# S ~amp; m Sentence Examples

The sum and product of two quaternions are defined by the formulae mi ase + F+lases = (a s + 133) es 2arer X ZO,es = Fiarfseres, where the products e,e, are further reduced according to the following multiplication table, in which, for example, the eo e1 e2 e3 second line is to be read eieo = e1, e 1 2 = - eo, e i e 2 = es, eie3 = - e2.

The time rate of increase of momentum of the fluid inside S is )dxdydz; (5) and (5) is the sum of (I), (2), (3), (4), so that /if (dpu+dpu2+dpuv +dpuw_ +d p j d xdyd z = o, (b)` dt dx dy dz dx / leading to the differential equation of motion dpu dpu 2 dpuv dpuv _ X_ (7) dt + dx + dy + dz with two similar equations.

Denoting by S(v) the sum of all the values of AS up to any assigned velocity v, (is) S(v) =E(OS)+ a constant, by which S(v) is calculated from AS, and then between two assigned velocities V and v, V AT, = vAv or rvvdv vgp gp' and if s feet is the advance of a shot whose ballistic coefficient is C, (17) s=C[S(V) - S(v)].

He deduced the variations of the mean temperature of a section of a bar from the sum S of the E.M.F.'s of a number of couples, inserted at suitable equal intervals 1 and connected in series.

Much of the Principia consists of synthetical deductions from definitions and axioms. But the discovery of the centripetal force of the planets to the sun is an analytic deduction from the facts of their motion discovered by Kepler to their real ground, and is so stated by Newton in the first regressive order of Aristotle - P-M, S-P, S-M.

This done, as the major is convertible, the analytic order - P-M, S-P, S-M - was easily inverted into the synthetic order - M-P, S-M, S-P; and in this progressive order the deduction as now taught begins with the centripetal force of the sun as real ground, and deduces the facts of planetary motion as consequences.

Lastly, Wundt's view is an interesting piece of eclecticism, for he supposes that induction begins in the form of Aristotle's inductive syllogism, S-P, S-M, M-P, and becomes an inductive method in the form of Jevons's inverse deduction, or hypothetical deduction, or analysis, M-P, S-M, S-P. In detail, he supposes that, while an " inference by comparison," which he erroneously calls an affirmative syllogism in the second figure, is preliminary to induction, a second " inference by connexion," which he erroneously calls a syllogism in the third figure with an indeterminate conclusion, is the inductive syllogism itself.

S-M, of which Newton has left so conspicuous an example in his Principia.

South of the central lowlands the so-called Smaland highlands extend over the old province of Smaland in the south-east, and lie roughly south of Lake Vetter and of Gothenburg, S m aland where.

The greatest length of the former island, from north to south, is about s m.

AdvertisementThe number is divisible (i) by io if it ends in o; (ii) by 5 if it ends in o or 5; (iii) by 2 if the last digit is even; (iv) by 4 if the number made up of the last two digits is divisible by 4; (v) by 8 if the number made up of the last three digits is divisible by 8; (vi) by 9 if the sum of the digits is divisible by 9; (vii) by 3 if the s l um of the digits is divisible by 3; I 3=31 2 9 =32 3 27=33 481 =34 (viii) by II if the difference between the sum of the 1st, 3rd, 5th,.

If we suppose that s is not quite constant, but increases or diminishes slightly with change of temperature according to a linear formula s=50-1-2cT (in which so represents the constant part of s, and c may have either sign), we obtain a more general formula which is evidently the sum of the two previous solutions and may be made to cover a greater variety of cases.

The simplest invariant is S = (abc) (abd) (acd) (bcd) cf degree 4, which for the canonical form of Hesse is m(1 -m 3); its vanishing indicates that the form is expressible as a sum of three cubes.

The connecting link between the general use of the signet, which was required by the Roman law for legal purposes, but which had died out by the 7th century, and the revival of seals in the middle ages is to be found in the chanceries Early of the Merovingian and Carolingian sovereigns, where s m $d seval the practice of affixing the royal seal to diplomas appears to have been generally maintained (see Diplomatic).

The world's largest public corporation by revenue as well as the largest private employer, Walmart was founded by Sam Walton in 1962.

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