Chapter XII: Applications (1)

(i.) _Systems of Measures._[1]

118. _Metric System._--The metric system was adopted in France at the end of the 18th century. The system is decimal throughout. The principal units of length, weight and volume are the _metre, gramme_ (or _gram_) and _litre_. Other units are derived from these by multiplication or division by powers of 10, the names being denoted by prefixes. The prefixes for multiplication by 10, 10^2, 10^3 and 10^4 are _deca-, hecto-, kilo-_ and _myria-_, and those for division by 10, 10^2 and 10^3 are _deci-, centi-_ and _milli-_; the former being derived from Greek, and the latter from Latin. Thus _kilogramme_ means 1000 grammes, and _centimetre_ means 1/100 of a metre. There are also certain special units, such as the _hectare_, which is equal to a square hectometre, and the _micron_, which is 1/1000 of a millimetre.

The metre and the gramme are defined by standard measures preserved at Paris. The litre is equal to a cubic decimetre. The gramme was intended to be equal to the weight of a cubic centimetre of pure water at a certain temperature, but the equality is only approximate.

The metric system is now in use in the greater part of the civilized world, but some of the measures retain the names of old disused measures. In Germany, for instance, the _Pfund_ is 1/2 kilogramme, and is approximately equal to 1(1/10) lb. English.

119. _British Systems._--The British systems have various origins, and are still subject to variations caused by local usage or by the usage of particular businesses. The following tables are given as illustrations of the arrangement adopted elsewhere in this article; the entries in any column denote multiples or submultiples of the unit stated at the head of the column, and the entries in any row give the expression of one unit in term of the other units.

LENGTH

+-------+-------+-------+--------+----------+---------+
| Inch. | Foot. | Yard. | Chain. | Furlong. | Mile. |
+-------+-------+-------+--------+----------+---------+
| 1 | 1/12 | 1/36 | 1/792 | 1/7920 | 1/63360 |
+-------+-------+-------+--------+----------+---------+
| 12 | 1 | 1/3 | 1/66 | 1/660 | 1/5280 |
+-------+-------+-------+--------+----------+---------+
| 36 | 3 | 1 | 1/22 | 1/220 | 1/1760 |
+-------+-------+-------+--------+----------+---------+
| 792 | 66 | 22 | 1 | 1/10 | 1/80 |
+-------+-------+-------+--------+----------+---------+
| 7920 | 660 | 220 | 10 | 1 | 1/8 |
+-------+-------+-------+--------+----------+---------+
| 63360 | 5280 | 1760 | 80 | 8 | 1 |
+-------+-------+-------+--------+----------+---------+

WEIGHT (AVOIRDUPOIS)

+--------+--------+--------+----------+----------------+---------+
| Ounce. | Pound. | Stone. | Quarter. | Hundredweight. | Ton. |
+--------+--------+--------+----------+----------------+---------+
| 1 | 1/16 | 1/224 | 1/448 | 1/1792 | 1/33840 |
+--------+--------+--------+----------+----------------+---------+
| 16 | 1 | 1/14 | 1/28 | 1/112 | 1/2240 |
+--------+--------+--------+----------+----------------+---------+
| 224 | 14 | 1 | 1/2 | 1/8 | 1/160 |
+--------+--------+--------+----------+----------------+---------+
| 448 | 28 | 2 | 1 | 1/4 | 1/80 |
+--------+--------+--------+----------+----------------+---------+
| 1792 | 112 | 8 | 4 | 1 | 1/20 |
+--------+--------+--------+----------+----------------+---------+
| 33840 | 2240 | 160 | 80 | 20 | 1 |
+--------+--------+--------+----------+----------------+---------+
(Also 7000 grains = 1 lb. avoirdupois.)

120. _Change of System._--It is sometimes necessary, when a quantity is expressed in one system, to express it in another, The following are the ratios of some of the units; each unit is expressed approximately as a decimal of the other, and their ratio is shown as a continued product (S 116), a few of the corresponding convergents to the continued fraction (S 117) being added in brackets. It must be remembered that the number expressing any quantity in terms of a unit is _inversely proportional_ to the magnitude of the unit, i.e. the number of new units is to be found by multiplying the number of old units by the ratio of the old unit to the new unit.

Yard 9144 10000 11 884 8225 /11 32 8 4 235\
----- = ----- = ----- = -- . --- . ---- ... ( --,-- = -.-,--- )
Metre 10000 10935 12 385 8224 \32 35 7 5 257/.

Inch 25400 10000 5 66 1651 /5 33 127\
---------- = ----- = ----- = - . -- . ---- ... ( -, --, --- )
Centimetre 10000 3937 2 65 1650 \2 13 50/.

Mile 16093 10000 8 185 2369 /8 37 103\
--------- = ----- = ----- = - . --- . ---- ... ( -, --, --- )
Kilometre 10000 6214 5 184 2368 \5 23 64/.

Square Yard 8361 10000 5 306 15250 /5 51 250\
------------ = ----- = ----- = - . --- . ----- ... ( -, --, --- )
Square Metre 10000 11960 6 305 15249 \6 61 299/.

Acre 4047 10000 2 85 5320 /2 17 380\
------- = ----- = ----- = - . -- . ---- ... ( -, --, --- )
Hectare 10000 24711 5 84 5321 \5 42 939/.

Quart 11365 10000 8 175 8976 /8 25 408\
----- = ----- = ----- = - . --- . ---- ...( -, --, --- )
Litre 10000 8799 7 176 8975 \7 22 359/.

Pound 4536 10000 1 10 484 29391 /1 5 44 303\
---------- = ----- = ----- = - . -- . --- . ----- .. ( -, --, --, --- )
Kilogramme 10000 22046 2 11 485 29392 \2 11 97 668/.

