sure it burned well. Then Camp Rest-a-While looked just like its name—a place where boys and girls, as well as men and women could come and have a nice rest, near the beautiful lake.

When everything was nearly finished, and it was about time to start getting supper, a man came rowing along the shore of the lake in a boat. He called to Mr. Brown:

"Hey, there! Is this where you want your boat left?"

"Yes, thank you. Tie it right there," answered Daddy Brown.

"Oh, is that going to be our boat?" asked Bunny, in delight.

"Yes," answered his father, "I wrote to a man up here that has boats to let, to bring us a nice one. We'll use it while we are in camp. But you children must never get in the boat without asking me, or your mother. You mustn't get in even when it's tied to the shore."


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74 "We won't!" promised Bunny and Sue. Once they had gotten in a boat that they thought was tied fast, but it had floated away with them. They landed on an island in the river, and had some adventures, of which I have told you in the first book of this series.

Bunny and Sue remembered this, so they knew that sometimes it was not even safe to get in a boat which was tied fast, unless some older person was with them.

The man left the boat he had brought for Mr. Brown. It was a large one and would easily hold Bunny and Sue, as well as all the others at Camp Rest-a-While.

"Now for the roast potatoes!" cried Uncle Tad. "Come on, children! We'll start our campfire, for I see your mother getting the meat ready to cook, and it takes quite a while to roast potatoes out of doors."

The campfire was built between two big stones. Bunny and Sue bringing up the wood they had gathered. Uncle Tad lighted the fire, for it is not safe for children to handle matches, or even be near an open fire, unless some older person is with them. Bunny and


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Bunny Brown and His Sister Sue at Camp Rest-a-While Sue had often been told this, so they were very careful.

When the fire had blazed up good and hot, Uncle Tad let it cool down a bit. Then he raked away the red hot embers and put in them some nice, big, round potatoes. These he covered up in the hot ashes, and put on more wood.

"Now the potatoes are baking," he said. "They will be done in time for supper."

And what a fine supper it was—that first one in camp! Bunny and Sue thought they had never tasted anything so good. They all sat in the dining tent, and Mother Brown put the things on the table.

"Now where are your potatoes, Uncle Tad?" she asked.

"Here they are!" cried the old soldier, as he went to the campfire. He raked away the ashes and embers with a stick, and on a platter, made from a large piece of bark, off a tree, the old soldier poked out a number of round, black, smoking things.

"Why—why!" exclaimed Sue, in surprise. "I thought you baked potatoes, Uncle Tad!"


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76 "So I did, Sue."

"They look like black stones," said Bunny,

"You wait—I'll show you," laughed Uncle, Tad. He brought the bark platter to the table. Taking up a fork he opened one of the round, black, smoking things. Though the outside was burned black from the fire, the inside was almost as white as snow.

"There's baked potatoes for you!" cried Uncle Tad. "Put some salt and butter on them, and you never tasted anything better! But be careful—for they're very hot!"

Supper over, the dishes were washed and put away. Then there was nothing to do but wait until it was time to go to bed.

"And I think we're all tired enough to go early to-night," said Mother Brown.

"But, before we go," said her husband, "I think we will have a little row on the lake in our boat. It is not yet dark."

It was beautiful out on the water, and the sun, sinking down behind the hills, made the clouds look as though they were colored blue, pink, purple and golden.

Bunny and Sue were almost asleep when


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Bunny Brown and His Sister Sue at Camp Rest-a-While the boat was headed back toward shore, and their eyes were tight shut, when daddy and mother lifted them out to carry them up to Camp Rest-a-While. The children hardly awakened when they were undressed and put to bed, and soon every one was sound asleep, for it was a dark night.

Bunny Brown was sleeping in the outer part of the bedroom-tent, in a cot next to his father's. Just what made Bunny awaken he did not know. But, all at once the little fellow sat up on his cot, and looked with wide-open eyes toward the entrance. There was a lantern burning in the tent, and by the light of it Bunny Brown saw a big shaggy animal, standing on its hind legs, and sniffing with its black nose. At first Bunny could not make a sound, he was so frightened, but finally he screamed:

"Oh, Daddy! Daddy! Wake up! It's a bear! A bear! A big black bear in the tent!"

Then Bunny slipped down between the blankets and covered up his head with the bed clothes.


text: Bunny Brown and His Sister Sue at Camp Rest-a-While/Chapter 7


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was used to being suddenly aroused in the night by either Bunny or Sue, At home the children often awakened, and called out. Sometimes they would be dreaming, or perhaps they would want a drink of water. So Daddy Brown and Mrs. Brown were used to answering when they heard the children call out.

But it was something new to hear Bunny calling about a big, black bear. He had never done that before, though one time, when he ate too much bread and jam for supper, he screamed that there was an elephant in his room, and there wasn't at all. He had only dreamed it.

But this time Daddy Brown had plainly heard his little boy say:

"Oh, it's a bear! It's a bear!"


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Bunny Brown and His Sister Sue at Camp Rest-a-While Mr. Brown awakened, and sat up in his cot He looked over toward Bunny's bed, but could see nothing of the little fellow, for as I have told you. Bunny was covered up under the blankets and quilt. Even his head was covered.

Then Mr. Brown looked toward the entrance, or front door of the tent. And, to his surprise, he saw just what Bunny had seen, a big, shaggy, hairy animal, standing on its hind legs, with its black nose up in the air, sniffing and snuffing.

"Why—why!" exclaimed Mr. Brown, rubbing his eyes to make sure that he was wide awake, and that he was not dreaming, as he thought Bunny might have been. "Why—why! It is a bear!"

"Sniff! Snuff!" went the big, shaggy creature.

"Daddy—Daddy!" cried Bunny, his voice sounding faint and far off, because his head was under the covers. "Daddy, is—is he gone?"

"No, not yet," answered Mr. Brown.

"What is it? What's the matter?" called


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 {|
 * || DOUGLASS PLATE 4
 * | A
 * Climatic Cycles and Tree-Growth Plate 4A.jpg
 * | B
 * Climatic Cycles and Tree-Growth Plate 4B.jpg
 * }
 * | B
 * Climatic Cycles and Tree-Growth Plate 4B.jpg
 * }

A. Section of Scotch pine from Ös, Norway.

B. Section of Scotch pine from Dalarne, Sweden.


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80 Mrs. Brown, from behind the curtain, where she slept.

"Why," said Mr. Brown slowly. "It—it seems to be a—"

Then he stopped. He did not want to scare his wife or Sue, by telling them there was a bear in the tent, and yet there was.

"Oh, what is it?" cried Mrs. Brown again. "I heard Bunny crying! Is anything the matter with him?"

"No, he's all right," answered Bunny's papa. That was true enough. There was really nothing the matter with the little boy. He was just a bit frightened, that was all.

"But something is the matter," said Mrs. Brown, "I know there is! Why don't you tell me what it is?"

Daddy Brown did not know just what to do. He sat up in bed, thinking and looking first at the bear and then at Bunny. All Mr. Brown could see of Bunny was a heap under the bedclothes. But the bear was in plain sight, standing in the doorway of the tent, sniffing and snuffing near the lighted lantern.

Mr. Brown did not want to speak about the


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Bunny Brown and His Sister Sue at Camp Rest-a-While bear. He thought the big, shaggy creature looked quite gentle, and perhaps it would go away if no one harmed it. Perhaps it was just looking for something to eat, and as it couldn't find anything in the bedroom tent it might go to the one where the cooking was done.

