Dillingen (dil´ing-en), an old town, Bavaria, on the Danube, formerly the seat of a Jesuit university. Pop. 6291.
Dillon, John, Irish politician and agitator, born in Dublin in 1851, the son of John Blake Dillon (1816-66), a leader of the Young Ireland party. Educated at the Catholic University of Dublin and at the Royal College of Surgeons, he became a doctor of medicine. He identified himself with the Parnellite movement, and entered Parliament for Tipperary in 1880. An ardent Nationalist, not hesitating to incite his compatriots to lawlessness, he was sent to prison in 1888. Without a seat in Parliament from 1883 to 1885, he was returned in the latter year for East Mayo, which he represented thereafter. In 1918, after the death of John Redmond, he was elected chairman of the Irish Nationalist party, which, however, owing to the rise of the Sinn Fein party, was a nominal distinction only.
Dilman´, a town, Persia, province of Azerbijan, 75 miles west of Tabreez. Pop. estimated at 15,000.
Dilo´lo, a small lake in Angola, near the southern boundary of Belgian Congo, lat. 11° 22' S.; long. 22° 34' E.: regarded as the source of the Zambesi.
Dil´uents (Lat. diluere, to wash away), in medicine, are those substances which are taken to increase the proportion of fluid in the blood. They consist of water and watery liquors.
Dilu´vium, the name formerly given by geologists to certain gravels and comparatively recent deposits, which seemed to have been the result of a rush of water or deluge.
Dime (Fr. dîme, Lat. decimus, tenth), the term for the tenth part of a dollar or ten-cent piece in the United States of America, a silver coin whose English equivalent is about 5d. Hence the phrases dime novels, dime museums, &c.
Dimensions, Algebraical. There are three dimensions in space: length, breadth, and height or depth. An area is said to be of two dimensions because it has length and breadth only; a volume is of three dimensions. In algebra terms like x2, xy are said to be of two dimensions because there are two letters multiplied together, and their product would measure an area if each letter denoted a length. Similarly, x3, xyz are said to be of three dimensions, and the meaning is extended to cover the product of any number of letters. An expression of more than one term is said to be of the same degree as its term of highest dimensions. For example, 3x2y2z2 + 5xyz + 6x3 + 3x2y2 is said to be of the sixth degree because x2y2z2 = x × x × y × y × z × z is of six dimensions.
Dimensions, Physical. One of the aims of physical science is to express all its measurements in terms of the three fundamental units of length, mass, and time. A velocity, for example, is specified by the number of units of length traversed in the unit of time, so that we may write v = l ÷ t, or v = lt-1. On this account velocity is said to have the dimensions LT-1. Similarly, acceleration, being velocity added per unit time, has the dimensions of velocity ÷ time, or LT-2; and force, being proportional to mass and acceleration jointly, has the dimensions MLT-2.
When a physical law is expressed as an equation connecting the numbers of units of the quantities involved, every term in this equation must be of the same dimensions in any one of the fundamental units. This is the Principle of Dimensions, first stated by Joseph Fourier, founder of the theory of the conduction of heat. In order to see its truth, we have only to observe that an equation containing terms of different dimensions would give inconsistent results if the unit of length were varied. Suppose it to be suggested, for example, that the period of vibration t of a simple