(ii.) _Special Applications._

121. _Commercial Arithmetic._--This term covers practically all dealings with money which involve the application of the principle of proportion. A simple class of cases is that which deals with equivalence of sums of money in different currencies; these cases really come under S 120. In other cases we are concerned with a proportion stated as a _numerical percentage_, or as a _money percentage_ (i.e. a sum of money per L100), or as a _rate_ in the L or the shilling. The following are some examples. Percentage: _Brokerage, commission, discount, dividend, interest, investment, profit and loss._ Rate in the L: _Discount, dividend, rates, taxes._ Rate in the shilling: _Discount._

Text-books on arithmetic usually contain explanations of the chief commercial transactions in which arithmetical calculations arise; it will be sufficient in the present article to deal with interest and discount, and to give some notes on percentages and rates in the L. _Insurance_ and _Annuities_ are matters of general importance, which are dealt with elsewhere under their own headings.

122. _Percentages and Rates in the L._--In dealing with percentages and rates it is important to notice whether the sum which is expressed as a percentage of a rate on another sum is a part of or an addition to that sum, or whether they are independent of one another. Income tax, for instance, is calculated on income, and is in the nature of a deduction from the income; but local rates are calculated in proportion to certain other payments, actual or potential, and could without absurdity exceed 20s. in the L.

It is also important to note that if the increase or decrease of an amount A by a certain percentage produces B, it will require a different percentage to decrease or increase B to A. Thus, if B is 20% less than A, A is 25% greater than B.

123. _Interest_ is usually calculated yearly or half-yearly, at a certain rate per cent. on the principal. In legal documents the rate is sometimes expressed as a certain sum of money "per centum per annum"; here "centum" must be taken to mean "L100."

_Simple interest_ arises where unpaid interest accumulates as a debt not itself bearing interest; but, if this debt bears interest, the total, i.e. interest and interest on interest, is called _compound interest._ If 100r is the rate per cent. per annum, the simple interest on LA for n years is LnrA, and the compound interest (supposing interest payable yearly) is L[(1 + r)^n - 1]A. If n is large, the compound interest is most easily calculated by means of logarithms.

124. _Discount_ is of various kinds. Tradesmen allow discount for ready money, this being usually at so much in the shilling or L. Discount may be allowed twice in succession off quoted prices; in such cases the second discount is off the reduced price, and therefore it is not correct to add the two rates of discount together. Thus a discount of 20%, followed by a further discount of 25%, gives a total discount of 40%, not 45%, off the original amount. When an amount will fall due at some future date, the _present value_ of the debt is found by deducting discount at some rate per cent. for the intervening period, in the same way as interest to be added is calculated. This discount, of course, is not equal to the interest which the present value would produce at that rate of interest, but is rather greater, so that the present value as calculated in this way is less than the theoretical present value.

125. Applications to _Physics_ are numerous, but are usually only of special interest. A case of general interest is the measurement of _temperature._ The graduation of a thermometer is determined by the freezing-point and the boiling-point of water, the interval between these being divided into a certain number of degrees, representing equal increases of temperature. On the Fahrenheit scale the points are respectively 32 deg. and 212 deg.; on the Centigrade scale they are 0 deg. and 100 deg.; and on the Reaumur they are 0 deg. and 80 deg. From these data a temperature as measured on one scale can be expressed on either of the other two scales.

126. _Averages_ occur in statistics, economics, &c. An average is found by adding together several measurements of the same kind and dividing by the number of measurements. In calculating an average it should be observed that the addition of any numerical quantity (positive or negative) to each of the measurements produces the addition of the same quantity to the average, so that the calculation may often be simplified by taking some particular measurement as a new zero from which to measure.

AUTHORITIES.--For the history of the subject, see W.W.R. Ball,
_Short History of Mathematics_ (1901), and F. Cajori, _History of
Elementary Mathematics_ (1896); or more detailed information in M.
Cantor, _Vorlesungen uber Geschichte der Mathematik_ (1894-1901). L.
C. Conant, _The Number-Concept_ (1896), gives a very full account of
systems of numeration. For the latter, and for systems of notation,
reference may also be made to Peacock's article "Arithmetic" in the
_Encyclopaedia Metropolitana_, which contains a detailed account of
the Greek system. F. Galton, _Inquiries into Human Faculty_ (1883),
contains the first account of number-forms; for further examples and
references see D.E. Phillips, "Genesis of Number-Forms," _American
Journal of Psychology_, vol. viii. (1897). There are very few works
dealing adequately but simply with the principles of arithmetic.
Homersham Cox, _Principles of Arithmetic_ (1885), is brief and lucid,
but is out of print. _The Psychology of Number_, by J.A. McLellan and
J. Dewey (1895), contains valuable suggestions (some of which have
been utilized in the present article), but it deals only with number
as the measure of quantity, and requires to be read critically. This
work contains references to Grube's system, which has been much
discussed in America: for a brief explanation, see L. Seeley, _The
Grube Method of Teaching Arithmetic_ (1890). On the teaching of
arithmetic, and of elementary mathematics generally, see J.W.A.
Young, _The Teaching of Mathematics in the Elementary and the
Secondary School_ (1907); D.E. Smith, _The Teaching of Elementary
Mathematics_ (1900), also contains an interesting general sketch; W.
P. Turnbull, _The Teaching of Arithmetic_ (1903), is more elaborate.
E.M. Langley, _A Treatise on Computation_ (1895), has notes on
approximate and abbreviated calculation. Text-books on arithmetic in
general and on particular applications are numerous, and any list
would soon be out of date. Recent English works have been influenced
by the brief _Report on the Teaching of Elementary Mathematics_,
issued by the Mathematical Association (1905); but this is critical
rather than constructive. The Association has also issued a _Report on
the Teaching of Mathematics in Preparatory Schools_ (1907). In the
United States of America the _Report of the Committee of Ten_ on
secondary school studies (1893) and the _Report of the Committee of
Fifteen_ on elementary education (1893-1894), both issued by the
United States Bureau of Education, have attracted a good deal of
attention. Sir O. Lodge, _Easy Mathematics, chiefly Arithmetic_
(1905), treats the subject broadly in its practical aspects. The
student who is interested in elementary teaching should consult the
annual bibliographies in the _Pedagogical Seminary_; an article by D.
E. Phillips in vol. v. (October 1897) contains references to works
dealing with the psychological aspect of number. For an account of
German methods, see W. King, _Report on Teaching of Arithmetic and
Mathematics in the Higher Schools of Germany_ (1903). (W. F. Sh.)

