Coffer

“ The coffers are now brought forward, and the performer, removing the lids (with the moveable compartments) , allows the spectators to satisfy themselves that each coffer is full to the bottom, and that the contents are nothing more or less than what they appear to be. This being established, he returns to his table, and again puts the lids on the coffers, taking care that that which contains the beans shall be placed on the coffer containing the coffee-berries, and vice versâ. He now requests two of the younger spectators to step forward, and assist him with the trick. ”

“ And in a coffer it will store.
And so he took the ruddy gold,
And in a coffer it he laid;
Unknown to him proud Ellenlile
So sly therein herself convey’d.
p. 29He takes the man beneath his arm,
The coffer on his back he throws ”

“ The manners of the young man, his gestures, the way in which he took up his eye-glass, his affected superciliousness, his contemptuous glance at the coffer which had just given so much pleasure to the rich heiress, and which he evidently regarded as without value, or even as ridiculous,—all these things, which shocked the Cruchots and the des Grassins, pleased Eugenie so deeply that before she slept she dreamed long dreams of her phoenix cousin. ”

“ The Conversion of Series and Products into Continued Fractions. 1. A continued fraction may always be found whose nth convergent shall be equal to the sum to n terms of a given series or the product to n factors of a given continued product. In fact, a continued fraction
can be constructed having for the numerators of its successive convergents any assigned quantities p1, p2, p3, . . ., pn, and for their denominators any assigned quantities q1, q2, q3, . . ”

“ If the screw be turned through revolutions, as shown by the scale, and through an additional fraction, as shown by the divided circle, it will pass through times the pitch of the screw, and an additional fraction of the pitch determined by the ratio of the number of divisions read from 0 on the divided circle to the whole number into which it is divided. ”

“ The Ultimate Values of the Coefficients in Fourier’s Series.—If ƒ (x) is everywhere finite within the given interval −π to +π, it can be shown that an, bn, the coefficients of cos nx, sin nx in the series which represent the function, are such that nan, nbn, however great n is, are each less than a fixed finite quantity. ”

“ And in all these relations we may interchange in any way if we interchange in the same way It follows that, within the limits of stability, when we choose for any one of the differential coefficients the quantities following the sign in the numerators of the others together with as those which are to remain constant in differentiation, the value of the differential coefficient as thus determined will be at least as small as when one or more of the constants in differentiation are taken from the denominators, one being still taken from each fraction, and v as before being constant. ”

“ Its thickness must be all the way throughout equal, [Pg 69] and ought to be within one half quarter of an Inch the depth of the inside of the Coffin; because the matter it is Bedded in will raise it high enough. Its length and breadth must be about half an Inch less than the length and breadth of the inside of the Coffin: Because Justifiers of Wood, the length of every side, and almost the depth of the Stone, must be thrust between the insides of the Coffin and the outsides of the Stone, to Wedge it tight and steddy in its place, after the Press-man has Bedded it. ”

“ If we precede the series of convergents by 0/1 and , then the numerator (or denominator) of each term of the series 0/1, 1/0, a/1, ab+1/b . . ., after the first two, is found by multiplying the numerator (or denominator) of the last preceding term by the corresponding quotient and adding the numerator (or denominator) of the term before that. If a is zero, we may regard 1/b as the first convergent, and precede the series by 1/0 and 1/1.
(ii) Each convergent is a fraction in its lowest terms.
(iii) The convergents are alternately less and greater than the true value. ”

“ To multiply by 25, annex two ciphers and divide by 4. To divide by 25, multiply by 4 and strike off the last two figures, which leaves the quotient; one fourth of the last two figures, taken as one number, is the remainder. To multiply a number by 9, annex a cipher, and subtract the number, which is equivalent to taking the number ten times, and then subtracting it once. To multiply by 99, annex two ciphers and subtract the number, &c.
In order that a number may be divisible by 2 without remainder, its units’ figure must be an even number. ”

“ Also let us agree that a grey counter in a compartment shall mean that it is 'empty', that is, that there are no Cakes in it. In the following Diagrams, I shall put '1' (meaning 'one or more') where you are to put a red counter, and '0' (meaning 'none') where you are to put a grey one.
As the Subject of our Proposition is to be "new Cakes", we are only concerned, at present, with the upper half of the cupboard, where all the Cakes have the attribute , that is, "new." ”

“ Annex ciphers until there are twice as many places following the units’ place as there are to be decimal places in the root; extract the nearest square root of this number, and mark off the given number of decimals. Or, more simply: Divide the number into periods, so that the units’ figure shall be the last of a period; proceed in the usual way; and if, when decimals follow the units’ place, there is one figure on the right, in a period by itself, annex a cipher in bringing down that period, and afterwards let each new period consist of two ciphers. ”

“ To find the coefficients of the beginning days of succeeding divisions and subdivisions of the tonalamatl, add the black numbers to the red numbers immediately preceding them in each case, and, after subtracting all the multiples of 13 possible, the resulting number will be the coefficient of the beginning day desired. ”

“ We can have matters so arranged that we may have to make, if we like, ten turns of the screw in order to move the cross wires from one graduation to the next, and we may have the milled head of the screw itself divided into 100 divisions, so that we shall be able to divide each of the ten turns into 100, or the whole division into 1,000 parts. ”

“ When two bodies, A and B, combine in multiple proportions; for instance, 10 parts of A combine with 7 of B, to form one compound, and with 14 to form another, we are directed by some authors to take the smallest combining proportion of one body as representative of the elementary particle or atom of that body. ”

