pendulum of length l is given by the formula t = 2πl/g, where g denotes the acceleration of a falling body. The dimensions of the expression on the right are L ÷ (LT-2), or T2, whereas the term t on the left has dimensions T1. Suppose the unit of length is the foot and the unit of time the second, so that g = 32, and let l = 3. We find in this case t = 6π/32, so that the period is 3π/16 seconds. But if we change the unit of time to one minute, g becomes 32 × 60 × 60, and the formula gives t = 6π/(32 × 60 × 60), so that the period is 3π/(16 × 60 × 60) minutes.
The two results are obviously inconsistent. If, however, we take the correct formula, namely t = 2π√(l/g), we find on trial that we obtain the same value for the period however we change the unit of time or the unit of length. Both sides are in this case of dimensions T1.
The principle of dimensions provides therefore a useful check on the accuracy of formulæ. But it does much more than this. It often gives very valuable information about the relations of physical phenomena in cases where these relations are far too complicated to be completely worked out by mathematical analysis. To mention but one example, it is by the use of this principle that modern naval architecture is able to predict the behaviour of ocean-going ships from experiments in ponds on small-scale models.
Dimin´utive, in grammar, a word having a special affix which conveys the idea of littleness, and all other ideas connected with this, as tenderness, affection, or contempt. The opposite of diminutive is augmentative. In Latin, diminutives almost always ended in -lus, -la, or -lum; as Tulliola, meum corculum, little Tullia my dear, or little heart; homunculus, a manikin. The Italian is particularly rich in diminutives and augmentatives, such compound diminutives as fratellinucciettinetto (a diminutive of frate, brother) being sometimes employed. Among English diminutive affixes are -kin, as in manikin, a little man; pipkin, a little pipe; -ling, as in gosling, a little goose; darling, that is, dearling, or little dear; and -et, as in pocket, from poke, a bag or pouch; tablet, a little table. Diminutives are not confined to nouns, and dandle, scribble, tipple, are examples of diminutive verbs, and greenish, whitish, are diminutives of adjectives. Diminutives are also formed, in colloquial and familiar language, by adding -y or -ie to the names, as Charley, Mousie, &c.
Dim´ity, a stout cotton fabric, ornamented in the loom either by raised stripes or fancy figures. It is usually employed white, as for bed and bedroom furniture.
Dimorph´ism, in crystallography, the crystallization of a body in forms belonging to two different systems, or in incompatible forms of the same system, a peculiarity exhibited by sulphur, carbon, &c.
Dimorphism, in botany. See Heterostyly.
Dinajpur´, a town, Hindustan, Bengal, capital of a district of same name, 205 miles north of Calcutta; pop. 12,500.—The district covers an area of about 4118 sq. miles; pop. 1,687,860.
Dinan (dē-nän), a town, France, department of Côtes-du-Nord (Brittany), on the Rance, 14 miles south of St. Malo. It was besieged and captured by the English under the Duke of Lancaster in 1359, but retaken by Du Guesclin. It stands on a steep hill nearly 200 feet above the river, is surrounded by high old walls pierced with four gates, and is a picturesque and interesting old place. In the cathedral of St. Sauveur the heart of Bertrand du Guesclin is buried. Pop. 11,410.
Dinant (dē-nän), a town, Belgium, in the province and 14 miles S. of Namur; picturesquely and strongly situated on the Meuse; a place of antique appearance. The town house was once the palace of the Princes of Liége. The town was destroyed by the Germans in 1914. It is one of the most popular Belgian summer resorts. Pop. 7690.