FOOTNOTE:

[1] See also WEIGHTS AND MEASURES.

ARIUS ([Greek: Areios]), a name celebrated in ecclesiastical history, not so much on account of the personality of its bearer as of the "Arian" controversy which he provoked. Our knowledge of Arius is scanty, and nothing certain is known of his birth or of his early training. Epiphanius of Salamis, in his well-known treatise against eighty heresies (_Haer._ lxix. 3), calls him a Libyan by birth, and if the statement of Sozomen, a church historian of the 5th century, is to be trusted, he was, as a member of the Alexandrian church, connected with the Meletian schism (see MELETIUS OF LYCOPOLIS), and on this account excommunicated by Peter of Alexandria, who had ordained him deacon. After the death of Peter (November 25, 311), he was received into communion by Peter's successor, Achillas, elevated to the presbytery, and put in charge of one of the great city churches, Baucalis, where he continued to discharge his duties with apparent faithfulness and industry after the accession of Alexander. This bishop also held him in high repute. Theodoret (_Hist. Eccl._ i. 2) indeed does not hesitate to say that Arius was chagrined because Alexander, instead of himself, had been appointed to the see of Alexandria, and that the beginning of his heretical attitude is, in consequence, to be attributed to discontent and envy. But this must be rejected, for it is a common explanation of heretical movements with the early church historians, and there is no evidence for it in the original sources. However, Arius was ambitious. Epiphanius, using older documents, describes him as a man inflamed with his own opinionativeness, of a soft and smooth address, calculated to persuade and attract, especially women: "in no time he had drawn away seven hundred virgins from the church to his party." When the controversy broke out, Arius was an old man.

The real causes of the controversy lay in differences as to dogma. Arius had received his theological education in the school of the presbyter Lucian of Antioch, a learned man, and distinguished especially as a biblical scholar. The latter was a follower of Paul of Samosata, bishop of Antioch, who had been excommunicated in 269, but his theology differed from that of his master in a fundamental point. Paul, starting with the conviction that the One God cannot appear substantially ([Greek: ousiodos]) on earth, and, consequently, that he cannot have become a person in Jesus Christ, had taught that God had filled the man Jesus with his Logos ([Greek: sophia]) or Power ([Greek: dynamis]). Lucian, on the other hand, persisted in holding that the Logos became a person in Christ. But since he shared the above-mentioned belief of his master, nothing remained for him but to see in the Logos a second essence, created by God before the world, which came down to earth and took upon itself a human body. In this body the Logos filled the place of the intellectual or spiritual principle. Lucian's Christ, then, was not "perfect man," for that which constituted in him the personal element was a divine essence; nor was he "perfect God," for the divine essence having become a person was other than the One God, and of a nature foreign to him. It is this idea which Arius took up and interpreted unintelligently. His doctrinal position is explained in his letters to his patron Eusebius, bishop of the imperial city of Nicomedia, and to Alexander of Alexandria, and in the fragments of the poem in which he set forth his dogmas, which bears the enigmatic title of "Thalia" ([Greek: Thaleia]), used in Homer, in the sense of "a goodly banquet," most unjustly ridiculed by Athanasius as an imitation of the licentious style of the drinking-songs of the Egyptian Sotades (270 B.C.). From these writings it can even nowadays be seen clearly that the principal object which he had in view was firmly to establish the unity and simplicity of the eternal God. However far the Son may surpass other created beings, he remains himself a created being, to whom the Father before all time gave an existence formed out of not being ([Greek: ex ouk onton]); hence the name of _Exoukontians_ sometimes given to Arius's followers. On the other hand, Arius affirmed of the Son that he was "perfect God, only-begotten" ([Greek: plaeraes theos monogenaes]); that through him God made the worlds ([Greek: aiones], ages); that he was the product or offspring of the Father, and yet not as one among things made ([Greek: gennaema all ouch ton gegenaemenon]). In his eyes it was blasphemy when he heard that Alexander proclaimed in public that "as God is eternal, so is his Son,--when the Father, then the Son,--the Son is present in God without birth ([Greek: agennaetos]), ever-begotten ([Greek: aeigenaes]), an unbegotten-begotten ([Greek: agennaetogenaes])." He detected in his bishop Gnosticism, Manichaeism and Sabellianism, and was convinced that he himself was the champion of pure doctrine against heresy. He was quite unconscious that his own monotheism was hardly to be distinguished from that of the pagan philosophers, and that his Christ was a demi-god.

For years the controversy may have been fermenting in the college of presbyters at Alexandria. Sozomen relates that Alexander only interfered after being charged with remissness in leaving Arius so long to disturb the faith of the church. According to the general supposition, the negotiations which led to the excommunication of Arius and his followers among the presbyters and deacons took place in 318 or 319, but there are good reasons for assigning the outbreak of the controversy to the time following the overthrow of Licinius by Constantine, i.e. to the year 323. In any case, from this time events followed one another to a speedy conclusion. Arius was not without adherents, even outside Alexandria. Those bishops who, like him, had passed through the school of Lucian were not inclined to let him fall without a struggle, as they recognized in the views of their fellow-student their own doctrine, only set forth in a somewhat radical fashion. In addressing to Eusebius of Nicomedia a request for his help, Arius ended with the words: "Be mindful of our adversity, thou faithful comrade of Lucian's school ([Greek: sulloukianistaes])"; and Eusebius entered the lists energetically on his behalf. But Alexander too was active; by means of a circular letter he published abroad the excommunication of his presbyter, and the controversy excited more and more general interest.