Bunker Blue was still sound asleep, and so was Uncle Tad. Nor had Sue, sleeping next to her mother, in the other part of the tent, been awakened. Just Bunny Brown, and his father and mother were wide awake. Oh, yes, of course the bear was not asleep. I forgot about that. His little black eyes blinked, and opened and shut, and he wrinkled up his rubber-like nose as he snififed the air.

"Well, aren't you going to tell me what it is? What's the matter in there? What happened?" asked Mother Brown. "If you don't tell me"

By this time Bunny Brown made up his mind that he would be brave. He uncovered one eye and peered out from beneath the bed clothes. His first sight was of the bear, who was still there.


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82 "Oh! Oh!" cried Bunny. "It is a bear! It's a big, black bear! I didn't dream it! It's real! a real, big, black bear!"

Mrs. Brown heard what her little boy said.

"Oh, Walter!" she cried to her husband. "Throw something at it. Here's my shoe—throw that. I've got two shoes, but I can only find one. Throw that at the bear and make him go away!"

Mrs. Brown threw over the curtain, that divided the tent into two parts, one of her shoes.

She really had two shoes, but when she felt under her cot in the dark, she could only find one. You know how it is when you try to find anything in the dark, even if it's a drink of water in the chair at the head of our bed. You move your hand all over, and you think some one must have come in and taken the water away. And when you get a light you find that, all the while, your hand was about an inch away from the glass. It was that way with Mrs. Brown's other shoe.

But she threw one over the curtain, calling out again:


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Bunny Brown and His Sister Sue at Camp Rest-a-While "Hit him with that, Walter! Hit the bear with my shoe!"

But there was no need for Mr. Brown to do anything. The shoe thrown by Bunny's mother sailed through the tent. Straight at the bear it went, and before the shaggy creature could get out of the way, the shoe hit him on the end of the nose.

"Bunk!" went the shoe.

"Wuff!" grunted the bear.

Now you know a bear's nose is his most tender part. You could hit him on his head, or on his back, or on his paw—that is if you were brave enough to hit a bear at all—but you would not hurt him, hardly any, unless you hit him right on the end of his soft and tender nose. That's the best place to hit a bear if you want to drive him away, out of your tent, or anything like that. Hit him on the nose.

"Whack!" went Mrs. Brown's shoe on the end of the bear's nose.

"Wuff!" grunted the bear, and down he dropped on all four paws.

Now Mrs. Brown really did not mean to


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84 hit the bear. She was just tossing her shoe over the curtain so her husband might have something to throw at the bear, and, as it happened, she hit the bear by accident.

Of course it might have been better if one of Mr. Brown's shoes had hit the bear. I mean it would have been better for the Brown family, but worse for the bear. Because Mr. Brown's shoes were larger and heavier than his wife's. But then, it turned out all right anyhow.

For, no sooner did the bear feel Mrs. Brown's shoe hit him on the nose, than he cried out:

"Wuff!"

Then he turned quickly around, and ran out of the tent.

"Did you throw my shoe at him? Did you make him go away?" asked Mrs. Brown. "Because if you didn't, Walter, I've found my other shoe now, and I'll throw that to you."

"You won't need to, my dear," said Mr. Brown with a laugh. "One shoe was enough. You hit the bear yourself!"

"I did?"


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Bunny Brown and His Sister Sue at Camp Rest-a-While "Yes, and he's gone. It's all right, Bunny. You can put your head out now. The bear is gone."

Bunny peeped with one eye, and when he saw that the big, shaggy creature was no longer there, he put his whole head out. Then, with a bound he jumped out of bed, and ran toward the back part of the tent, where his mother and sister were sleeping.

"Where you going. Bunny?" asked his father. "There's no more danger; the bear has gone."

"I—I'm just going in here to get my pop gun, so if the bear comes back—" Bunny said, "My pop gun is in here."

"Oh," said Mr. Brown, "I thought you were going to crawl in bed with your mother."

"Oh, no—no!" Bunny quickly answered, shaking his head. "I—I just want my pop gun. But," he went on, "if mother wants me to get in bed with her, and keep the bear away, why I will. Don't be afraid. I'll get in bed with you, Mother!"

"Oh, I guess the bear won't come back," said Mr. Brown with a laugh.


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86 "Well, I'll get in bed with mother anyhow," said Bunny. "I'll have my pop gun all ready."

By this time Uncle Tad, Bunker Blue and Sue had been awakened by the talk. Outside the tent Splash could be heard barking, and there was a noise among the trees and bushes that told that the bear was running away.

"I—I hope he doesn't bite our dog," said Bunny.

"Oh, I guess Splash will know enough to keep away from the bear," replied Mr, Brown. "Besides, I think the bear was only a tame one, anyhow."

"A tame bear?" asked Uncle Tad, as he was told all that had happened.

"Yes. He didn't act at all like a wild one. Besides, there aren't any wild bears in this part of the country. This was a tame one all right."

"Where did it come from?" asked Mrs. Brown.

"Oh, I think it got away from some man who goes about the country making the bear do tricks. Probably in the morning we'll see


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Bunny Brown and His Sister Sue at Camp Rest-a-While the man looking for his bear," answered her husband.

And that is just what happened. There was no more trouble that night. Everyone went to sleep again, Bunny in the cot with his mother; though when he was asleep and slumbering soundly, she carried him back to his own little bed near his father.

Soon after breakfast the next morning, when they were talking about the bear scare in the night, along came a man, who looked like an Italian organ-grinder. He said he had a pet, tame bear, who had broken away from where he was tied, in the night.

And it was this bear who had wandered into the tent where Bunny was sleeping. Where the bear was now no one knew, but the Italian said he would walk off through the woods, and see if he could not find his pet, which he had trained to do many tricks.

Two or three days later, Mr. Brown heard that the bear was safely found, so there was no more need to worry about his coming into the tent at night.

That day Daddy Brown, with the help of


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88 Uncle Tad and Bunker Blue printed a big cloth sign which they hung up between two trees. The sign read:

"There," said Daddy Brown, "now the postman will know where to find us when he comes with letters."

"Oh, do they have mail up here?" asked Sue.

"No, daddy is only joking," said her mother. "I guess we'll have to go to the post office for letters."

One day, when they had been in camp about a week. Bunny and Sue, with the others, returned from a walk in the woods. As they came near the "dining-room tent," as they called it, they saw a ragged boy spring up from the table with some pieces of bread and meat, and dash into the bushes.

"Hold on there! Who are you? What do you want?" cried Daddy Brown. But the ragged boy did not stop running. He wanted to hide in the bushes.


text: Bunny Brown and His Sister Sue at Camp Rest-a-While/Chapter 8


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Author:Augustin Poulain

Contributions to the Catholic Encyclopedia

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FINANCIAL] of the passenger’s journey in the United States is reported to be about 32 m.; in Great Britain it is undoubtedly less, but no record is published. Of the total train mileage in America more than half is freight; in Great Britain much more than half is passenger.

France.—Railway accidents in France are recorded in a shape somewhat different from that found in either Great Britain or America. The principal items for the years 1906 and 1907 are shown in Table XVI. The length of railways in the republic was 39,963 km. (24,832 m.), the number of persons employed on them was rather less than 300,000, the number of passengers carried annually being between 450 and 500 millions. The number of passengers (36) killed in train accidents in 1907 was equal to 0·0759 per million passengers carried and 0·0024 per million kilometres travelled by passengers, or 0·1503 per million kilometres travelled by trains. The most significant item in the table, 36 passengers killed in train accidents, is perhaps to be considered as abnormally large, the totals under this head for the preceding six years beginning with 1901 being 7, 35, 3, 18, 4, 14, or an average of 11·57 per year. The French secretary of Public Works, who has furnished these statistics, keeps also similar records of the local or light railways, on which the number of fatal accidents appears to be exceedingly small.

