DIA 



DIA 



on the number of stamina, considered as 

 distinct. Some pea-bloom, or butterfly- 

 shaped flowers, have five stamina, or male 

 organs, as monnieria ; some six, as fuma- 

 tory ; some eight, as milk-wort ; some 

 ten, as broom, bladder-sena, lupine, la- 

 dy's-finger, vetch, and the far greater 

 number of butterfly-shaped flowers. It 

 is only the last order that is included in 

 the natural family papilionacese j the re- 

 maining four genera are distributed a- 

 mong other families, to which they have, 

 at least, an equal alliance. The names 

 given by former botanists to the extensive 

 class of plants in question are much more 

 characteristic of their nature and ap- 

 pearance, than that of diadelphia. The 

 figure of the flowers and fruit never va- 

 ries ; the latter being always of the pod- 

 kind, the former of the butterfly shape. 

 On the other hand, the two sets of united 

 stamina, the only classic character ex- 

 pressed in the Linnaean title, are never 

 to be traced without difficulty ; for one 

 of the sets only is properly united ; the 

 other consisting of a single filament, 

 which, in most plants, adheres so closely 

 to its kindred set, that it cannot be sepa- 

 rated without the application of a pin or 

 needle for that purpose. In some, even, 

 no separation can be effected by this 

 means. 



-f- DIADEM, in heraldry, is applied to 

 certain circles, or rims, serving to inclose 

 the crowns of sovereign princes, and to 

 bear the globe and cross, or the flower 

 de luces for their crest. The crowns of 

 sovereigns are bound, some with a great- 

 er, and some with a less number of dia- 

 dems. The bandage about the heads of 

 moors on shields is also called diadem, in 

 blazoning. 



DIAERESIS, in grammar, the division 

 of one syllable into two, which is usually 

 noted by two points over a letter, as au- 

 lai', instead of aulze, dissoliienda, for dis- 

 bolvenda. 



DIAGNOSTIC, in medicine, a term 

 given to those signs which indicate the 

 present state of a disease, its nature and 

 cause. 



DIAGONAL, in geometry, a right line 

 drawn across a quadrilateral figure, from 

 one angle to another, by some called the 

 diameter, and by others the diameter of 

 the figure. Thus A C, (.Plate IV. Mis- 

 eel, fig. 7.) is called a diagonal. 



It is demonstrable, 1. That every dia- 

 gonal divides a parallelogram into two 

 equal parts. 2. That two diagonals drawn 

 in any parallelogram bisect each other. 

 3. A line F G, passing through the mid- 



dle point of the diagonal of a parallelo- 

 gram, divides tile figure into two equai 

 parts. 4. The diagonal of a square is in- 

 commensurable with one of its sides. 5. 

 That the sum of the squares of the two 

 diagonals of every parallelogram is equal 

 to the sum of the squares of the four 

 sides. This proposition is of great use 

 in the theory of compound motions ; 

 for, in an oblique angled parallelogram, 

 the greater diagonal being the subtense 

 of an obtuse, and the lesser of an acute 

 angle, which is the complement of the 

 former, if the obtuse angle be conceiv- 

 ed to grow till it be infinitely great with 

 regard to the acute one, the great diago- 

 nal becomes the sum of the two sides, 

 and the lesser one nothing. Now two 

 contiguous sides of a parallelogram being 

 known, together with the angle they in- 

 clude, it is easy to find one of the diago- 

 nals in numbers, and then the foregoing 

 proposition gives the other. This second 

 diagonal is the line that would be des- 

 cribed by a body, impelled at the same 

 time by two forces which should have 

 the same ratio to each other, as the 

 contiguous sides have, and act in those 

 two directions; and the body would de- 

 scribe this diagonal in the same time 

 as it would have described either of the 

 contiguous sides in, if only impelled by 

 the force corresponding thereto. 6. In 

 any trapezium, the sum of the squares of 

 the four sides is equal to the sum of the 

 squares of the two diagonals, together 

 with four times the square of the dis- 

 tance between the middle points of the 

 diagonals. 7. In any trapezium, the sum 

 of the squares of the two diagonals is 

 double the sum of the squares of two 

 lines bisecting the two pairs of opposite 

 sides. 8. In any quadrilateral inscribed 

 in a circle, the rectangle of the two 

 diagonals is equal to the sum of the two 

 rectangles under the two pairs of oppo- 

 site sides. 



DIAL. Dials are of various construc- 

 tions, some being horizontal, others ver 

 tical,,and others moveable, so as to apply 

 to any particular latitude at pleasure. 

 The use of a dial is to indicate the. 

 hour, which is done by means of a wire, 

 or by a triangular board, &c. placed at 

 right angles to the face or index. This 

 triangular piece is called the stile, or 

 gnomon, and is made to point due north : 

 it should be perfectly vertical, and the 

 dial's face, on which the hours are mark- 

 ed, should be equally divided thereby ; 

 the line of 12 being in a true direction 

 with the stile. This line of direction is. 