It reached even the ears of Constantine. Now sole emperor, he saw in the one Catholic church the best means of counteracting the movement in his vast empire towards disintegration; and he at once realized how dangerous dogmatic squabbles might prove to its unity. His letter, preserved by the imperial biographer, Eusebius of Caesarea, is a state document inspired by a wisely conciliatory policy; it made out both parties to be equally in the right and in the wrong, at the same time giving them both to understand that such questions, the meaning of which would be grasped only by the few, had better not be brought into public discussion; it was advisable to come to an agreement where the difference of opinion was not fundamental. This well-meaning attempt at reconciliation, betraying as it did no very deep understanding of the question, came to nothing. No course was left for the emperor except to obtain a general decision. This took, place at the fist oecumenical council, which was convened in Nicaea (q.v.) in 325. After various turns in the controversy, it was finally decided, against Arius, that the Son was "of the same substance" ([Greek: homoousios]) with the Father, and all thought of his being created or even subordinate had to be excluded. Constantine accepted the decision of the council and resolved to uphold it. Arius and the two bishops of Marmarica Ptolemais, who refused to subscribe the creed, were excommunicated and banished to Illyria, and even Eusebius of Nicomedia, who accepted the creed, but not its anathemas, was exiled to Gaul. Alexander returned to his see triumphant, but died soon after, and was succeeded by Athanasius (q.v.), his deacon, with whose indomitable fortitude and strange vicissitudes the further course of the controversy is bound up.

It only remains for us here to sketch what is known of the future career of Arius and the Arians. Although defeated at the council of Nicaea, the Arians were by no means subdued. Constantine, while strongly disposed at first to enforce the Nicene decrees, was gradually won to a more conciliatory policy by the influence especially of Eusebius of Caesarea and Eusebius of Nicomedia, the latter of whom returned from exile in 328 and won the ear of the emperor, whom he baptized on his death-bed. In 330 even Arius was recalled from banishment. Athanasius, on the other hand, was banished to Treves in 335. During his absence Arius returned to Alexandria, but even now the people are said to have raised a fierce riot against the heretic. In 336 the emperor was forced to summon him to Constantinople. Bishop Alexander reluctantly assented to receive him once more into the bosom of the church, but before the act of admission was completed, Arius was suddenly taken ill while walking in the streets, and died in a few moments. His death seems to have exercised no influence worth speaking of on the course of events. His theological radicalism had in any case never found many convinced adherents. It was mainly the opposition to the Homoousios, as a formula open to heretical misinterpretation, and not borne out by Holy Writ, which kept together the large party known as Semiarians, who under the leadership of the two Eusebiuses carried on the strife against the Nicenes and especially Athanasius. Under the sons of Constantine Christian bishops in numberless synods cursed one another turn by turn. In the western half of the empire Arianism found no foothold, and even the despotic will of Constantius, sole emperor after 351, succeeded only for the moment in subduing the bishops exiled for the sake of their belief. In the east, on the other hand, the Semiarians had for long the upper hand. They soon split up into different groups, according as they came to stand nearer to or farther from the original position of Arius. The actual centre was formed by the _Homoii_, who only spoke generally of a likeness [Greek: homoiotaes] of the Son to the Father; to the left of them were the _Anomoii_, who, with Arius, held the Son to be unlike [Greek: anomoios] the Father; to the right, the _Homoiousians_ who, taking as their catchword "likeness of nature" [Greek: homoiotaes kat ousian], thought that they could preserve the religious content of the Nicene formula without having to adopt the formula itself. Since this party in the course of years came more and more into sympathy with the representatives of the Nicene party, the _Homoousians_, and notably with Athanasius, the much-disputed formula became more and more popular, till the council summoned in 381 at Constantinople, under the auspices of Theodosius the Great, recognized the Nicene doctrine as the only orthodox one. Arianism, which had lifted up its head again under the emperor Valens, was thereby thrust out of the state church. It lived to flourish anew among the Germanic tribes at the time of the great migrations. Goths, Vandals, Suebi, Burgundians and Langobardi embraced it; here too as a distinctive national type of Christianity it perished before the growth of medieval Catholicism, and the name of Arian ceased to represent a definite form of Christian doctrine within the church, or a definite party outside it.

The best account of the proceedings, both political and theological,
may be found in the following books:--H.M. Gwatkin, _Studies of
Arianism_ (2nd edit., Cambridge, 1900); A. Harnack, _History of Dogma_
(Eng. trans., 1894-1899); J.F. Bethune-Baker, _An Introduction to the
Early History of Christian Doctrine_ (London, 1903); W. Bright, _The
Age of the Fathers_ (London, 1903). Cardinal Newman's celebrated
_Arians of the Fourth Century_ is interesting more from the
controversial than from the historical point of view. See also Paavo
Snellman, _Der Anfang des arianischen Streites_ (Helsingfors, 1904);
Sigismund Rogala, _Die Anfange des arianischen Streites_ (Paderborn,
1907). (G. K.)

ARIZONA (from the Spanish-Indian _Arizonac_, of unknown meaning,--possibly "few springs,"--the name of an 18th-century mining camp in the Santa Cruz valley, just S. of the present border of Arizona), a state on the S.W. border of the United States of America, lying between 31 deg. 20' and 37 deg. N. lat. and 109 deg. 2' and 114 deg. 45' W. long. It is bounded N. by Utah, E. by New Mexico, S. by Mexico and W. by California and Nevada, the Colorado river separating it from California and in part from Nevada. On the W. is the Great Basin. Arizona itself is mostly included in the great arid mountainous uplift of the Rocky Mountain region, and partly within the desert plain region of the Gulf of California, or Open Basin region. The whole state lies on the south-western exposure of a great roof whose crest, along the continental divide in western New Mexico, pitches southward. Its altitudes vary from 12,800 ft. to less than 100 ft. above the sea. Of its total area of 113,956 sq. m. (water surface, 116 sq. m.), approximately 39,000 lie below 3000 ft., 27,000 from 3000 to 5000 ft., and 47,000 above 5000 ft.