Germany.—The number of persons killed on the railways of the German Empire in the year 1907 was 1249, classified as in Table XVII. This number does not include suicides and attempts at suicide, of which there were 333, all but 24 being successful. In these statistics, the third item, “other persons,” includes post office and customs officials and other persons connected with the railway service, as well as railway officers and servants off duty. The totals of passengers killed and injured in train accidents are not separated from those killed and injured from other causes, but ratios are given showing that for four years no passengers were killed in this class.

The methods of financing railway enterprises, both new projects and existing lines, have been influenced very largely by the attitude of the state and of municipal authorities. Railways may be built for military reasons or for commercial reasons, or for a combination of the two. The Trans-Siberian railway was a military necessity if Russia was to exercise dominion throughout Siberia and maintain a port on the Yellow Sea or the Sea of Japan. The Union Pacific railroad was a military necessity to the United States if the authority of the national government was to be maintained in the Far West. The cost of such ventures and the detailed methods by which they are financed are of relatively small importance, because they are not required to earn a money return on the investment. To a less degree, the same is true of railways built for a special instead of a general commercial interest. The Baltimore & Ohio railroad was built to protect and further the commercial interests of the city of Baltimore; the Cincinnati Southern railway is still owned by the city of Cincinnati, which built the line in the ’seventies for commercial protection against Louisville, Ky. From a commercial point of view such ventures are differentiated from railway projects built for general commercial reasons because they do not depend on their own credit. The government, national or local, furnishes the borrowing power, and makes the best bargain it can with the men it designates to operate the line.

Where a railway is built for general commercial reasons, however, it must furnish its own credit; that is to say, it must convince investors that it can be worked profitably and give them an assured return on the funds they advance. The state is interested in the commercial railway venture as a matter of public policy, and because it can confer or withold the right of eminent domain, without which the railway builder would be subjected to endless annoyance and expense. This governmental sanction has been obtainable only with difficulty, and after the exercise of numerous legal forms, in Great Britain and on the continent of Europe. In the United States, on the other hand, it has been obtained with considerable ease. In the earlier years of American railway building, each project was commonly the subject of a special law; then special laws were in turn succeeded by general railway laws in the several states, and these in turn have come to be succeeded in most parts of the country by jurisdiction vested in the state railway commission. Each of these changes has tended to improve the existing status, to legitimize railway enterprise, and to safeguard capital or investment.

The laws regulating original outputs for capital were strictly drawn in Great Britain and on the continent of Europe; in America they were drawn very loosely. As a result it has been far easier for the American than for the European railway builder to take advantage of the speculative instinct in obtaining money. Instead of the borrowing power being restricted to a small percentage of the total capital, as in European countries, most of the railway mileage of America has been built with borrowed money, represented by bonds, while stock has been given freely as an inducement to subscribe to the bonds on the XXII. 27

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Rh theory that the bonds represented the cost of the enterprise, and the stock the prospective profits. As a natural result weak railway companies in the United States have frequently been declared insolvent by the courts, owing to their inability in periods of commercial depression to meet their acknowledged obligations, and in the reorganization which has followed the shareholders have usually had to accept a loss, temporary or permanent.

The situation in Great Britain has been wholly different. The debt in that country is relatively small in amount, and is not represented by securities based upon hypothecation of the company’s real property, as with the American railway bond, resting on a first, second or third mortgage. But British share capital has been issued so freely for extension and improvement work of all sorts, including the costly requirements of the Board of Trade, that a situation has been reached where the return on the outstanding securities tends to diminish year by year. Although this fact will not in itself make the companies liable to any process of reorganization similar to that following insolvency and foreclosure of the American railway, it is probable that reorganization of some sort must nevertheless take place in Great Britain, and it may well be questioned whether the position of the transportation system of that country would not have been better if it had been built up and projected on the experience gained by actual earlier losses, as in the United States.

Thus the characteristic defect in the British railway organization has been the tendency to put out new capital at a rate faster than has been warranted by the annual increases in earnings. The American railways do not have to face this situation; but, after a long term of years, when they were allowed to do much as they pleased, they have now been brought sharply to book by almost every form of constituted authority to be found in the states, and they are suffering from increased taxation, from direct service requirements, and from a general tendency on the part of regulating authorities to reduce rates and to make it impossible to increase them. Meantime, the purchasing power of the dollar which the railway company receives for a specified service is gradually growing smaller, owing to the general increases year by year in wages and in the cost of material. The railways are prospering because they are managed with great skill and are doing increasing amounts of business, though at lessening unit profits. But there is danger of their reaching the point where there is little or no margin between unit costs of service and unit receipts for the service. It will probably be inevitable for American railway rates to trend somewhat upward in the future, as they have gradually declined in the past; but the process apparently cannot be accomplished without considerable friction with the governing authorities. The attitude of the courts is not that the railways should work without compensation, but that the compensation should not exceed a fair return on funds actually expended by the railway. This is in line with the provisions in the Constitution of the United States regarding the protection of property, but the difficulty in applying the principle to the railway situation lies in the fact that costs have to be met by averaging the returns on the total amount of business done, and it is often impossible, in specific instances, to secure a rate which can be considered to yield a fair return on the specific service rendered. Hence losses in one quarter must be compensated by gains in another—a process which the law, regarding only the gains, renders very difficult.

The growth of railways has been accompanied by a world-wide tendency toward the consolidation of small independent ventures into large groups of lines able to aid one another in the exchange of traffic and to effect economics in administration and in the purchase of supplies. Both in England and in America this process of consolidation has been obstructed by all known legislative devices, because of the widespread belief that competition in the field of transportation was necessary if fair prices were to be charged for the service. But the general tendency to regulate rates by authority of the state has apparently rendered unnecessary the old plan of rate regulation through competition, even if it had not been demonstrated often and again that this form of regulation is costly for all concerned and is effective only during rare periods of direct conflict between companies. Nevertheless, in spite of difficulties, consolidation has gone on with great rapidity. When Mr E. H. Harriman died he exercised direct authority over more than 50,000 m. of railway, and the tendency of all the great American railway systems, even when not tied to one another in common ownership, is to increase their mileage year by year by acquiring tributary lines. The smaller company exchanges its stock for stock of the larger system on an agreed basis, or sells it outright, and the bondholders of the absorbed line often have a similar opportunity to exchange their securities for obligations of the parent company, which are on a stronger basis or have a broader market. Similarly in Great Britain there is a tendency towards combination by mutual agreement among the companies while they still preserve their independent existence.

