To enable the reader to compare the several groups of Nitzsch with the families of L'Herminier, the numbers applied by the latter to his families are suffixed in square brackets to the names of the former; and, disregarding the order of sequence, which is here immaterial, the essential correspondence of the two systems is worthy of all attention, for it obviously means that these two investigators, starting from different points, must have been on the right track, when they so often coincided as to the limits of what they considered to be, and what we are now almost justified in calling, natural groups.'
The expressions in square brackets are in each case to be taken as relating to the extreme values x =xo and x=xm, as in §§ 75 and 76.
- Premising that they are more or less scattered, and that several lie on the same plane, the following list gives the majority of the inhabited islands from south to north, the number within brackets indicating the population.
In case neither of the above methods can be applied, brackets should be used at each floor level or a continuous deep beam or girder carried all around the building.
5,462,198 is (6) (5) (4) (3) (2) (I) (o) 5462 I 9 8 the small figures in brackets indicating the successive powers.
In the first place, they lead to an understanding of what is meant by the use of brackets and by such a statement as 3(7+2) = 3.7+3 ï¿½ 2.
After the creation of the canton (1815) the numbers were (those for the city are enclosed within brackets) 48,489 (25,289), the city rising in 1837 to 33,714, and in 1843 to 36,452.
At intermediate stations the roofs are often carried on brackets fixed to the walls of the station buildings, and project only to the edge of the platforms. At larger stations where both the platforms and the tracks are covered in, there are two broad types of construction, with many intermediate variations: the roof may either be comparatively low, of the " ridge and furrow " pattern, borne on a number of rows of pillars, or it may consist of a single lofty span extending clear across the area from the side walls.
In such cases, however, the correct native form should be added within brackets, as Florence (Firenze), Leghorn (Livorno), Cologne (Coln) and so on.
If ai, bx, cx be different forms we obtain, after development of the squared determinant and conversion to the real form (employing single and double dashes to distinguish the real coefficients of bx and cz), a(b'c"+b"c'-2 f'f") +b(c'a"+c"a'-2g'g") +c(a' +a"b'-2h'h")+2f(g'h"+g"h'-a' + 2g (h ' f"+h"f'-b'g"-b"g')+2h(f'g"+f"g'-c'h"-c"h'); a simultaneous invariant of the three forms, and now suppressing the dashes we obtain 6 (abc+2fgh -af t - bg 2 -ch2), the expression in brackets being the S well-known invariant of az, the vanishing of which expresses the condition that the form may break up into two linear factors, or, geometrically, that the conic may represent two right lines.
In the bibliography at the close of this article (referred to by leaded arabic numerals in brackets throughout these pages), the titles of works are given which contain detailed information as to the genera and species of each order or sub-order, their geographical distribution and their habits and economy so far as they have been ascertained.
(vi.) Any compound operation not coming under the above descriptions is to have its meaning made clear by brackets, the use of a pair of brackets indicating that the expression between them is to be treated as a whole.
The inscription (on a stone now lost) is as follows, the words and letters in brackets being the conjectural restorations of scholars: - " [Cere] ri sacrum [D.
Integrating the first term within brackets by parts, it becomes - fo de Remembering that 0(o) is a finite quantity, and that Viz = - (z), we find T = 4 7rp f a, /.(z)dz (27) When c is greater than e this is equivalent to 2H in the equation of Laplace.
Cylindrical or tapering from The numbers in square brackets  refer to the bibliography at the end of this article; but when the number is preceded by the word Hydrozoa, it refers to the bibliography at the end of the articl Hydrozoa.
These monuments, a conspicuous feature of Palmyrene architecture, took the form of statues placed on brackets projecting from the upper part of the pillars which lined the principal thoroughfares.
B., we obtain by comparison with the middle series the symbolical representation of all symmetric functions in brackets () appertaining to the quantities p i, P2, P3,ï¿½ï¿½ï¿½ To obtain particular theorems the quantities a l, a 2, a 3, ...a, n are auxiliaries which are at our entire disposal.