_Physical Features._--Three characteristic physiographic regions are distinctly marked: first the great Colorado Plateau, some 45,000 sq. m. in area, embracing all the region N. and E. of a line drawn from the Grand Wash Cliffs in the N.W. corner of the state to its E. border near Clifton; next a broad zone of compacted mountain ranges with a southern limit of similar trend; and lastly a region of desert plains, occupying somewhat more than the S.W. quarter of the state. The plateau region has an average elevation of 6000-8000 ft. eastward, but it is much broken down in the west. The plateau is not a plain. It is dominated by high mountains, gashed by superb canyons of rivers, scarred with dry gullies and washes, the beds of intermittent streams, varied with great shallow basins, sunken deserts, dreary levels, bold buttes, picturesque mesas, forests and rare verdant bits of valley. In the N.W. there is a giddy drop into the tremendous cut of the Grand Canyon (q.v.) of the Colorado river. The surface in general is rolling, with a gentle slope northward, and drains through the Little Colorado (or Colorado Chiquito), Rio Puerco and other streams into the Grand Canyon. Along the Colorado is the Painted Desert, remarkable for the bright colours--red, brown, blue, purple, yellow and white--of its sandstones, shales and clays. Within the desert is a petrified forest, the most remarkable in the United States. The trees are of mesozoic time, though mostly washed down to the foot of the mesas in which they were once embedded, and lying now amid deposits of a later age. Blocks and logs of agate, chalcedony, jasper, opal and other silicate deposits lie in hundreds over an area of 60 sq. m. The forest is now protected as a national reserve against vandalism and commercialism. Everywhere are evidences of water and wind erosion, of desiccation and differential weathering. This is the history of the mesas, which are the most characteristic scenic feature of the highlands. The marks of volcanic action, particularly lava-flows, are also abundant and widely scattered.

Separating the plateau from the mountain region is an abrupt transition slope, often deeply eroded, crossing the entire state as has been indicated. In localities the slope is a true escarpment falling 150 and even 250 ft. per mile. In the Aubrey Cliffs and along the Mogollon mesa, which for about 200 m. parts the waters of the Gila and the Little Colorado, it often has an elevation of 1000 to 2000 ft., and the ascent is impracticable through long distances to the most daring climber. It is not of course everywhere so remarkable, or even distinct, and especially after its trend turns southward W. of Clifton, it is much broken down and obscured by erosion and lava deposits. The mountain region has a width of 70 to 150 m., and is filled with short parallel ranges trending parallel to the plateau escarpment. Many of the mountains are extinct volcanoes. In the San Francisco mountains, in the north central part of the state, three peaks rise to from 10,000 to 12,794 ft.; three others are above 9000 ft.; all are eruptive cones, and among the lesser summits are old cinder cones. The S.E. corner of Arizona is a region of greatly eroded ranges and gentle aggraded valleys. This mountain zone has an average elevation of not less than 4000 ft., while in places its crests are 5000 ft. above the plains below. The line dividing the two regions runs roughly from Nogales on the Mexican border, past Tucson, Florence and Phoenix to Needles (California), on the W. boundary. These plains, the third or desert region of the state, have their mountains also, but they are lower, and they are not compacted; the plains near the mountain region slope toward the Gulf of California across wide valleys separated by isolated ranges, then across broad desert stretches traversed by rocky ridges, and finally there is no obstruction to the slope at all. Small parts of the desert along the Mexican boundary are shifting sand.

_Climate._--As may be inferred from the physical description, Arizona has a wide variety of local climates. In general it is characterized by wonderfully clear air and extraordinarily low humidity. The scanty rainfall is distributed from July to April, with marked excess from July to September and a lesser maximum in December. May and June are very dry. Often during a month, sometimes for several months, no rain falls over the greatest part of Arizona. Very little rain comes from the Pacific or the Gulf of California, the mountains and desert, as well as the adverse winds, making it impossible. Rain and snow fall usually from clouds blown from the Gulf of Mexico and not wholly dried in Texas. The mountainous areas are the only ones of adequate precipitation; the northern slope of the Colorado Plateau is almost destitute of water; the region of least precipitation is the "desert" region. The mean annual rainfall varies from amounts of 2 to 5.5 in. at various points in the lower gulf valley, and on the western border to amounts of 25 to 30 in. in the mountains. The highest recorded maximum in Arizona is 35 in. The proportion of perfectly clear days in the year varies at different points from a half to two-thirds; of the rest not more than half are without brilliant sunshine part of the day. Local thunderstorms and cloud-bursts are a characteristic phenomenon, inundating limited areas and transforming dried-up streams into muddy torrents carrying boulders and debris. Often in the plateau country the dry under-air absorbs the rain as it falls; and rarely in the Hopi Country do flooded gullies "run through" to the Little Colorado. The country of the cliff-dwellers in the N.E. is desert-like. Only points high in altitude catch much rain. Mountain snows feed the Gila, the Little Colorado, and the Colorado rivers. The Colorado, apart from the Gila, draws little water from Arizona. The mountain zone W. of Prescott drains into the Colorado, and to the S. and E. into the Gila; and the latter is by far the heavier drainage in volume. The floods come in May and June, and during the wet season the rivers, all with steep beds in their upper courses, wash along detritus that lower down narrows, and on smaller streams almost chokes, their courses. These gradients enable the inconstant streams tributary to the Colorado to carve their canyons, some of which are in themselves very remarkable, though insignificant beside the Grand Canyon. Many streams that are turned in spring or by summer cloud-bursts into torrents are normally mere water films or dry gulches. Even the Gila is dry in its bed part of the year at its mouth near Yuma. From the Gila to the southern boundary the parched land gives no water to the sea, and the international boundary runs in part through a true desert. In the hot season there is almost no surface water. Artesian wells are used in places, as in the stock country of the Baboquivari valley.