Location.—An ideal line of railway connecting two terminal points would be perfectly level and perfectly straight, because in that case the resistance due to gradients and curves would be eliminated (see § ) and the cost of mechanical operation reduced to a minimum. But that ideal is rarely if ever attainable. In the first place the route of a railway must be governed by commercial considerations. Unless it be quite short, it can scarcely ever be planned simply to connect its two terminal points, without regard to the intervening country; in Order to be of the greatest utility and to secure the greatest revenue it must be laid out with due consideration of the traffic

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text: Author:Armand-Prosper Faugère

title: Author:Armand-Prosper Faugère


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 plate 9,. When the analyzer is turned at a small angle to the lines of the sweep, each transparent line shows the full curve or a substantial part of it in its varying light intensities. 'These numerous reproductions are all parallel to each other, separated by equal dark lines, and each one is displaced longitudinally with reference to its neighbors, thus presenting the characteristics of the differential pattern. By twisting the analyzer with reference to the sweep while the two remain in parallel planes, different periods may be tested; for as the analyzer twists, each reproduction varies in respect to its length and its displacement from its adjoining neighbors above and below. When a period is formed it shows itself, just as in the original differential pattern, by rows of dark and light spots in alinement more or less perpendicular to the analyzing lines, as in plate 9,. These light and dark rows are analogous to interference fringes and are identical with the elaborate but provokingly useless designs on a wire screen in front of its reflection in a window, or with the parallel fringes when two sets of parallel lines are held at a slight inclination to each other. Alinements are always best recognized by holding the paper edgewise and looking at the diagram at a low angle rather than in a perpendicular direction.

The analyzing plate resembles a coarse grating with equally spaced parallel lines. Much difficulty was experienced in making it. It is most satisfactory if made on glass with strong contrast between the opaque and transparent parts. The grating now in use was produced by photographing a 10-foot sheet of coordinate paper upon which 165 lines of black gummed paper had been carefully fastened. The coordinate lines permitted the spacing to be done with exactness. The width of the transparent space throughout was three-tenths of the distance from center to center. This was carefully photographed by a good lens at different distances. Glass prints were made from each negative and are still in use.

Theory. — The formula for the period is very simple: Let y = length of curve in years or other time-unit employed. l = length of curve image across sweep lines in centimeter or other unit of length. s = spacing center to center of analyzing lines in unit of length. Then$${l \over s}$$ = number of analyzing lines in curve when lines are parallel to sweep. $${ys \over l}$$ = number of years in 1 line when lines are parallel to sweep.


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Rh By means of this diagram one can discover at a glance the origin of many of the periods which Michelson thought were illusory and in which opinion he was largely right. We can plainly see a 9.3-year period in the early part of the curve. Let us call this part of the sequence A and its broken continuation near the center S, and the lower and later part giving the 11.4-year period C. Thus we get at once three periods, 9.3, 11.4, and something over 13 years. If, now, we bring the average A into line with the average C as the periodograph does, we get 11.4 years. If we bring the average A into line with the C, we get close to 10 years. If we bring into line A and the heavier parts of C, we get 8.4 years or thereabouts. And at 5.6 years we find a period which is just half of C and at 4.7 the half of A, and so on. It is like a checker-board of trees in an orchard; they line up in many directions with attractive intensity. But plate 9,, helps remove some of the complexity of the sunspot problem. It shows us that while these various periods are apparent, they are improbable and needless complications. The diagram supplies a basis for profitable judgment in the matter. Hence to avoid just such awkward cases as the sunspot curve, a differential pattern is considered to be a necessary accompaniment of the periodogram in doubtful cases.

Production of differential pattern.—The work described above, consisting particularly in the production of a periodogram from the differential pattern, was done at Harvard College Observatory in 1913. The next fundamental improvement in the apparatus was in 1914, and consisted in a method of producing the differential pattern without all the labor of cutting out the curves. It was simply the combination of a certain kind of focal image called a "sweep" and an analyzing plate. A single white or transparent curve on a black background is all that is now needed as a source of light. An image of this is formed by a positive cylindrical lens with vertical axis. In the focal plane image so produced each crest of the curve is represented by a vertical line or stripe and the whole collection of vertical lines looks as if it has been swept with a brush unevenly filled with paint and producing heavy and faint parallel lines. Each of these lines represents in its brightness the ordinate of the corresponding crest. The sweep of the sunspot numbers is shown in plate 9,. Any straight line whatever in any direction across this sweep truly represents the original curve, not as a rising and falling line but in varying light-intensity. A plate with equally spaced parallel opaque lines, called the analyzer or analyzing plate, is placed in the plane of this sweep. These lines may be seen in


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A. Periodogram of the sunspot numbers, 1755-1911. Corrugations show periods. The numbers give length of period in years. The white line is the year 1830 and shows phase.

B. Differential pattern used in making the periodogram, consisting of the sunspot curve mounted in multiple.

C. Same pattern photographed out of focus to show discontinuities in the vertical lines.

D. Sweep of sunspot numbers, 1755-1911.

E. Differential pattern of sunspot numbers made by the periodograph process.


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88 But the photographic summation may be done at any slant instead of only in the vertical, and therefore the sensitive plate may be made to summate these curves through a long range of periods. In order to get a long range of periods, the diagram was mounted on an axis with clock-work and slowly rotated in front of a camera with a cylindrical lens for objective, a horizontal slit in the focal plane, and a sensitive plate passing slowly downward across the slit by clock mechanism. In this way a full range of possible periods come under the summing process, and when a real period is vertical the crests of the curves form vertical lines which come down as a series of dots or beads in the slit. When no period is in the vertical the light coming through the slit is uniform. Of course, there is a practical limit to the different angles at which the diagram may be viewed. An angle too far in one direction, making the tested period very small, would require a great number of duplications of the curve, while too great an angle the other way, making the tested period very large, catches the curve in the nonsymmetrical form and introduces errors. In the periodograms actually made of the sunspot curve the minimum period tested was 7 years and the maximum 24. One notes especially that this is a continuous process and that all periods from the minimum to the maximum are tested.

Application to length of sunspot period. — The interest in the sunspot period makes a special consideration of plate 9,, worth while. This figure is a photograph of plate 9,, taken out of focus for the purpose of calling attention to certain general features. In the eye naturally turns to the sharp outlines and notes its minute details. In the crests of  are changed into large blotches connecting somewhat with their nearest neighbors and varying in intensity. The alinement which they form in a nearly vertical direction is a graphic representation of the period. If the line were exactly vertical the period would be 10 years. The slant to the right shows more than 11. If the line were straight the period would be constant. It is evident that there are several irregularities in it. Having a number of exactly similar lines side by side, the irregularities are repeated in each and thus strike the consciousness with the effect of repeated blows. These irregularities are the discontinuities referred to by Turner in connection with his hypothesis. It is evident at a glance that the sunspot sequence divides itself into three parts, namely, a 9.3-year period, 1750-1790; then an interval of readjustment, 1800-1830, with a 13-year period; and lastly an 11.4-year period lasting to the present time (values approximate). But the latter is not perfectly constant, for after 1870 there is a change in intensity. The breaks thus shown and Turner's dates of discontinuity are compared in table 6.


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Rh. from 1755 to 1911. The existence of a rhythm in any specified period is indicated by a beaded or corrugated effect. A line across the corrugations gives in fact the rhythmic vibrations of the cycle. On a moment's examination this periodogram shows much of the information which has been under discussion for many years. The 11-year period is the most pronounced, but it is not so superior to all others as would be expected. It may be of any duration from 11.0 to 11.8 years, but 11.4 is a good average. There is obviously a period somewhere between 9.5 and 10.5 years and one between 8.0 and 8.8, but it is less conspicuous. Faint indications of periods are found near 14 years. The double of 8.4 is seen between 16 and 17 years. The double of the 10-year period shows near the 20 and at 22 the double of the 11 begins.

