Machines multiply our labor and increase our ability to do work.
But the old abuses continuing to multiply, the Prussian towns and gentry at last took their affairs into their own hands, and formed a so-called Prussian League, which demanded an equal share in the government of the country.
(ii.) In the same way, if we multiply the table by c, the sum of the first n numbers in any column is equal to the nth number in the next following column.
Without a hydroid phase; the medusa develops directly from the actinula larva, which may, however, multiply by budding.
The outcome has been to raise the dignity of the calling, to induce persons of a superior class to adopt it in increasing numbers, to enlarge the demand for their services, and to multiply the means of educating them.
To obtain the real form we multiply out, and, in the result, substitute for the products of symbols the real coefficients which they denote.
Others have a special faculty of consuming dry, powdery vegetable and animal refuse, and are liable to multiply in manufactured products of this nature, such as mouldy cheese.
We can multiply out this expression so as to obtain a series of monomials of the form 9(sl is2 2 s3 3 ...).
(v.) When we have to multiply two multinomials arranged according to powers of x, the method of detached coefficients enables us to omit the powers of x during the multiplication.
In a multiply connected space, like a ring, with a multiply valued velocity function ¢, the liquid can circulate in the circuits independently of any motion of the surface; thus, for example, 4) =mB=m tan - l y/x (5) will give motion to the liquid, circulating in any ring-shaped figure of revolution round Oz.
Suppose that the dielectric has a constant K, then we must multiply both sides by K and the expression for the energy per unit of volume of the field is equivalent to z DE where D is the displacement or polarization in the dielectric.
His Hamburg interests continued from that date onwards to multiply in something like geometrical progression.
Mesentericus do not develop below 15° C.; but if it be introduced into the alimentary canal of a child the spores will rapidly multiply, and in such cases large quantities of gas, giving rise to flatulency, will be formed, and possibly also poisonous decomposition products of albuminoid matter.
Thus the Society for Promoting Christian Knowledge (founded 1698), besides its other activities, has done much to cheapen and multiply copies of the Scriptures, not only in English and Welsh, but in many foreign languages.
The use of the slips for the purpose of multiplication is now evident; thus to multiply 2085 by 736 we take out in this manner the multiples corresponding to 6, 3, 7, and set down the digits as they are obtained, from right to left, shifting them back one place and adding up the columns as in ordinary multiplication, viz.
The set of ten rods is thus equivalent to four sets of slips as described above, and by their means we may multiply every number less than II,irr, and also any number (consisting of course FIG.
Of course two sets of rods may be used, and by their means we may multiply every number less than 111,111,111 and so on.
In the first, a cleavage follows each nuclear division; in the second, the nuclei multiply by division a number of times, and then the ovum divides into as many blastomeres as there are nuclei present.
To perpetuate and multiply the choicer varieties, peaches and nectarines are budded upon plum or almond stocks.
Each number in the table) by a, and for the second series we multiply it by b, and the terms and their successive sums are given for the first series by the first and the second columns, and for the second series by the second and the third columns.
To multiply A 1 by a scalar, we apply the rule A = A1E = E (Eat) ea, and similarly for division by a scalar.
These micro-organisms having found in the tissues everything favourable for their needs, rapidly multiply and very soon produce serious results.
These being freed from the normal inhibiting power of the neighbouring elements, multiply and go on to the formation of a new growth.
Nothing could be more false than the common opinion that as a financier his sole expedient was to multiply the emissions of assignats.
In the scale of C the intervals from the key-note, the frequency ratios with the key-note, the successive frequency ratios and the successive intervals are as follows: - If we pass through two intervals in succession, as, for instance, if we ascend through a fourth from C to F and then through a third from F to A, the frequency ratio of A to C is a, which is the product of the ratios for a fourth 4, and a third I That is, if we add intervals we must multiply frequency ratios to obtain the frequency ratio for the interval which is the sum of the two.
The principle of the method is to multiply the given prime (supposed to consist of 4, 5 or 6 figures) by such a factor that the product may be a number within the range of the factor tables, and such that, when it is increased by I or 2, the prime factors may all be within the range of the logarithmic tables.
To destroy the first 6 multiply by 1- 0006 giving 1000063361744, and multiplying successively by i- 00006 and 1-.
Taking as an example the calculation of the Briggian logarithm of the number 43,867, whose hyperbolic logarithm has been calculated above, we multiply it by 3, giving 131,601, and find by Gray's process that the factors of 1.31601 are (I) 1.316 (5) I.
