In such cases the immediate damage done may be slight; but the effects of prolonged action and the summation of numerous attacks at numerous points are often enormotis, certain of these leafdiseases costing millions sterling annually to some planting and agricultural communities.
F m +Z(D2f1) (Dif2)f3...fm+Z(D3f1) f 2 f fm, the summation in a term covering every distribution of the operators of the type presenting itself in the term.
Thus the heat of formation of anhydrous zinc sulphate, ZnSO 4j which cannot be determined directly, may be arrived at by summation (in Hess's units) as follows: Heats of formation are still determined for the most part in a precisely similar manner.
Y ...a n v, the summation being for all permutations of the n numbers, is called the determinant of the n 2 quantities.
Being a separation of (n1 1 n' 2 n3 3 ...) and the summation being in regard to all such separations.
Multiplying out the right-hand side and comparing coefficients X1 = (1)x1, X 2 = (2) x2+(12)x1, X3 = (3)x3+(21)x2x1+ (13)x1, X4 = (4) x 4+(31) x 3 x 1+(22) x 2+(212) x2x 1 +(14)x1, Pt P2 P3 P1 P2 P3 Xm=?i(m l m 2 m 3 ...)xmlxm2xm3..., the summation being for all partitions of m.
APn 1 2 3 ' the summation being for all permutations of the indices which result in different terms. The function is written (plp2p3ï¿½4n) for brevity, and repetitions of numbers in the bracket are indicated by exponents, so that (p1p1p2) is written (p1p 2).
(ix.) The extension of n (r), and therefore of n [r ], to negative and fractional values of n, enables us to extend the applicability of the binomial coefficients to the summation of series (ï¿½ 46 (ii.)).
He was of the opinion that the summation of minute differences had played a preponderating if not exclusive part in the formation of species.
In this case the work done by the internal forces will be represented by ~fRpqdrpq, when the summation includes every pair of particles, and each integral is to be taken between the proper limits.
+an we may write in general D s f = ZD(p l p 2 p 3 ï¿½ï¿½) the summation being for every partition (piP2p3...) of s, and D(p iP2 p 3 ...)f being =2 (Dpifi)(DP2f2) (DL'h3f3)f4...f,n.
An application of the method is to the summation of a recurring series, i.e.
The practical bearings of a science, it will be granted, are simply, as it were, the summation of its facts, with the legitimate conclusions from them, the natural application of the data ascertained, and have not necessarily any direct relationship to its pursuit.
Hence, if the angle which the tangent at the extremity of the ordinate u 0 makes with the axis of x is denoted by fie, we have area from uo to u1= 2h(uo + ui) - -- i i h 2 (tan y l - tan t u 2 = Wu ' + u2) - 1 Tih 2 (tan 4,2 - tan um-1 t0 26 m, - 2 h(um-1 + um) i h (tan 4, m - and thence, by summation, A =C I - i i h 2 (tan - tan 1,1/o).
There is not much difficulty in detecting the difference tone by a resonator if it is held, say, close to the reeds of a harmonium, and Helmholtz succeeded in detecting the summation tone by the aid of a resonator.
Further, Rucker and Edser, using a siren as source, have succeeded in making a fork of the appropriate pitch respond to both difference and summation tones (Phil.
But there is no doubt that it is very difficult to detect the summation tone by the ear, and many workers have doubted the possibility, notwithstanding the evidence of such an observer as Helmholtz.
The total shear at a b is S = R-E(W1+W2 ...) where the summation extends to all the loads to the left of the section.
The differences OD and DI are thus calculated, while the values of D(v) and I (v) are obtained by summation with the arithmometer, and entered in their respective columns.
In any region of velocity where it is possible to represent p with sufficient accuracy by an empirical formula composed of a single power of v, say v m, the integration can be effected which replaces the summation in (to), (16), and (24); and from an analysis of the Krupp experiments Colonel Zabudski found the most appropriate index m in a region of velocity as given in the following table, and the corresponding value of gp, denoted by f (v)or v m lk or its equivalent Cr, where r is the retardation.