The preliminary part of producing this periodogram is the construction of the "differential pattern" shown in plate 9,. This pattern is the optical counterpart of a set of columns of numbers arranged for addition, as when one summates a series of annual measures on a 10-year period, for example. The series is arranged in order with the first 10 years in the first line, the second 10 in the second line, and so on. In the case of the pattern the lines are made indefinitely long, so that the optical addition may be done in other directions than merely straight downward, for by making the additions on a slant a different period comes under test.

In order to produce this pattern the sunspot curve was cut out in white paper and pasted in multiple on a black background. The left end of each of the upper lines is the date 1755. Each successive line is moved 10 years to the left, so that passing from above vertically downward each line represents a date 10 years later than its predecessor. This continues from 1755 to 1911, and the lower 10 lines show the latter date at their right ends. It is not necessary that any of the lines should be full length, as we use only a part of each. By passing the eye downward from the top, a period near 10 years will show itself at once by a succession of crests in vertical alinement. If the crests form a line at some angle to the vertical, then the period they indicate is not exactly 10 years. It is more if the slant is to the right and less if to the left. The horizontal lines are spaced the equivalent of 5 years. Hence, if we measure the angle made between a vertical line and a line joining two crests in successive horizontal lines, we may easily calculate by simple formulas the period indicated.

Since the photometric values of all the curves in the diagram are proportional to the plotted ordinates, the photographic summation of the whole pattern in a vertical direction is almost an exact analogue of a numerical summation. This summation is simply done by a positive cylindrical lens with vertical axis. This brings down on the plate a series of vertical lines or stripes. If, now, we cut across these lines with a horizontal slit, the light coming through this slit from one end to the other will be the summation of the diagram in the vertical.


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86 scale could easily be cast in all sizes upon a plotted curve. But all these methods of equal spacing on a plotted curve leave far too much to the individual judgment of the investigator.

A method of periodic analysis well adapted to the work in hand has been developed by the writer as the need for it became more and more evident. Along with the feeling of need for rapid analysis was the increasing recognition of the desirability of some process which would place mere individual judgment and personal equation as far in the background as possible.

Schuster's periodogram. — In 1898, Schuster suggested the use of the word "periodogram" as analogous to the word spectrogram; that is, a periodogram is a curve or a photograph which indicates the intensity of time periods just as the spectrogram indicates intensity of space-periods or wave-lengths. The spectrogram commonly gives its intensities by varying photographic density along a band of progressive wave-lengths. For the periodogram Schuster made simply a plotted curve, of which the abscissæ represented progressive time-periods and the ordinates represented intensities. He made a mathematical analysis of the sunspot numbers and constructed a periodogram which is reproduced in figure 30. It shows periods at its crest at 4.38, 4.80, 8.36, 11.125, and 13.50 years.

The optical periodogram. — It is, of course, not necessary that the periodogram should take the form of a plotted curve with intensities represented by ordinates, nor yet need it be exactly like a spectrogram showing intensities by density. The first periodogram produced by the writer is shown in plate 9,. It is an analysis of the sunspot


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 Need for such analysis.—During these modern times of rainfall and sunspot records we may compare such records with tree-growth and obtain the interesting correlations exhibited in the last two chapters; but the tree records extend centuries and even thousands of years back of the first systematic weather or sun records of any kind. Without being over-precise or exhaustive, it is interesting to note that California weather records began about 1851. Records on the Atlantic coast began largely in the half-century before that date. London has a rainfall record since 1726, Paris since 1690, and Padua since 1725. Good sunspot records began about 1750, but the number of maxima and minima is known between 1610 and 1750, although the exact dates are uncertain. All this does not carry us very far back, but it serves as an excellent basis for the correct interpretation of the record in the trees.

It would be possible to apply correlation formulas to the Arizona tree records and perhaps to the sequoias and construct a probable rainfall record for long periods of time, but apart from Huntington's study of the "Climatic Factor in History," the chief use of such a record would be in studying the laws which govern rainfall; and this is best done through cycles. We shall find that the sunspot cycle plays an important rôle in rainfall. But we find traces of the solar cycle in nearly all of our tree groups, and evidently the way to read the trees is to study first of all their alphabet of cycles. Hence the best methods of identifying cycles must be used.

Proportional dividers. — If a short series of observations is to be tested for a single period, it can be done by mathematics, but it will take many hours and give a result in terms so precise as often to deceive. This, for example, has been the difficulty with the mathematical solution of the sunspot curve. It seems to the writer that the safer way to solve such a curve is by a graphic process, plotting the curve and applying equal intervals along it. An extremely good instrument for this purpose is the multiple-point proportional dividers. By a system of pivots and bars, 16 or more points are maintained in a straight line and at equal intervals, while the space between two successive points may be drawn out from one-eighth inch to one inch. The remarkable persistence of the half sunspot period in the early Flagstaff trees was detected in this way.

The projection of equal spacing on curves as long as 12 to 15 feet has been done by a 10-foot india-rubber band with small metal clips pinched on at regular intervals. As the band was stretched all the intervals were enlarged by equal amounts, and periodic phenomena were detected. Similar use could be made of the sharp shadows cast by the glowing carbon of an arc-light. The shadow of a transparent


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84 slower-moving latitudes on each side would present much mechanical disturbance and favor the formation of local vortices. Such a process as this would be accompanied by the increased radiation in sunspot maximum which has been observed. If this hypothesis has a basis of fact, it is probable that the increased radiation at that time would come from the sun's equator, where there are no spots. Increased rotational movement of the equatorial zone at the sunspot maximum should be susceptible of observation by spectroscopic means. The meaning of the slow movement of this spot-forming zone toward the equator, as sunspot maximum changes to minimum, is not clear under this hypothesis; nor does one see why the secondary spot described by Hale (1919) should have its definite location following the principal spot, nor why the magnetic polarity of spots changed near the last sunspot minimum. These phenomena, recently observed by Hale and his collaborators, point toward causes within the sun.

Length of the sunspot period. — For many years Newcomb's figure of 11.13 years has been commonly quoted. However, recently some of the best authorities say frankly that it may be anywhere from 11 years to nearly 12 years. Schuster (1898-1906) discussed analytically the best known sunspot numbers, those since 1750. This has been followed by the work of Kimura (1913), and especially Turner (1913) and Michelson (1913). In general, the analyses by Schuster and Kimura, and by Turner in his earlier papers, produce a large number of possible periods of small amplitude. Michelson, however, goes to the other extreme. "Indeed," he says, "it would seem that with the exception of the 11-year period and possibly a very long period (of the order of 100 years) the many periods found by previous investigators are illusory." Turner in his hypothesis referred to above reduces the number to a few, which supply a basis for his reasoning. Michelson had favored a period of about 11.4 years and Turner says that only this 11.4-year period is sensible at the present time.

Tree-growth and solar activity. — The correlation shown in this chapter suggests a possible use of the annual rings of trees in the study of solar activity. There are two lines which such a study might take. An intensive line already mentioned includes the search for wet-climate trees showing the solar rhythm in their growth and the determination of the conditions under which they produce this curve. An extensive line of study is obviously possible also in reconstructing, as far as possible, a history of the sunspot cycle from very old trees. The yellow pines of Arizona give evidence that 500 years ago the cycle was operating very much as now. The sequoias, if correctly interpreted, already carry the history back over 3,000 years, and beyond that fossil trees may stretch the time covered in part at least into millions of years.


