Four-place Logarithms

Here and there in the text small additions have heen made, the treatment of the important subject of transport numbers has been extended. Tables of atomic weights, and of four-place logarithms from Mr. Castle s Mathematical Tables published by Messrs. Macmillan and Co., have also been added as appendices. These additions, it is hoped, will increase the usefulness of the work. ... 

The above is an incomplete list, given to illustrate the level of preparation we are presuming in this text. If you find very much of this list partly or wholly unfamiliar, you don t have to give up, but have a good general chemistry textbook available for study and reference—and use it Some useful general chemistry books are listed at the end of the chapter. A four-place table of logarithms will be necessary a set of ball-and-stick models and a chemical handbook will be very helpful, as would be a small electronic calculator or slide rule to carry out the simple arithmetic required for many of the exercises. 

In nearly all practical chemical calculations, a precision of only two to four significant figures is required. Therefore the student need not perform multiplications and divisions manually. Even if an electronic calculator is not available, an inexpensive 10-in slide rule is accurate to three significant figures, and a table of 4-place logarithms is accurate to four significant figures. 

Wells s New Six-Place Logarithmic Tables. 60 cts. Pocket edition, small type 36 cts Wells s Four-Place Tables. 25 cts. 

The numerical value of the gamma function has been tabulated for all values of n between 1 and 2 to twelve decimal places. By the aid of such a table, the approximate value of all definite integrals reducible to gamma functions can be calculated as easily as ordinary trigonometrical functions, or logarithms. There are four cases ... 

Table V. gives the value of log10r(w) to four decimal places for all values of n between 1 and 2. It has been adapted from Legendre s tables to twelve decimal places in his Exercises de Calcul Integral, Paris, 2, 18, 1817. For all values of n between 1 and 2, log T(w) will be negative. Hence, as in the ordinary logarithmic tables of the trigonometrical functions, the tabular logarithm is often increased by the addition of 10 to the logarithm of T(w). This must be allowed for when arranging the final result.

There are four types of the polymer blends (i) Additive blends whose melt viscosity follows Equation 18.3, (ii) Blends with a positive deviation of from Equation 18.3. These include blends with strong interphase interactions, (iii) Blends with a negative deviation from the logarithmic additivity, which is typical of incompatible components with weak interphase interactions, (iv) Blends that show both positive and negative deviations of py from the additive values (such a relationship is typical of materials in which structural changes take place during flowing). 

---