The temperature of Arizona is somewhat higher than that of points of equal latitude on the Atlantic and Gulf of Mexico coasts. In the mountains on the plateau it ranges from that of the temperate zone to that of regions of perpetual snow; S. of the mountains it ranges from temperate heats in the foothills to semi-tropic heat in the lower valleys of the Gila and Colorado. The average annual temperature over the region N. of 34' N. is about 55 deg.; that of the region S. is about 68 deg. The warmest region is the lower Gila valley. Here the hottest temperature of the year hovers around 130 deg., the mean for the hottest month (July) is about 98 deg., and the mean for the year is from 68.9 deg.-74.4 deg. F. at different points. Some parts of the Santa Cruz valley are equally hot. In the hottest (western) portions of the true desert on the Mexican border the daily maximum temperature is about 110 deg. F.; but owing to the rapid radiation in the dry, clear, cloudless air the temperature frequently falls 40-50 deg. in the night. The coldest points on the high plateau have annual means as low as 45-48 deg., and a mean for the coldest month at times below 20 deg. F. The range from high to low extreme on the plateau may be as great as 125 deg., but in the S.W. it is only about 70-80 deg. F. The daily variation (not uncommonly 60 deg. F.) is of course greatest in the most arid regions, where radiation is most rapid. And of all Arizona it should be said that owing to the extreme dryness of the air, evaporation from moist surfaces is very rapid,[1] so that the high temperatures here are decidedly less oppressive than much lower temperatures in a humid atmosphere. The great difference between absolute and sensible temperature is a very important climatic characteristic of Arizona. Generally speaking, during two-thirds of the year the temperature is really delightful; the nights are cool, the mornings bracing, the days mild though splendid. Intense heat prevails in July, August and September. In lowness of humidity (mean annual relative humidity at Yuma about 39, at Phoenix 36.7, at Tucson 37.8) and clarity of atmosphere, southern Arizona rivals Upper Egypt and other famous arid health resorts.

_Fauna and Flora._--Within the borders of Arizona are areas representative of every life zone save the humid tropical. From the summit of the San Francisco Mountains one may pass rapidly through all these down into the Painted Desert. The Boreal-Canadian, Transition and Upper Sonoran embrace the highlands. Coyotes are very common; wild cats and mountain lions are fairly plentiful. Deer and antelope are represented by various species. Prairie-dogs, jack-rabbits, crows and occasional ravens, quail, grouse, pheasants and wild turkeys are also noteworthy in a rather scant animal life. Characteristic forms of the Upper Sonoran zone are the burrowing owl, Nevada sage-thrush, sage-thrasher and special species of orioles, kangaroo rats, mice, rabbits and squirrels. The Lower Sonoran covers the greatest part of southern and western Arizona, as well as the immediate valleys of the Colorado and Little Colorado rivers. Its animal life is in the main distinguished in species only from that of the Upper Sonoran belt, including among birds, the desert sparrow, desert thrasher, mocking-bird, hooded oriole; and among mammals small nocturnal species of kangaroo rats, pocket mice, mice and bats. Jaguars occasionally stray into Arizona from Mexico. Lizards and toads are conspicuous in the more desert areas. Snakes are not numerous. The Gila-monster, tarantula, the scorpion and thelyphonus, scolopender and julus occur in some localities in the rainy season. The Arid-Tropical zone is represented by a narrow belt along the lower Colorado river, with a short arm extending into the valley of the Gila. The country is so arid that it supports only desert birds and mammals. Camels were very successfully employed as pack animals on the Tule desert in the palmy days of Virginia City, Nevada, before the advent of railways.

The general conditions of distribution of the fauna of Arizona are shown even more distinctly by the flora. There are firs and spruces on the mountains, characteristic of the Boreal zone; pines characteristic of the Transition zone; pinon juniper, greasewood and the universally conspicuous sage-brush, characteristic of the Upper Sonoran zone. In the Lower Sonoran belt, soapweed, acacias (Palo Verde or _Parkinsonia torreyana_), agaves, yuccas and dasylirions, the creosote bush and mesquite tree, candle wood, and about seventy-five species of cactuses--among them omnipresent opuntiae and great columnar "Chayas"--make up a striking vegetation, which in its colours of dull grey and olive harmonizes well with the rigidity and forbidding barrenness of the plains. It has exercised profound influence upon the industries, arts, faiths and general culture of the Indians. In places the giant cactus grows in groves, attaining a height of 40 and even 50 ft. The mesquite varies in size from a tangled thorny shrub to a spreading tree as much as 3 ft. in diameter and 50 ft. high; it is normally perhaps half as high, and 6-8 in. in diameter. Enduring hardily great extremes of heat and moisture, it is throughout the arid South-west the most important, and in many localities the only important, native tree. From the great juicy, leafless, branchless stalk of the yucca, soap is prepared, and strong fibres useful in making paper, rope and fabrics. The fibre of the agave is also made into rope and its juice into pulque. The canaigre grows wild and is also cultivated. It is easy to exaggerate greatly the barrenness of an arid country. There are fine indigenous grasses that spring up over the mesas after the summer rains, furnishing range for live-stock; some are extraordinarily independent of the rainfall. In the most arid regions there is a small growth of green in the rainy season, and a rich display of small wild-flowers, as well as the enormous flower clusters of the yucca, and blooms in pink and orange, crimson, yellow and scarlet of the giant cactus and its fellows. Even in the Mexican border, desert oak, juniper and manzanita cover the mountains, and there is a vigorous though short-lived growth of grasses and flower from July to October. The cliff-dweller country supports a scant vegetation--a few cottonwood in the washes, a few cedars on the mesas.

Continuous forest areas are scant. A fair variety of trees--cottonwood, sycamore, ash, willow, walnut and cherry--grow in thickets in the canyons, and each mountain range is a forest area. Rainfall varying with the altitude, the lower timber line below which precipitation is insufficient to sustain a growth of trees is about 7000 ft., and the upper timber line about 11,500 ft. Oaks, juniper, pinon, cedars, yellow pine, fir and spruce grow on the mountains and over large areas of the plateau country.[2] The Coconino forest is one of the largest unbroken pine forests (about 6000 sq. m.) in the United States. Since 1898 about 86% of the wooded lands have been made reservations, and work has been done also to preserve the forest areas in the mountains in the south-east, from which there are few streams of permanent flow to the enclosing arid valleys.

