Correct Unity

Later, the Biographies continues, Zhang moved to Sichuan and received the revelation of the teaching of Correct Unity (Zhengyi) from Laozi. After that, he finally had the means to purchase the ingredients needed to compound the Nine Elixirs. 

One should also know how the Three Caverns and the Four Supplements support and complete each other. The Codes and Precepts from the Scriptures and Charts of Correct Unity Zhengyi jingtu kejie pin) says ... 

The Normative Scripts of Correct Unity (Zhengyi fawen) honor the Dao and its Virtue they revere [all] the Three Caverns, and offer the Three Vehicles (sansheng) to the view. (Daojiao yishu, 2.iib-i2a)... 

Precepts and Codes of the Celestial Master s Teaching, from the Normative Scripts of Correct Unity]. Contains materials originally dating from the third century. Daozang, CT 789. 

Here x is the fractional contribution of the inverted component of an assumed racemic twin. It should be zero if the absolute structure is correct, unity if it has to be inverted, and somewhere in between if racemic twinning is genuinely present (note that the value can only be judged together with its standard uncertainty). Thus the above formulae apply with n = 1 and the twin law R= (—1 0 0,0—1 0,0 0 —1). This matrix is the default matrix for TWIN, therefore the two following commands refine racemic twins. 

P the other terms provide corrections which at low or moderate pressure are close to unity. To use Equation (2), we require vapor-pressure data and liquid-density data as a function of temperature. We also require fugacity coefficients, as discussed in Chapter 3. 

If the data are correlated assuming an ideal vapor, the reference fugacity is just the vapor pressure, P , the Poynting correction is neglected, and fugacity coefficient is assumed to be unity. Equation (2) then becomes... 

In this expression, cos 0 is the average value of cos 0 the weighting factor used to evaluate the average is given by the Boltzmann factor exp(-V /RT), where R is the gas constant in the units of and T is in degrees Kelvin. Note that the correction factor introduced by these considerations reduces to unity if... 

If we disregard the term in brackets in Eq. (8.112)-which we shall call f(y) and which is close to unity for values of x that are not too different from 1/2-this expression gives the same result for the excluded volume of the coil as given by Eq. (8.104) from a comparison of Eqs. (8.97) and (8.103). We may regard f(y) as a correction factor which is required for Eq. (8.104) to be valid as the difference 1/2 - x increases. In the next section we shall discuss the implications of Eq. (8.112) in greater detail. 

FIG. 10-31 Typical pump performance curve. The curve is shown for water at 85 F. If the specific gravity of the fluid is other than unity, BHP must he corrected. 

Compressibility of Natural Gas All gases deviate from the perfect gas law at some combinations of temperature and pressure, the extent depending on the gas. This behavior is described by a dimensionless compressibility factor Z that corrects the perfect gas law for real-gas behavior, FV = ZRT. Any consistent units may be used. Z is unity for an ideal gas, but for a real gas, Z has values ranging from less than 1 to greater than 1, depending on temperature and pressure. The compressibihty faclor is described further in Secs. 2 and 4 of this handbook. 

Throughout this section the hydronium ion and hydroxide ion concentrations appear in rate equations. For convenience these are written [H ] and [OH ]. Usually, of course, these quantities have been estimated from a measured pH, so they are conventional activities rather than concentrations. However, our present concern is with the formal analysis of rate equations, and we can conveniently assume that activity coefficients are unity or are at least constant. The basic experimental information is k, the pseudo-first-order rate constant, as a function of pH. Within a senes of such measurements the ionic strength should be held constant. If the pH is maintained constant with a buffer, k should be measured at more than one buffer concentration (but at constant pH) to see if the buffer affects the rate. If such a dependence is observed, the rate constant should be measured at several buffer concentrations and extrapolated to zero buffer to give the correct k for that pH. 

The quantity on the left side of the equation is referred to as the logarithm of the rate constant corrected for protonation often the correction term is negligible. If the activity coefficient term on the right side is negligible, Eq. (8-104) predicts a linear relationship between the corrected log kobs and —//o, the slope being unity. A similar treatment of the A-Se2 mechanism also predicts a linear plot of log fcobs against —Ho-... 

As originally proposed, the Zucker-Hammett hypothesis states that for A1 reactions log kobs is linear in —Ho, whereas for A2 reactions log kobs is linear in log ch+. This latter statement is now known not to be generally correct. Moreover, the slopes of plots against —Ho often differ from unity. Bunnett and Olsen... 

Power-factor can be rated at unity, leading, or even lagging. The synchronous motor can supply corrective kvar to counteract lagging power factor caused by induction motors or other inductive loads. 

The usual synchronous motor power factors are unity (1.0) or 0.8 leading. Values of 0.7 or 0.6 leading will give more leading correction to an otherwise lagging system. 

The induction motor usually requires irom 0.3 to 0.6 reactive magnetizing kva per hp of operating load, but an 0.8 leading power factor synchronous motor will deliver from 0.4-0.6 corrective magnetizing kva per hp depending on the mechanical load carried. Thus, equal connected hp in induction and 0.8 leading power factor synchronous motors will result in an approximate unity power factor for the system. 

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