“ The statical energy of an infinitesimal element of volume may be represented by where is a quadratic function of the components of displacement Since for that element of volume may be regarded as linear functions of and diff. coeff., we may regard as a quadratic function of and diff, coeff., or as a linear function of the seventy-eight squares and products of these quantities. ”

“ The introduction of partial differential coefficients enables us to solve at once for a surface a problem analogous to the problem of tangents for a curve; and it also enables us to take the first step in the solution of the problem of maxima and minima for a function of several variables. ”

“ But if we analyze any one of these compound words, Finger-hut, for instance, we shall perceive that while each of the so-called elements of combination, Finger and Hut, has a distinct meaning, which enters into the more specific meaning of the compound, yet they are not, in any true sense, elements, or, in other words, that they are not the ultimate elements of the compound words. ”

“ Ae But as the whole Key, inverted, is koppa, so q, inverted, is none other than b; and the elements of this letter b (a semicircle and a straight line) are actually formed no less than eight times in the key by means of the ‘ binding’ lines and the central circle. If, then, the Key indeed represented the key of the melody sung by Sergius, I had at last (remembering the flat delineation of the figure) the tangible result of B flat. ”

“ In the inorganic world the perceptible mass of matter is certainly not an individual being, a unum per se, but only a collection of individual atoms or molecules, a unum per accidens. Whether the molecule or the atom of the chemically elementary body is the “individual,” cannot be determined with any degree of certitude. It would appear, however, that every specifically distinct type of inorganic matter, whether compound or elementary, requires for its existence a certain minimal volume, by the sub-division of which the type is substantially changed ”

“ For a differential coefficient is a limit, and the limit of a function at a given value of its argument expresses a property of the aggregate of the values of the function corresponding to the aggregate of the values of the argument in the neighbourhood of the given value. ”

“ These form a compact series; between any two there are always an infinite number of others. Now omit the dot at the beginning of each, and we have a compact series consisting of all finite integers except such as divide by 10. If we wish to include those that divide by 10, there is no difficulty; instead of starting with .1, we will include all decimals less than 1, but when we remove the dot, we will transfer to the right any 0's that occur at the beginning of our decimal. ”

“ Expansion of Functions in Series of Legendre's Coefficients.—If it be assumed that a function given arbitrarily in the interval to , can be represented by a series of Legendre's coefficients and it be assumed that the series converges in general uniformly within the interval, the coefficient a can be determined by using (19) and (20) ; we see that the theorem (19) plays the same part as the property , does in the theory of the expansion of functions in series of circular functions. ”

“ Multiplying conjugate pairs together, attributing proper signs to each product, and adding, we find from the properties of the minors of a determinant that the coefficient of a term such as , is zero, unless the quantities s,t,p,q,r,... are all different. When these quantities are different the coefficient is simply the determinant with a proper sign. ”

“ The Coptic language is not an inflected one; and it has very few affixes. There are many prefixes to its nouns and verbs, which before the former are articles or demonstrative pronouns. Between these prefixes and the noun or verb, pronominal infixes are introduced, by which possession is denoted in the case of a noun, and the subject in that of a verb. Thus, ran is "a name;" pi-ran, "the name;" pe-v-ran, "his name;" i, is the verbal root, "come;" a, the prefix of the past tense; and a-v-i, "he came." Some nouns take affixes, as jo-v, "his head." ”

“ ON PERMUTATIONS AND
COMBINATIONS.
204. If a number of counters, distinguished by different letters, be placed on the table, and any number of them, say four, be taken away, the question is, to determine in how many different ways this can be done. Each way of doing it gives what is called a combination of four, but which might with more propriety be called a selection of four. Two combinations or selections are called different, which differ in any way whatever; thus, abcd and abce are different, d being in one and e in the other, the remaining parts being the same. ”

“ One mistake in the pattern does not necessarily do away with the efficacy of a comb, as a Panggang man once said, “It is like a gap or hole in a bird-trap: the bird can hop through it, but it is always a question whether it sees the gap.” ”

“ The unequall sections of a spheare we have reserved for this place: Because they are comprehended of a surface both sphearicall and conicall, as is the sectour. As also of a plaine and sphearicall, as is the section: And in both like as in a Circle, there is but a greater and lesser segment. And the sectour, as before, is considered in the center.
18. The sectour of a spheare is a segment of a spheare, which without is comprehended of a sphearicall within of a conicall bounded in the center, the greater of a concave, the lesser of a convex. ”

“ Now the symbol of each variable or constant, is placed at the top of a column capable of containing any required number of digits.
Under this arrangement, when any formula is required to be computed, a set of operation cards must be strung together, which contain the series of operations in the order in which they occur. Another set of cards must then be strung together, to call in the variables into the mill, the order in which they are required to be acted upon. ”

“ It will be evident, that if the copper was shifted from right to left through a space equal to two figures of a number, and, at the same time, the type sector so shifted as to bring the punches corresponding to the figures of the number successively under the bent lever, an engraved impression of the number might thus be obtained upon the copper by the continued action of the bent lever. ”

“ Do you not know, young man, that with the ordinary ten ciphers, using all at a time, but without any repetition, you can make three million two hundred and sixty-eight thousand and eight hundred different numbers, and that if you use the same cipher more than once in the number, these millions of combinations will be enormously increased! ”

“ The process of combing consists of subjecting the card sliver to the operations of the automatic wool comber, which straightens the fibers and removes all short and tufted pieces of wool. Combing is a guarantee that every fiber of the wool lies perfectly straight, and that all fibers follow one after the other in regular order. ”