A partition is separated into separates so as to produce a separation of the partition by writing down a set of partitions, each separate partition in its own brackets, so that when all the parts of these partitions are reassembled in a single bracket the partition which is separated is reproduced.
Denote by brackets () and  symmetric functions of the quantities p and a respectively.
Remark, too, that we are in association with non-unitary symmetric functions of two systems of quantities which will be denoted by partitions in brackets ()a, ()b respectively.
This rule as to using brackets is not always observed, the convention sometimes adopted being that multiplications or divisions are to be performed before additions or subtractions.
(vii.) The only exception that may be made to the above rule is that an expression involving multiplication-dots only, or a simple fraction written with the solidus, may have the brackets omitted for additions or subtractions, provided the figures are so spaced as to prevent misunderstanding.
21 }- &c. } It will be seen that the expression in curled brackets in each line after the first is obtained from the corresponding expression in the preceding line by a definite process; viz.
The whole disposition of pillars, posts, brackets and rafters is harmonically arranged according to some measure of the standard of length.
Above these ties are the cornice brackets and beams, corresponding in general design to the cornice of the walls, and the intermediate space is filled with open carvings of dragons or other characteristic designs.
The inner face is smooth, but the back is strengthened with angle brackets at the corners.
The calculation of the expressions in brackets may be simplified by taking the pairs in terms from the outside; by finding the successive differences of uo + um, ill + um_l, ..., or of uI u i +umi, ..
In order to find the corrections in respect of the terms shown in square brackets in the formulae of § 75, certain ordinates other than those used for C 1 or T I are sometimes found specially.
(In the following statistics those for the city are enclosed within brackets.) In 1900 this population was thus divided in point of religion: Romanists, 67,162 (49,9 6 5), Protestants, 62,400 (52,121), and Jews 1119 (r081).
It emerges because in all judgments on textual matters it is presupposed that they will be acted on, that a reading accepted will remain in the text, a rejected one obelized, enclosed between brackets or removed, and, in this last case, something else substituted in its place.
Temporary copings of wood, which may be fixed by means of permanent iron brackets just below the stone coping, are extremely useful in spring for the protection of the blossoms of fruit trees.
The archiepiscopal sees (the suffragan sees, if any, being placed after each in brackets) are Catania (Acireale), Messina (Lipari, Nicosia, Patti), Monreale (Caltanissetta, Girgenti), Palermo (Cefalu, Mazara, Trapani), Syracuse (Caltagirone, Noto, Piazza Armerina).
6d.; each of the numbers in brackets indicating the number of units in one denomination that go to form a unit in the next higher denomination.
Letters in brackets are missing in the original: letters which are dotted beneath are doubtful.
The brief comments in brackets, appended above to the arguments, merely indicate what has been said or can be said on the other side.
The table gives their partial dispersions for six different regions of the spectrum also expressed (in brackets below) as fractional parts of the dispersion from C to F.
- -)Engelso In order that these conditions may obtain, the quantities in the brackets must be zero, since the factor aug is not zero.
The following are suffragan or assistant bishoprics (the names of the dioceses to which each belongs being given in brackets): Dover, Croydon (Canterbury), Beverley, Hull, Sheffield (York), Stepney, Islington, Kensington (London), Jarrow (Durham), Guildford, Southampton, Dorking (Winchester), Barrow-inFurness (Carlisle), Crediton (Exeter), Grantham (Lincoln), Burnley (Manchester), Thetford, Ipswich (Norwich), Reading (Oxford), Leicester (Peterborough), Richmond, Knaresborough (Ripon), Colchester, Barking (St Albans), Swansea (St.
Lattice bars, fillers, brackets, &c., add just so much more weight without increasing the section, and must be allowed for; the method of riveting the sections together must also be taken into account.
(The words in brackets are, inserted to avoid the difficulty, at this stage, of saying that every number is a factor of o, though it is of course true that o.
C. Lodge (New York, 9 vols., 1885-1886, and 12 vols., 1904); all references above are first to the latter edition, secondly (in brackets) to the former.