The first, and most important, is that the quotient is placed above the dividend.
This quotient is called the change of entropy, and may be denoted by (4,"-0').
+ 1/n+ 271+ ., where, after the n th partial quotient, the cycle of partial quotients b 1, b2, ..., b n recur in the same order, is the type of a recurring simple continued fraction.
Experiment, however, showed that while the quotient on the left hand of this equation was fairly constant for a great number of substances, yet its value was not gR but 7 R; this means that the critical density is, as a general rule, 3.7 times the theoretical density.
If we divide n 9 by n P, the quotient is of course 1.
In long division the divisor is put on the left of the dividend, and the quotient on the right; and each partial product, with the remainder after its subtraction, is shown in full.
The potential difference of the ends of the low resistance is at the same time measured on the potentiometer, and the quotient of this potential difference by the known value of the low resistance gives the true value of the current passing through the ammeter.
To Find The Year Of The Cycle, We Have Therefore The Following Rule: Add Nine To The Date, Divide The Sum By Twenty Eight; The Quotient Is The Number Of Cycles Elapsed, And The Remainder Is The Year Of The Cycle.
In short division the divisor and the quotient are placed respectively on the left of and below the dividend, and the partial products and remainders are not shown at all.
In incomplete partition the quotient is 3, and the remainders 11 and 17 are in effect disregarded; if, after finding the quotient 3, we want to know what remainder would be produced by'a direct division, the simplest method is to multiply 3 by 2 4 0 and subtract the result from 935.
By 12 gives quotient 3d.
The weight per acre, the saccharine contents of the juice, and the quotient of purity compared favourably with the best results obtained in Germany or France, and with those achieved by the Suffolk farmers, who between 1868 and 1872 supplied Mr Duncan's beetroot sugar factory at Lavenham; for the weight of their roots rarely reached 15 tons per acre, and the percentage of sugar in the juice appears to have varied between 10 and 12.
Hence, to find the Golden Number N, for any year x, we have N= (- 19 ' 1) which gives the following rule: Add i to the date, divide the sum by 19; the quotient is the number of cycles elapsed, and the remainder is the Golden Number.
The determination of a quotient is equivalent to completion of the diagram by entry of the number when the unit and the product are given.
I) to any other adiabatic 0", the quotient H/o of the heat absorbed by the temperature at which it is absorbed is the same for the same two adiabatics whatever the temperature of the isothermal path.
- Divide the year of the Hegira by 30; the quotient is the number of cycles, and the remainder is the year of the current cycle.
Any quaternion may now be expressed in numerous simple forms. Thus we may regard it as the sum of a number and a line, a+a, or as the product, fly, or the quotient, be-', of two directed lines, &c., while, in many cases, we may represent it, so far as it is required, by a single letter such as q, r, &c.
Is equal to the quotient when 12 pence are formed into units of 4d.; each of these numbers being said to be obtained by dividing 12 by 4.
Is - Pr times II in., and therefore call 1 - 3 1 - the quotient when 3 in.
Treating x as the unknown quotient corresponding to the original dividend, we obtain successive dividends corresponding to quotients x-200, x- 230 and x-231.
The advantage of the Austrian arrangement of the quotient lies in the indication it gives of the true value of each partial quotient.
A modification of the method, corresponding with D of § ioi, is shown in G; the fact that the partial product 08546 is followed by two blank spaces shows that the figure 2 represents a partial quotient 200.
Division by a Mixed Number.-To divide by a mixed number, when the quotient is seen to be large, it usually saves time to express the divisor as either a simple fraction or a decimal of a unit of one of the denominations.
Hence_li y ` A 1n where A li and A li, are minors of the complete determinant (a11a22...ann)ï¿½ an1 ant ï¿½ï¿½ï¿½an,n-1 or, in words, y i is the quotient of the determinant obtained by erasing the i th column by that obtained by erasing the n th column, multiplied by (-r)i+n.
If we divide the sum of x 2 and a 2 by the sum of x and a, we get a quotient x - a and remainder 2a 2, or a quotient a - x and remainder 2x 2, according to the order in which we work.
&c., where p+pq is the quantity whoseTi power or root is required, p the first term of that quantity, and q the quotient of the rest divided by p, m the power, which may be a positive or negative integer or a fraction, and a, b, c, &c., the several terms in order, In a second letter, dated the 24th of October 1676, to Oldenburg, Newton gave the train of reasoning by which he devised the theorem.
Divide The Hebrew Year By 19; Then The Quotient Is The Number Of The Last Completed Cycle, And The Remainder Is The Year Of The Current Cycle.
This corrected pull is then divided by the weight of the vehicles hauled, in which must be included the weight of the dynamometer car, and the quotient gives the resistance per ton of load hauled at a certain uniform speed on a straight and level road.
To Find If A Year Is Intercalary Or Common, Divide It By 30; The Quotient Will Be The Number Of Completed Cycles And The Remainder Will Be The Year Of The Current Cycle; If This Last Be One Of The Numbers 2, 5, 7, 10, 13, 16, 18, 21, 24, 26, 29, The Year Is Intercalary And Consists Of 355 Days; If It Be Any Other Number, The Year Is Ordinary.
From the purely geometrical point of view, a quaternion may be regarded as the quotient of two directed lines in space - or, what comes to the same thing, as the factor, or operator, which changes one directed line into another.
Thus, in place of his general tri-quaternion we might deal with products of an odd number of point-plane-scalars (of form, uq+wr) which are themselves point-plane-scalars; and products of an even number which are octonions; the quotient of two point-plane-scalars would be an octonion, of two octonions an octonion, of an octonion by a point-plane-scalar or the inverse a point-plane-scalar.
In the case of a terminating simple continued fraction the number of partial quotients may be odd or even as we please by writing the I last partial quotient, a n as a n - I +1.
When we can solve this equation we have an expression for the n th convergent to the fraction, generally in the form of the quotient of two series, each of n terms. As an example, take the fraction (known as Brouncker's fraction, after Lord Brouncker) I I 2325 2 72 2 + 2 + 2 + 2 + ...
B,, Y the numerator (or denominator) of the last preceding term by the corresponding quotient and adding the numerator (or denominator) of the term before that.
Lambert for expressing as a continued fraction of the preceding type the quotient of two convergent power series.
Thus, to divide i by i +x algebraically, we may write it in the form I+o.x+o.x 2 +o.x 3 +o.x 4, and we then obtain I I +0.x+0.x2+0.x3 '+0.x4 = I' x+x2 - x 3 + x4 I+x I+x' where the successive terms of the quotient are obtained by a process which is purely formal.
The Above Expression Must Therefore Be Diminished By The Number Of Units In 4, Or By () W (This Notation Being Used To Denote The Quotient, In A Whole Number, That Arises From Dividing X By 4).
Clifford considers an octonion p+wq as the quotient of two motors p+wv, p'+wo'.
The capacity is then obtained as the quotient of the whole charge by this potential.
Nevertheless, it has been found in practice, when syrups with low quotient of purity and high quotient of impurity are being treated, injecting the feed at a number of different points in the pan does reduce the time required to boil the pan, though of no practical advantage with syrups of high quotient of purity and free from the viscosity which impedes circulation and therefore quick boiling.
The quotient thus obtained decreases as the conditions are more favourable, and, on the whole, it seems to form a good index to the merit of the respective countries from the standpoint of vital forces.
Cayley, however, has shown that, whatever be the degrees of the three equations, it is possible to represent the resultant as the quotient of two determinants (Salmon, l.c. p. 89).