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Rh H. H. Turner (1913; cf. Sampson, 1914) has worked out an hypothesis which is stimulating, even if not yet acceptable. He supposes that the Leonid swarm of meteors, revolving once in about 33 years in a very eccentric orbit, is at the basis of the sunspot recurrence. These meteors were observed in countless swarms, filling the sky for a few nights in November 1799, and again in 1833 and 1866. In 1899 they were expected, but failed to appear in large numbers, having probably been swerved to one side through the attraction of some planet. Turner finds that they have passed near Saturn several times in the last 2,000 years. At some of these encounters a quantity of meteors may have been detached and losing their own velocity may have fallen nearly straight toward the sun, grazing its outer surface in their circuit at a velocity of 400 miles per second, then swinging out to aphelion near their place of encounter, and completing their revolution in about 11 years. Successive returns of the main Leonid swarm, approaches of Saturn, and perhaps even the influence of other planets would be sufficient to perturb this meteoric swarm and cause the variations in period observed. On their terrific flight close to the sun many would be caught in the sun's outer atmosphere, thus in some way causing sunspots.

This hypothesis attempts to explain the period and its irregularities, including the double and triple period. I refer to it at some length because the investigation of trees gives evidence not only of climatic variations in the sunspot period, but of double and triple sunspot periods and possibly of still larger fluctuations. Turner's hypothesis warrants further discussion to explain why the spots appear in sub-tropical latitudes but not at the solar equator. In the planetesimal hypothesis of Chamberlin and Moulton, the rotation of the sun on its axis is attributed to the material falling back upon it after receiving a slight orbital motion from the visiting star. The authors state that the process may still be going on. This view is sustained by arguments based on the zodiacal light and on meteors, both of which seem best explained as planetesimal matter not yet returned to the solar mass. Matter as yet unabsorbed would very likely consist of particles which had been given just enough orbital motion to escape the surface of the sun on their periodic return. The particles for the most part would then have extremely eccentric orbits and pass close to the sun's surface at tremendous velocity. They would be moving largely in the plane of the solar system and consequently would pass close to the sun's equator. If finally caught in the sun's atmosphere, friction would reduce their motion, turning a large part of it into heat and a part into forward movement of the sun's atmosphere. Thus the planetesimal hypothesis explains the equatorial acceleration. A large meteoric group, as suggested by Turner, is therefore consistent with the hypothesis. The undefined zone between the accelerated equator and the


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82 From the description above it is easily seen that the sunspots are not likely to be in themselves the fundamental solar activity, but rather an index of something else, and possibly a very sensitive index, for the percentage change in spot numbers is hundreds of times as great as the percentage changes in measured radiation between sunspot maxima and minima.

Suggested causes of sunspots. — The cause of sunspots is still a matter of conjecture, and there is no generally accepted hypothesis to explain them. There is analogy to our clouds in that both indicate decreased temperature. In their limitation to certain latitudes they resemble the belts of Jupiter. The belts of Jupiter are roughly the lines of division between the powerful easterly equatorial current and the slower moving zones on either hand; and indeed this has been suggested as an explanation of the particular location in latitude of the sunspots, for there is an increase in speed of rotation of the sun's surface as the equator is approached. Their periodic character is very difficult to explain. Fundamental periodic changes in the body of the sun have been suggested and, in the absence of better explanations, some such statement hazily indicating the direction in which explanation is to be sought, is perhaps the best that we can do. Planetary influence, however, has often been proposed as the cause. The near agreement between the revolution period of Jupiter and the sunspot period has naturally attracted attention. Stratton (1911-1912) has made a very interesting study of the appearance, continuance, and disappearance of spots on portions of the sun facing toward or away from Jupiter and Venus. A few per cent more spots do originate and disappear on the "afternoon" of the side facing Venus than on other longitudes, but he considers the case of physical relationship not proven.

Planetary influence is sought in a theory proposed by W. J. Spillman (1915). In this theory gravitation is assumed to be due to pressure variations in the ether arising from electronic rotation in the attracting body. The varying speed of a planet in its orbit between perihelion and aphelion, involving varying quantities of energy, requires, he says, an interchange between the kinetic energy of the plant and the atomic energy of the central attracting body. This atomic energy is in the vibrations of the electrons, but he thinks it is likely to affect both the temperature and the electric activity of the central body. The effect in this way of Jupiter and Saturn would exceed the sum of all the other planets combined and is therefore the only one considered. The effect of Jupiter with its substantial variations in distance between perihelion and aphelion predominates, and we have a marked resemblance between the sunspot curves since 1770 and the differential planetary effect. One notices that this interchange of energy would presumably affect all parts of the sun alike and that therefore we could not expect an excess of sunspots on the side facing Jupiter.


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Rh THE SUNSPOTS AND THEIR POSSIBLE CAUSES.

If the sunspots are an index of some solar activity so far reaching as to affect our climate and vegetation, it is well to note very briefly their appearance and the suggested causes of their periodic character.

Appearance — At first view sunspots are small black areas appearing from time to time on the sun. In actual size they vary from a few hundred miles in diameter to more than a hundred thousand. Rarely seen by the naked eye, the vast majority are only discovered through the telescope; hence it was only after the invention of that instrument that records of them were kept and their nature investigated. As Hale (1908) has found, they are cooling places; they merely look black by contrast with their more intensely bright background. His remarkable photographs show that they often have a rotation about their own center. They usually come in groups between latitude 5° and 25° in each hemisphere of the sun and are almost continuously changing in small details. Their life is usually less than one rotation of the sun.

Schwabe in 1851 announced their periodic character with maxima every 11 years. During sunspot maximum a small telescope will show 5 to 20 spots, but during the minimum one may search for weeks without finding a spot that can be certainly recognized. Records of the numbers of spots were specially collected by Wolf for many years and later by Wolfer of Zurich. At the present day many observatories are taking daily photographs of them. The term relative sunspot number was invented to convey an idea of the average number of spots visible at any one time under favorable circumstances. The number actually counted receives a simple correction for unfavorable weather or small telescope, so that the published numbers shall be as nearly standard as possible.

While the spot appears black and may possibly be sinking into the sun, it is usually attended by intensely bright areas or faculæ and even by prominences which are often violently explosive, ejecting matter hundreds of thousands of miles from the sun's surface. Thus the sunspot maximum indicates increased activity at the surface of the sun, which, according to Abbot (1913 and 19132), is actually sending us increased heat radiation. During the maximum the magnetic condition of the earth is profoundly affected, as evidenced by northern lights, magnetic storms, earth currents, and variations of the earth's magnetic constants. This relation to the earth's magnetism has been recognized from the first discovery of the periodicity of sunspots. But the effect of the change of solar radiation on climate and ordinary weather elements is more obscure. General effects on climatic conditions have been admitted as probable by Penck (1914), but in general the great weight of opinion has been against a traceable effect of solar activity on weather or climate.


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Rh crosses were placed upon the central ring, which was usually the largest of the group. These crosses are well shown in plate 4,. Their dates were noted during the measuring. In figure 26 the ordinates give the number of maximum marks found in each date throughout the whole

80 sections. The more recent dates show higher crests because there are more trees. In the second line is the sunspot curve. The matching of the crests of the two curves is unmistakable. The secondary tree-crest at sunspot minimum is very regular, as would be expected from the inclusion of the three groups of figure 24, some of which are evident reversals. This test is only qualitative, but seems to the writer to offer substantial support to the quantitative relation shown in figure 25.

Windsor (Vermont) correlation. — An interesting sidelight is thrown on this type of correlation by the American curves from Windsor, Vermont.