In his history of the Arietidae Hyatt points out that toward the close of the Cretaceous this entire group of ammonites appears to have been affected with some malady; the unrolled forms multiply, the septa are simplified, the ornamentation becomes heavy, thick, and finally disappears in the adult; the entire group ends by dying out and leaving no descendants.
These young individuals can themselves multiply by equal binary fission, giving Anterior flagellum; Posterior flagellum; Longitudinal striations nemes); Cytoplasmic vacuole.
The actinula, when free, may multiply by larval budding, but in all cases both the original actinula and all its descendants become converted into medusae, so that there is no alter nation of generations.
Appertaining to the function (li'l32l3...), each separation having a specification m" ` ' 8 m ï¿½2s m ï¿½38 multiply b P (is 2s 3s .ï¿½ï¿½), P Y by ls!
+aï¿½xn multiply each side by I +px, thus introducing a new quantity A; we obtain (1 +a1x) (1+a2x)...(1 -Fanx)(1+,ux) = 1+(a1 +1a)x + (a2+1aa1)x2+...
To obtain the corresponding theorem concerning the general form of even order we multiply throughout by (ab)2' 2c272 and obtain (ab)2m-1(ac)bxc2:^1=(ab)2mc2 Paying attention merely to the determinant factors there is no form with one factor since (ab) vanishes identically.
Thus, to multiply x 3 -2x+1 by 2x 2 +4, we write the process +I +0-2+I +2+0+4 +2+0-4+2 +0+0 - 0+0 +4+0-8+4 +2+0+0+2-8+4 giving 2x 5 + 2x 2 -8x+4 as the result.
For a time after entry they multiply, obtaining the nitrogen necessary for their nutrition and growth from the free nitrogen of the air, the carbohydrate required being supplied by the pea or clover plant in whose tissues they make a home.
During this period the bacteria multiply and most of them assume a peculiar thickened or branched form, in which state they are spoken of as bacteroids.
Multiply, therefore, the number of Armenian years elapsed by 365; add the number of days from the commencement of the current year to the given date; subtract 176 from the sum, and the remainder will be the number of days from the 1st of January 553 to the given date.
The enormous rate at which aphids multiply under favourable conditions makes them of the greatest economic importance, since the growth of immense numbers of the same kind of plant in close proximity - as in ordinary farm-crops - is especially advantageous to the insects that feed on them.
I was 40 fathoms in depth, we multiply the depth by the rate of inclination, 40 X 8 = 320 fathoms, which gives the point at which the coal seam A should reach the surface.
In ordinary sound waves the displacement is very minute, perhaps of the order 105 cm., so that we multiply it perhaps by ioo,000 in forming the displacement curve.
It is, therefore, further recommended (a) that the milk be rapidly cooled or chilled, as the lower the temperature the less do the bacteria multiply, (b) that contamination during railway transit be avoided by dustproof locked milk cans.
Not to multiply examples further, it may suffice to refer to (a) the apparent belief that the serpent tempted Eve to unchastity (2 Cor.
If the number is incommensurable or consists of more than seven figures, we can take the first seven figures of it (or multiply and divide the result by any factor, and take the first seven figures of the result) and proceed as before.
The indifferent parasites exhibit an alternation of resting, attached phases with active periods, during which they multiply actively and become very abundant in the insect.
We have to multiply a01; -alas+a2 by ao, -aif32+a2 and we obtain ao (3 - aoal(f31N2 +01133) +aoa2(SI+13) -i-a?31a2 - aIa2(31 + 02) + al, 131+02 = b, 131132 = b t'i +s2 = 2bob2, and clearing of fractions R 1,5 = (a o b 2 - a2 b o) 2 + (a i b o - aobi) (aib2 - a2b1).
Concordia discors pointed out the absurdity of the constant tendency to multiply oaths, while "remonstrances," "narratives," "queries," "prescriptions," "vindications," "declarations" and "statements" were scattered broadcast.
These varieties tend to multiply, and it is difficult to reduce them all to a few types.
As any bacteria present in the milk tend to multiply rapidly on the way to the consumer, it is mainly a question of the time which elapses before consumption.
But if the little bit I've got's not stopping me from trying to multiply it to something better, how can you be worried about this kid of yours?
(f, 4)) k +(f, 4)) k +ï¿½(f, 4/) k +aï¿½(1, 4)')k; and, moreover, if we require to find the kth transvectant of one linear system of forms over another we have merely to multiply the two systems, and take the k th transvectant of the separate products.
- As is the case with the Oligochaeta, the Polychaeta furnish examples of species which multiply asexually by budding.