_Soil._--The soils in the southern part of Arizona are mainly sandy loams, varying from light loam to heavy, close adobe; on the plateaus is what is known as "mesa" soil; and along the rivers are limited overflow plains of fine sediment--especially along the Colorado and the river Verde. These soils are in general rich, but deficient in nitrogen and somewhat in humus; and in limited areas white alkaline salts are injuriously in excess. Virgin soils are densely compact. By far the most useful crops are leguminous green manures, especially alfalfa, which grows four to seven cuttings in a year and as a soil flocculator and nitrogen-storer has proved of the greatest value. The greatest obstacle to agriculture is lack of water. Artesian wells are much used in the south-east. For the reservation of the water-partings--in the past considerably denuded by lumbermen and ranchmen--the increase of the forest areas, and the creation of reservoirs along the rivers, to control their erratic flow[3] and impound their flood waste for purposes of irrigation, much has been done by the national government. The irrigated areas are only little spots along the permanent streams. In 1900 the farm area was only 2.7% of the total area of the state and only 0.31% was actually improved (including Indian reservations, 0.35%; in 1906, 0.92% was cultivated); of the land actually under crops, 88.5% was irrigated. The improved acreage more than quintupled from 1880 to 1900. The total irrigated area in 1900 was 185,000 acres and in 1902, 247,250 acres. The increase in land values by irrigation from 1890 to 1900 is estimated at $3,500,000. A reservoir was begun in 1904 just below the junction of the Tonto and the Salt with capacity to store 1,330,000 acre-ft. for irrigation, and develop also an electric power sufficient to pump underground water for an additional 50,000 acres at the lowest estimate[4] of lands lying too high for supply by gravity. Another important undertaking begun about the same time was the throwing of an East Indian weir dam (the only one in the United States) across the Colorado near Yuma, and the confinement of both sides of the lower Gila and Colorado with levees.

_Agriculture._--Strawberries and Sahara dates; alfalfa, wheat, barley, corn and sorghum; oranges, lemons, wine grapes, limes, olives, figs, dates, peanuts and sweet potatoes; yams and sugar beets, show the range of agricultural products. The date palm fruits well; figs grow luxuriantly, though requiring much irrigation; almonds do well if protected from spring frosts; sea-island cotton grows in the finest grades, but is not of commercial importance. The country about Yuma is particularly suited to subtropical fruits. Temperate fruits--peaches, pears, apples, apricots and small fruits--do excellently; as do all important vegetables. The fruit industry is becoming more and more important. Farming is very intensive, and crop follows crop in swift succession; in 1905 the yield of barley per acre, 44 bushels, was greater than in any other state or territory, as was the farm price per bushel on the 1st of December, 81 cents; the average yield per acre of hay was the highest in the Union in 1903, 3.46 tons, the general average being 1.54 tons, was fourth in 1904, 2.71 tons (Utah 3.54, Idaho 3.07, Nevada 3.04), the general average being 1.52 tons, and was highest in 1905, 3.75 tons, the general average for the country being 1.54 tons; and in the same three years the average value per acre of hay was greater in Arizona than in any other state of the Union, being $35.78 in 1903, $40.22 in 1904, and $46.39 in 1905, the general averages for the country being $13.93, $13.23 and $13.11 respectively, for the three years. Of the total farm acreage of the state 97.6% were held in 1900 by the whites; and of these 80.2% owned in whole or in part the land they cultivated.

Stock-raising is a leading industry, but it has probably attained its full development. The over-stocking of the ranges has caused much loss in the past, and the almost total eradication of fine native grasses over extended areas. Of the neat cattle (7,042,635) almost 98%, and of the sheep (861,761) almost 100%, were in 1900 pastured wholly or in part upon the public domain. The extension of national forest reserves and the regulations enforced by the United States government for the preservation of the ranges have put limits to the industry. In 1900 the value of live-stock represented 15.7% of the capital invested in agriculture; the value of animals sold or slaughtered for food ($3,204,758) was half the total value of all farm products ($6,997,097). Ostrich farms have been successfully established in the Salt river valley since 1893; in 1907 there were six farms in the Salt river valley, on which there were about 1354 birds; the most successful food for the ostrich is alfalfa.

_Minerals._--Mining is the leading industry of Arizona. Contrary to venerable traditions there is no evidence that mining was practised beyond the most inconsiderable extent by aborigines, Spanish _conquistadores_, or Jesuits. In 1738 an extraordinary deposit of silver nuggets, quickly exhausted (1741), was discovered at Arizonac. At the end of the 18th century the Mexicans considerably developed the mines in the south-east. The second half of the 19th century witnessed several great finds; first, of gold placers on the lower Gila and Colorado (1858-1869); later, of lodes at Tombstone, which flourished from 1879-1886, then decayed, but in 1905 had again become the centre of important mining interests; and still later the development of copper mines at Jerome and around Bisbee. Several of the Arizona copper mines are among the greatest of the world. The Copper Queen at Bisbee from 1880-1902 produced 378,047,210 lb. of crude copper, which was practically the total output of the territory till after 1900, when other valuable mines were opened; the Globe, Morenci and Jerome districts are secondary to Bisbee. Important mines of gold and silver, considerable deposits of wolframite, valuable ores of molybdenum and vanadium, and quarries of onyx marble, are also worked. Low-grade coal deposits occur in the east central part of the state and near the junction of the Gila and San Pedro rivers. Some fine gems of peridot, garnet and turquoise have been found. The mineral products of Arizona for 1907 were valued at $56,753,650; of which $51,355,687 (more than that of any other state) was the value of copper; $2,664,000, gold; and $1,916,000, silver. In 1907 the legislature passed an elaborate act providing for the taxation of mines, its principal clause being that the basis of valuation for taxation in each year be one-fourth of the output of the mines in question for the next preceding year.

