DIATOMACE^. 209 DIAZ. generally believed to be a degenerate form of sexuality. The diatoms are common in both fresh and salt waters, "and constitute one of the chief sources of food-supply for the lower marine and lacustrine animals, and through those for the higher organisms. Their siliceous skeletons, which fall to the bottom, favor their ready entombment and pres- ervation as fossils, and tlieir lowly organization suggests the hypothesis that their remains may be found in roeks of the Cambrian and Ordovi- cian series, which contain the oldest foraminifera and radiolarians. They are not, however, posi- tively known to occur in rocks of older than L'pper Cretaceous age, which contain species that ditfer little from those now living, and that belong almost entirely to living genera. In Tertiary time they were exceedingly abundant, and in many parts of the world their remains, with little adnlixture of other materials, form deposits of considerable thickness and economic importance. These deposits constitute an impor- tant source of abrasive materials, and the prod- ucts are known under such names as tripoli, dia- tomaceous earth (qq.v), Richmond earth, elec- tro-silicon, kieselguhr, etc. These diatom de- posits are most common in Miocene rocks of both marine and fresh-water origin. In some rocks particular species of diatoms form the bulk of definite layers: different localities have their peculiar generic assemblages. The majority of Tertiary diatoms are of species still living. Dia- toms have been reported as liaving been found is the ash of English coal burned in Rome, but English investigators, after the most careful search, have failed to detect them at home. See -•Abrasives. DIATOMA'CEOUS or INTTJSO'RIAL EARTH iGer. Bcrtnnehl) . A white or grayish powdir of extreme fineness, composd almost en- tirely of the indestructible siliceous frustules or cell-walls of diatoms. The earth has accumulated in beds of considerable thickness in past geologi- cal ages, and such beds are now being found on the bottoms of some fresh-water lakes and on the sea-floor. Owing to the angular nature and hardness of its component particles, diatoma- ceous earth has valuable abrasive properties: it is also employed as an absorbent in the manu- facture of dynamite, and as an insulating ma- terial for boilers and stcani-pipe coverings. De- posits of diatomaceous earth abound in the Tertiary and Quaternary formations of many countries. In the United States it has been mined in Virginia. Maryland. Connecticut, New York, and in some of the Western States. The output in inOO was 1375 tons. DI'ATONIC SCALE (Lat. diatonwuf), from Ok. Siaroi'iKJv, tlintonikon, from Sidroms, dia- ionon, outstretched, from 5iaT4tKti', diateinein, to stretch out, from Std, din. through + retveiv, lehwin. to stretch : connected with Lat. lenuis, Skt. tanu, Ger. diinn. Eng. thin). This scale in music is one in which there are seven notes in the inten-al of an octave at intervals given by the ratios 24 : 27 : 30 : .32 : .30 : 40 : 4.5. Thu=. if a note whose freqviency is 240 is taken as the key-note, there will be the following notes in the interval of an octave: 240, 270, 300, 320, 3C0, 400, 450, and the octave of 240 will give the next note, 480, The notes in the lower and upper octaves would then iv 120, 13.5, 150, 160, 180, 200, 225, and 480, 540, 600, 640, 720, 800, 900 ; etc. It is evident that the ratios of these various notes are the simplest possible. Thus the ratios 1 : 2, 1 : 3, 1 : 4, 2 : 3, 3 : 4, etc., occur. I'or this reason chords on this scale are in the great- est possible harmony. (See Acoustics.) If, however, music composed with the key-note 240 is transposed to the key 300, the diatonic scale required would be 300,5} X 300,11 X 300,f J X 300,if X 300, etc. ; that is, 300, 3371,2, 375, 400, 450, etc. But some of these notes do not occur in the original scale with the key-note 240; and. for this reason, the diatonic scale is unsatisfactory. Other scales are now used, which include a great- er number of notes in the interval of the octave. .See !Mrsic. DI'ATRIBE (IVn.,, diatriha, discussion, Gk. SiarpL^-ij, diatribe, disputation, from Siarpl^eiv, din- trihciii, to discuss, frmnSid. iliti. through +Tpl^eii/, tribciu, to rub). A disputation, or critical exer- cise. A name originally given to a critical examination of a literary work, and at a later period to :i bitter and violent criticism, either written or spoken, on any subject, in any depart- ment of literature. DIAZ, de'as, PoRFiHio ( 1830—). A President of Mexico. He was born at Oaxaca, of Spanish parentage, and was studying law in his native town when tlie war with the United States broke out. Young Diaz entered a militia regi- ment in 1847 and thenceforth devoted himself to a military career. In 1854 he commanded a bat- talion under Alvarez in the contest against Santa Anna. Two years later he identified himself with Juarez and the Liberal Party, and in 1861 was elected Deputy to the National Congress. He soon resigned to take the field, and won a victory over the reactionist Marquez at Jalat- laco. During the French intervention he won a high reputation as one of the most skillful and courageous of the patriot leaders. In May, 1863, while directing the defense of Puebla. he was forced to surrender, but escaped shortly after and went to Oaxaca, where he raised a new force and made considerable headway against the French. In February, 1865, he was again captured, but es- caped once more, and once more reappeared at the head of an army he had brought together at Oaxaca. He gradually forced the invading troops to adopt the defensive, and after the evacuation of Mexico by the French, he advanced to Puebla and took the city. A[>ril 2. 1867. On .lune 21 he entered the City of Mexico. In the same year he was a candidate for the Presidency against .Juarez, but being defeated, withdrew to his es- tates. He never ceased plotting against the Gov- ernment, however, and his intrigues occasionally broke out in the form of armed revolts against Juarez and his successor, Lerdo de Tejada. He was twice forced to flee the country — in 1872. and again in 1876. Returning quickly on both occa- sions, Diaz succeeded in the latter year in defeat- ing his enemies at Tecoac (November 16th). He finally drove Lerdo out and in May, 1877. he became President. Order was restored in a remarlcably short time. Diaz soon managed