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78 In seeking further evidence of sunspot correlation, advantage was taken of certain statistics recorded while measuring the various sections. Before making the measures or identifying the rings in any way, the groups of rings larger than the average were sought out and


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Rh which neither allowed himself to regard as conclusive. In the immense work of Hellmann (1906) upon the rainfall of the North German drainage area, it is this inconspicuous maximum which he finds the more important of the two.


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Rh


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 {|
 * || DOUGLASS PLATE 8
 * | A
 * Climatic Cycles and Tree-Growth Plate 8A.jpg
 * | B
 * Climatic Cycles and Tree-Growth Plate 8B.jpg
 * }
 * | B
 * Climatic Cycles and Tree-Growth Plate 8B.jpg
 * }

A. Section of Scotch pine from Eberswalde, Prussia, showing solar rhythm.

B. Another section from the same forest, showing same rhythm.


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 Dry-climate tests.— In the work of 1907 (published 1909) upon the first group of 25 yellow pines from 1700 to 1900 A. D., several long sequences of variation in a 5 to 6 year period were noted. These were compared with rainfall records at Prescott and in southern California and the crests of rainfall and growth appeared to coincide in date. It was then seen that the temperature curve of southern California had a period and phase corresponding to the rainfall curve, but with the second minimum almost entirely suppressed, and that finally this temperature curve resembled in form and phase the inverted curve of sunspot numbers. In connection with the publication referred to (1909), a set of curves was prepared to show these relationships. This set is partly reproduced in figure 34, page 104. In the original drawing the tree-curve was the least satisfactory, which was to be expected, as no real certainty in the dating of rings existed at that time. After cross-identification the tree-curve was again integrated for the 11-year period and far better results were obtained. This new curve is given in the figure referred to.

This type of integrated curve gives many facts in a very condensed form. A differential or detailed form of presentation should accompany it, as in figure 25, showing the full series of individual observations and beside it the curve with which it is to be compared. The differential study of the Arizona trees will be taken up in connection with cycles, but can be summarized in the statement that in the last 160 years 10 of the 14 sunspot maxima and minima have been followed about four years later by pronounced maxima and minima in the tree-growth. Also, during some 250 years of the early growth of these trees, they show a strongly marked double-crested 11-year variation.

Wet-climate reaction. — In the very first group of continental trees studied, those obtained at Eberswalde near Berlin, the remarkable fact was recognized at once that 13 trees from one of those carefully tended German forests show the 11-year sunspot curve since 1830 with accuracy. The variation in the trees is shown in plate 8. The arrows on the photographs are not to call attention to the larger growth, but to mark the years of maximum sunspots. The other trees of that group do not show quite so perfect rhythm as do the marked radii shown, but are like the other parts of these sections, showing strongly a majority of the maxima. Taking the group as a whole, the agreement is highly conspicuous, and the maximum growth comes within 0.6 year of the sunspot maximum. The Eberswalde curves arranged in two groups and compared with the sunspot curve were shown in figure 9, page 38.

In the group of six sections from south Sweden, which were measured subsequently in Stockholm, a spruce (Picea excelsa) was discovered which shows the sunspot rhythm with the same striking clarity as the


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Rh into meteorological districts. Yet, in spite of local differences, mountain regions may be alike in major characteristics, for all the Prescott groups, though differing among themselves, cross-identify excellently with the Flagstaff trees 60 miles away. The sequoias also cross-identify perfectly in mountain localities 50 miles apart, showing that there is enough similarity in different parts of the high Sierras to cause the trees to agree in many variations.

Arizona and California. — Fully 450 miles intervene between the sequoias of California and the pines of Arizona, yet there are strong points of identity between them in the last 300 years. The dates of notably small rings are much alike in each. The details of this comparison have not yet been fully studied, but they support the idea long since expressed (1909) that Arizona and California, especially its southern half, form parts of a large district which has similarity in certain variations. A long acquaintance with this region throws light on the details of this similarity. The winter precipitation, which is largely in the form of snow at the altitude of the trees studied, has the major influence on tree-growth, for it is largely conserved near the trees, whereas the summer rains are usually torrential and the water quickly flows away. The winter storms moving in an easterly direction reach the coast region first and after about 24 hours are felt in Arizona. Thus, in spite of the coast range of mountains and the intervening low-level deserts, each winter storm passes over both regions and causes an evident similarity between them. In a large view they belong to a single meteorological district.

Meteorological districts and solar correlation. — In searching for a link of connection between solar variation and meteorological changes, we must bear in mind the effect of possible reversals in neighboring meteorological districts, such as noted above in Norway. It may be the lack of such precaution which has caused many meteorologists to condemn at once the suggested connection between the distant cause and the nearby effect. We must remember that districts may be small in area, and in combining many together we may neutralize the result for which we are in search. Some illustration of correlation found in small districts will be given in the final chapter.


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72 trees is probably not as good in details as Huntington's samples from young and sensitive trees. His material is well worth cross-identifying and dating with care, and then comparing with any records of snowfall which can be obtained from the sequoia groves. It is greatly to be regretted that Fresno, 65 miles away and at 5,000 feet lower elevation, is the nearest point where precipitation records can be obtained for a period long enough to be of value.

Future work.— It will be very interesting to find whether the characteristics of the correlation at Prescott are general in arid climates and dry soils and whether practical formulas for conservation in moist soils or climates can be worked out. When this is done the significance of the study of annual rings will be greatly increased.

The study above described raised emphatically the question as to the extent of the region or district from which comparative rain records should be selected. Such a meteorological district could be defined as one in which homogeneous weather elements are found. But we immediately ask ourselves the questions: must all weather elements be alike in it or is it sufficient to have only rainfall (for example) essentially the same throughout; will the district remain constant through indefinite time or will it change; is the district for short-period weather changes the same as the district covered by secular changes. In the present discussion I have understood by meteorological districts such regions as may show similar or identical variations in some one weather element. It seems likely that a region which may show unity in small or rapid variations may not do so in large and slow variations, or more likely may be a small fraction of a region which will show unity in large variations.

Meteorological districts and growth of trees. — The cross-identification of trees over large areas has already suggested the use of annual rings as a possible aid in delineating meteorological districts. This function of the rings has received some exemplification in the present study. For instance, the pine trees of Norway differed in such a way that it was necessary to divide them into two classes, one of which came from the outer coast near sea-level and the other from the inner fjords and mountains. The trees from these different regions show strong reversal with reference to each other. Again, the trees from the lowlands about the Baltic Sea show marked similarity in their variations and indicate, as we would expect, a homogeneous district. Furthermore, groups from near the Alps show strong differences from the other European groups, as we might expect from our experience with the five groups from the mountainous country about Prescott. A rugged and mountainous region is very difficult to divide satisfactorily


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178 stretched out and the kind deed ready to follow it.

This suavity is not limited to any rank or condition. It extends all the way down from the prince to the poorest peasant. Some of our party driving out in a hackey-coach yesterday, met some German ladies in a coach with four horses, postillions, footmen in livery, and other marks of rank and wealth. What would Americans have done in a similar position? Probably looked away and seemed unconscious. And English ladies would have done the same, or, as I have seen them in Hyde Park, have leaned back in their carriages, and stared with an air of mingled indifference and insolence through their eyeglasses, as if their inferiors in condition could bear to be stared at. The German ladies bowed most courteously to the humble strangers in the hackney-coach.