_Manufactures._--The manufacturing industries are of relatively slight importance, though considerable promise attends the experiments with canaigre as a source of tannin. The Navaho and Moqui Indians make woollen blankets and rugs and the Pimas baskets. Onyx marbles of local source are polished at Phoenix. The capital invested in manufacturing industries increased from $9,517,573 in 1900 to $14,395,654 in 1905, or 51.3%, and the value of products from $20,438,987 in 1900 to $28,083,192 in 1905, or 37.4%. Of the total product in 1905 the product of the principal industry, the smelting and refining of copper ($22,761,981), represented 81.1%; it was 9.4% of all the smelting and refining of copper done in the United States in that year. The other manufactures were of much less importance, the principal ones being cars and general shop construction, including repairs by steam railway companies ($1,329,308), lumber and timber products ($960,778), and flour and grist mill products ($743,124).

Two transcontinental railway systems, the Southern Pacific and Santa Fe, were built across Arizona in 1878-1883. They are connected by one line, and a feeder runs S. into Sonora. The railway mileage of Arizona on the 1st of January 1908 was 1935.35 m.

_Population._--The population of Arizona in 1880 was 40,440; in 1890, 59,620; in 1900, 122,931 (including 28,623 reservation Indians not counted before); in 1910, 204,354. The native population is of the most diverse origin; the foreign element is equally heterogeneous, but more than half (in 1900, 14,172 out of 24,283 foreign-born) are Mexicans, many of whom are not permanent residents; after 1900, immigrants were largely mine labourers, and included Slavonians and Italians. The largest towns in 1900 were Tucson, Phoenix, which is the capital, Prcscott (pop. 3559), Jerome (pop. 1890, 250; in 1900, 2861); Winslow (pop. 1890, 363; in 1900, 1305), Nogales (pop. 1900, 1761), and Bisbee. The last was an insignificant mining camp in 1880, still unincorporated in 1900, but with an estimated population of 6000 in 1904. It is crowded picturesquely into several narrow confluent ravines. Railway connexion with El Paso was established in 1902. Douglas is another growing camp.

Over thirty Indian tribes are represented in the Indian schools of Arizona. The more important are the Hualapais or Apache-Yumas; the Mohaves; the Yavapais or Apache-Mohaves; the Yumas, whose lesser neighbours on the lower Colorado are the most primitive Indians of the United States in habits; the Maricopas; the Pimas and Papagoes, who figure much in early Arizona history, and who are superior in intelligence, adaptability, application and character; the Hopis or Moquis, possessed of the same good qualities and notably temperate and provident, famous for their prehistoric culture (Tusuyan); the Navaho, and the kindred Apaches, perhaps the most relentless and savage of Indian warriors. All the Indians of Arizona live on reservations save the few non-tribal Indians taxed and treated as active citizens. Even the Apaches after being whipped by relentless war into temporary submission have been bound by treaties which the gifts, vices and virtues of the reservation system have tempted them to observe. The Pimas and Papagoes were early converted by the Spaniards, and retain to-day a smattering of Christianity plentifully alloyed with paganism. Apaches, Pimas, Papagoes have been employed by the United States on great irrigation works, and have proved industrious and faithful labourers. In 1900 there were 1836 taxed Indians, 26,480 reservation Indians not taxed, and in addition many friendly Papagoes unenumerated.

In 1906 the Indian population was estimated as being 14% of the whole population of Arizona, and that they are singularly law-abiding is argued from the fact that in the same year the Indians furnished only 3% of the convicts in the territorial prison.

_Government and Education._--Arizona became a territory of the first (or practically autonomous) class in 1863. Her organic law thereafter until 1910 consisted of various sections of the Revised Statutes of the United States. From the beginning she had a territorial legislature. Congress retained ultimately direct control of all government, administration being in the hands of resident officials appointed by the president and Senate. Special mention must be made of the secret police, the Arizona Rangers, organized in 1901 to police the cattle ranges; they are "fearless men, trained in riding, roping, trailing and shooting," a force whose _personnel_ is not known to the general public. The legislature repealed the law licensing public gambling in 1907; enacted a law requiring the payment of $300 per annum as licence fee by retail liquor dealers; and provided for juvenile courts and probationary control of children. In 1907 the total tax valuation of property was $77,705,251; the net debt of the territory $1,022,972, and that of counties and towns $3,123,275. The receipts of the territorial treasury for the year ending on the 30th of June 1907 were $687,386, and the disbursements for the same period were $601,568. A homestead provision (1901) exempts from liability for debts (except mortgages or liens placed before the homestead claim) any homestead belonging to the head of a family, existing in one compact body and valued at not more than $2500; such a homestead a married man may not sell, lease or put a lien on without his wife's consent. Personal property to the value of $500 is exempt from the same liability. The public school system was established in 1871. A compulsory attendance law applies to children between 6 and 14 years of age, but it is not generally obeyed by the Mexican element of population. In 1907 there was an enrolment of 24,962 out of 33,167 children of school age; there were six high schools--three new in 1906; and the average number of school days was 128.4. In the fiscal year ending June 1907, the total receipts for schools were $697,762, and the expenditures were $701,102. Illiteracy is high, amounting in 1900 to 23.1% of native males, above 21 years of age, and 30.5% of foreign males, principally because of the large number of Indians, Chinese, Japanese and Mexicans in the state. There are two normal schools at Tempe (1886) and Flagstaff (1899), a university at Tucson with an agricultural experiment station that has done much for the industries of Arizona; there is a considerable number of Indian schools, the largest of which are maintained by the national government, and the funds of the university come largely from the same source. The first juvenile reform school, called the Territorial Industrial school, was opened in 1903 at Benson. The territorial prison, formerly at Yuma, was abandoned for a modern building at Florence, Pinal county; and a hospital for the insane is 3 m. from Phoenix.