When Both The Numbers Are Large, We Split Up One Of Them, Preferably The Multiplier, Into Separate Portions.
The two systems of logarithms for which extensive tables have been calculated are the Napierian, or hyperbolic, or natural system, of which the base is e, and the Briggian, or decimal, or common system, of which the base is io; and we see that the logarithms in the latter system may be deduced from those in the former by multiplication by the constant multiplier /loge io, which is called the modulus of the common system of logarithms.
If the distance between the disks could be made infinitely small each time, then the multiplier r would be 2, and the charge would be doubled each time.
The table of multiples will then be as in C. The next step is to arrange the multiplier and the multiplicand above the partial products.
Second in importance only to these are his researches in differential equations, notably the theory of the last multiplier, which is fully treated in his Vorlesungen fiber Dynamik, edited by R.
The second of these relations is an important one, as it shows that from a table of logarithms to base a, the corresponding table of logarithms to base b may be deduced by multiplying all the logarithms in the former by the constant multiplier i/logab, which is called the modulus of the system whose base is b with respect to the system whose base is a.
C. Schweigger (1779-1857) with his " multiplier " made an advance upon Oersted's discovery, by winding the wire conveying the electric current many times round the pivoted magnetic needle and thus increasing the deflection; and L.
It has been already mentioned that Schweigger invented in 1820 the " multiplier," and Nobili in 1825 the astatic galvanometer.
C. Schweigger's "multiplier," that is, by substituting for single wire circuits, voluminous coils (Trans.
When it is necessary to write the multiplicand before the multiplier, the symbol >e will be used, so that a will mean the same as a X b.
(Iv) To Multiply By 7, 8, 9, Ii Or 12, Treat The Multiplier As 10 3, 10 2, Io I, 10 1 Or 10 2; And Similarly For 13, 17, 18, 19, &C.
(V) To Multiply By 4 Or 6, We Can Either Multiply From The Left By 2 And Then By 2 Or 3, Or Multiply From The Right By 4 Or 6; Or We Can Treat The Multiplier As 5 I Or 5 1.
For elementary work the multiplicand may come immediately after the multiplier, as in D; the last figure of each partial product then comes immediately under the corre up to the multiplication of decimals and of approximate values of numbers, is to place the first figure of the multiplier under the first figure of the multiplicand, as in E; the first figure of each partial product will then come under the corresponding figure of the multiplier.
The principle is that 162.4 27 =100.4 2 7+ 60.4 2 7+ 2.4 2 7 = 1.42700+6.4270+2.427; but, instead of 427 writing down the separate products, we 6 427 (in effect) write 42700, 4270 and 427 in 2 4?7 separate rows, with the multipliers 1, 6, 2 69 174 in the margin, and then multiply each number in each column by the corresponding multiplier in the margin, making allowance for any figures to be " carried."
For multiplication by a proper fraction or a decimal, it is sometimes convenient, especially when we are dealing with mixed quantities, to convert the multiplier into the sum or difference of a number of fractions, each of which has i as its numerator.
The method E of § ioi being adopted, the multiplicand and the multiplier are written with a space after as many digits (of each) as will be required in the product (on the principle explained in § 1 01); and the multiplication is performed from the left, two extra figures being kept in.