Yesterday, at the table d'hôte, I observed a perpendicular old gentleman, who looked as if he had been born before any profane dreams of levelling down the steeps of aristocracy had entered the mind of man, and whose servant, in rich livery, as stiff as himself, was in waiting behind him, bow to the persons opposite to him as he took his seat, and to those on his right hand and his left. Soon after our landlord came to speak to him, and familiarly and quite acceptably, as it appeared, laid his hand on the nobleman's shoulder while addressing him.

Soon after we came here, a gentleman with whom we passed a few hours in a Rhine steamer met us


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Rh pond, but of the moving type, as if a belated supply from the snows came to hand and then passed on. The tree was assumed to receive moisture from the current year and from the first and second preceding years; and whichever of the three was greater, that one had the more effect. The application of this formula is shown in figure 20.

But on identifying the rings in the trees collected from that locality in 1915, and especially on finding the soft, delicate parts of the 1915 ring on D-5, it seemed fairly certain that the curve of growth given in figure 20 is one year in error through the omission of a final ring. The growth, then, which appeared to be 1902, for example, and for which a pronounced conservation was necessary, really came the year before,

and less conservation or none was needed. The comparison of the same rainfall curve with the old sequoias of the present series is given in figure 21. In this the agreement is not as good as at Prescott, but there is marked similarity in many details. My curve from very old


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70 3. From An an approximate Rn is found by the formula

4. This series of approximate rainfall Rn is smoothed and becomes the Sn of the formula.

5. Final values are then found by the proportion

It should be emphasized that the above formula for conservation is the one found to apply under dry climatic conditions. In moist climates the trees, so far as observed, seem to depend on other meteorological elements or combinations of elements.

The Prescott trees, as we have seen, even without correction give a record of rainfall with an accuracy of about 70 per cent. It is possible that the Flagstaff trees with their higher elevation, more certain rainfall, and more central location in the zone occupied by this species give somewhat more accurate records. They are probably much less often subjected to extremes of dryness, which throw the tree out of its equilibrium and cause it to produce an abnormally small set of rings. It seems likely, also, that the less compact soil, combined with a more abundant precipitation, produces a yearly growth more nearly proportional to the rainfall than at Prescott.

Summary. — In considering this reduction it seems fairly clear that (1) there is a strong correlation between rainfall and tree-growth; (2) the accuracy may be increased by introducing a conservation correction; (3) in dry soils this factor enters as a coefficient; (4) this coefficient depends on the state of activity of the tree; (5) in the Prescott trees this state of activity follows the curve of accumulated moisture.

Although the moisture-content of apparently dry ground may be a most important item, it is by no means certain that the observed accumulated moisture effects consist in actual moisture in the ground. It may be that they represent some vital condition of the tree. The matter is a very interesting one for future study.

Sequoia correlation with rainfall. — On his return from the big trees in 1912, Professor Huntington supplied me with a curve of sequoia growth obtained from many comparatively young trees which had been cut in the lower edge of Redwood Basin near Camp 6. On comparing these with his curve of rainfall in the San Joaquin Valley, compiled from records at Fresno and San Francisco, a close relation was not evident, but an additive formula

was used with encouraging results. This formula was designed to allow for strong conservation in the soil, not of the static type as in a


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Rh which the trees had exhibited in the preceding few years. But this average growth bore the same relation to the average or smoothed rainfall that the accumulated moisture bore to the smoothed rainfall. Hence the ratio between accumulated moisture and smoothed rainfall gave at once the required ratio between smoothed tree-growth and smoothed rainfall. These relations are shown in figures 16 and 17.

Accumulated moisture is simply the algebraic sum of the amounts by which all the years in a series from the start to and including the year desired depart from the mean. It may be expressed by a formula, thus

$$A_n=(R_1-M)+(R_2-M)+....(R_n-M)=R_1+R_2+R_3+...R_n-nM$$

and conversely

In this formula An is the accumluated moisture for the nth year of a series of consecutive years whose mean rainfall is M.

The simple empirical formula for the tree-growth Tn for the nth year of this series thus was found to be:

in which c and d are small constants found advantageous in reducing the accumulated moisture curve to proper scale. Sn is the reading of the smoothed rainfall curve and the term $$cM+d A_n$$ is the accumulated moisture expressed in values above a base-line instead of departures from a mean. In actual numbers this becomes

The mean value of the rainfall M is 17.1 inches. The application of this formula in calculating tree-growth at Prescott from the rainfall is shown in figure 18.

The reversal of the process in order to ascertain rainfall from tree-growth seems to be fully as accurate over this limited period, and its result is shown in figure 19, where the curve has an average accuracy of 82 per cent for individual years. In producing this reversal the following operations were performed:

1. A 5-year smoothed curve was made of the tree-growth. This gives us the term $$\frac{0.90M+\tfrac{1}{4}A_n}{250}$$ in the reversed formula

2. This term is multiplied by 1,000 and 3.6M subtracted, leaving An in inches.


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68 The first assumption in regard to conservation was that the ring-growth in any one year was built up by contributions from the current year and previous years in diminishing proportion. For example, it would be proportional to

in which Rn is the rainfall for the current year, Rn-1 that for the year preceding, etc. This may be called an additive correction. It did not

Fig. 15.—Relation of tree-growth and rainfall at Prescott, Arizona. Tree-growth and rainfall uncorrected.

Fig. 16.—Five-year smoothed curves of growth and rainfall.

Fig. 17.—Accumulated rain and smoothed tree-growth.

Fig. 18.—Actual tree-growth and growth calculated from rain.

Fig. 19.—Actual rain and rain calculated from tree-growth.

give satisfactory results for the Prescott trees, although a formula of this general type has been applied with some success to the sequoia, which grows in more moist soil.

The variations in the Prescott trees were seen to be proportional both to the rainfall of the year and to the average growth or activity


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Rh of the profits and losses of the preceding years. The "credit balance" in their books at the beginning of the year has only somewhat less importance than the income during the current year.

Mathematical relation of rainfall and growth. — In order to formulate the relation between rainfall and tree-growth, an effort was made to construct a mathematical formula for calculating the annual growth of trees when the rainfall is known. Any such formula must perform three principal functions: (1) reduce the mean rainfall to the mean tree-growth; (2) provide a correction to offset the decreasing growth with increasing age of the tree; and (3) express the degree of conservation by which the rain of any one year has an influence for several years. In a formula of universal application other factors will play a part, but for a limited group of trees in one locality they can be neglected.

The first process, namely, the reduction of the mean rainfall to the mean tree-growth, is a division by 250. This is the general factor K in the formula below. The second part, namely, the correction for the age of the tree, was practically omitted in forming the curves shown, since judging by the Flagstaff curves its effect would be very slight in the interval under discussion. In long periods it is an immensely important correction and its effect should always be investigated. Over the short periods used in this rainfall discussion the decrease of annual growth with age may be regarded as linear and an approximate formula is

Where Gn represents growth in any year n; Gy is growth in middle year of series y, and c is the rate of change per year, a constant which was 0.0043 in the last half century of the Flagstaff series. Over the whole interval from 1700 to 1900, in the first Flagstaff curve, the growth was approximately an inverse proportion to the square root of the time elapsed since the year 1690 and may be closely expressed in millimeters by the formula

Tn is here the mean tree-growth for the year n. If G be the mean size of rings, then the factor to be introduced in a general formula becomes

Character of the conservation term. — This factor has two important features: (1) in this arid climate it applies better as a coefficient than as an additive term, and (2) it gives a prominent place to "accumulated moisture" as commonly used in meteorology.