Now taking equation (72), and replacing tan B, as a variable final tangent of an angle, by tan i or dyldx, (75) tan 4) - dam= C sec n [I(U) - I(u)], and integrating with respect to x over the arc considered, (76) x tan 4, - y = C sec n (U) - f :I(u)dx] 0 But f (u)dx= f 1(u) du = C cos n f x I (u) u du g f() =C cos n [A(U) - A(u)] in Siacci's notation; so that the altitude-function A must be calculated by summation from the finite difference AA, where (78) AA = I (u) 9 = I (u) or else by an integration when it is legitimate to assume that f(v) =v m lk in an interval of velocity in which m may be supposed constant.
On the other hand, Huxley's summation of the primitive characters of all the mammals led him to an amphibian stem type, a prophecy which has proved faulty because based on erroneous analysis and comparison.
The sign of summation X is used in cases where there are several absorption bands, and consequently several similar terms on the right-hand side, each with a different value of A m.
Proceeding on this suggestion, and misled by the mathematical expression which he had given to Weber's law, Fechner held that a conscious sensation, like its stimulus, consists of units, or elements, by summation and increments of which conscious sensations and their differences are produced; so that consciousness, according to this unnecessary assumption, emerges from an integration of unconscious shocks or tremors.
By synthesis at a summation of "beats" or of simple contras tions in the compound, or "tetanic," or summed contraction of the skeletal muscles.
When muscle that has remained inactive for some time is excited by a series of single and equal stimuli succeeding at intervals too prolonged to cause summation the succeeding contractions exhibit progressive increase up to a certain degree.
GP2), (20) provided the summation ~ on the left hand be understood to include each pair of particles once only.
The total impulse in any finite interval of time is the integral of the impulses corresponding to the infinitesimal elements 3t into which the interval may be subdivided; the summation of which the integral is the limit is of course to be understood in the vectorial sense.
In strictness the angle is dependent upon the frequency, but if the dispersion be weak relatively to the double refraction, the product sin 24 - a)sin 2Ni - (3) has sensibly the same value for all terms of the summation, and we may write I=cos 2 (1 3 - a)/a 2 - sin 2 (1 ' - a) sin 2 (t ' - a 2 sin 2 2 This formula contains the whole theory of the colours of crystalline plates in polarized light.
Removing the summation signs in equation (52) in order to restrict its application to two points and dividing by the common time interval during which the respective small displacements ds and ds were made, it becomes Pdsfdt = Rds/dt, that is, Pv = Rv, which shows that the force ratio is the inverse of the velocity ratio.
Mag., 1878, 2, p. 500, or Rayleigh, Sound, § 386) that sounds of considerable intensity when heard by themselves are liable to be completely obliterated by graver sounds of sufficient force goes far to explain this, for the summation tones are of course always accompanied by such graver sounds.
Are obtained from the data by summation and multiplication; and the ordinary methods then apply for calculation of its volume.
On combining the two parts of the pressure which have been calculated, the aggregate impulsive pressure on dS in time dt is found to be dS ff f v1,1 (h 3 m 3 /7r 3)e h m(u2+v2+w2 >mu2dudvdw, where M denotes summation over all kinds of molecules.
Relation of Binomial Coefficients to Summation of Series.
Is a separation of (11 1 12213 3 ...) of specification (mM'8m"`28m"`3s...), placing s under the summation sign to denote the is Zs 3s specification involved, 141t412t!p31!...
1+Eaix+Esiy+ /al a2x 2 +Malt2xy -Z01023,2+ï¿½ï¿½ï¿½ The most general symmetric function to be considered is E 41 041 8424-3033..ï¿½ .conveniently written in the symbolic form (pigi p2g2 p3go...)ï¿½ Observe that the summation is in regard to the expressions obtained by permuting then suffixes I, 2, 3, ...n.