Quartering method

We composite or homogenize samples using a procedure, which is often referred to as the four quarters or the quartering method. The required equipment consists of a stainless steel pan or a tray and a stainless steel spoon or a scoop. To eliminate the need for decontamination between samples, these inexpensive supplies may be discarded after each sample. 

To perform the four quarters method, we follow these steps ... 

Figure 1.3 The cone and quarter method of sampling bulk materials.

The MAPE is a good measure of forecast error when the underlying forecast has significant seasonality and demand varies considerably from one period to the next Consider a scenario in which two methods are used to make quarterly forecasts for a product with seasonal demand that peaks in the third quarter. Method 1 returns forecast errors of 190, 200, 245, and 180 Method 2 returns forecast errors of 100,120,500, and 100 over four quarters. Method 1 has a lower MSE and MAD relative to Method 2 and would be preferred if either alterion was used. If demand is highly seasonal, however, and averages 1,000, 1,200, 4,800, and 1,100 in the four periods. Method 2 results in a MAPE of 9.9 percent, whereas Method 1 resnlts in a mnch higher MAPE, 14.3 percent. In this instance, it can be argued that Method 2 should be preferred to Method 1. 

Figure 1.2 Illustration of the cone and quartering method for reducing the sample size.

The correct treatment of boundaries and boundary effects is crucial to simulation methods because it enables macroscopic properties to be calculated from simulations using relatively small numbers of particles. The importance of boundary effects can be illustrated by considering the following simple example. Suppose we have a cube of volume 1 litre which is filled with water at room temperature. The cube contains approximately 3.3 X 10 molecules. Interactions with the walls can extend up to 10 molecular diameters into the fluid. The diameter of the water molecule is approximately 2.8 A and so the number of water molecules that are interacting with the boundary is about 2 x 10. So only about one in 1.5 million water molecules is influenced by interactions with the walls of the container. The number of particles in a Monte Carlo or molecular dynamics simulation is far fewer than 10 -10 and is frequently less than 1000. In a system of 1000 water molecules most, if not all of them, would be within the influence of the walls of the boundary. Clecirly, a simulation of 1000 water molecules in a vessel would not be an appropriate way to derive bulk properties. The alternative is to dispense with the container altogether. Now, approximately three-quarters of the molecules would be at the surface of the sample rather than being in the bulk. Such a situation would be relevcUit to studies of liquid drops, but not to studies of bulk phenomena. 

Hydrolysis (or saponification) of n-butyl acetate. Boil 4-5 g. of n-butyl acetate (Section 111,95) with 50 ml. of 10 per cent, sodium hydroxide solution under reflux until the odour of the ester can no longer be detected (about 1 hour). Set the condenser for downward distiUation and coUect the first 10 ml. of distillate. Saturate it with potassium carbonate, aUow to stand for 5 minutes, and withdraw all the Uquid into a small pipette or dropper pipette. AUow the lower layer of carbonate solution to run slowly into a test-tube, and place the upper layer into a small test-tube or weighing bottle. Dry the alcohol with about one quarter of its buUr of anhydrous potassium carbonate. Remove the alcohol with a dropper pipette and divide it into two parts use one portion for the determination of the b.p. by the Siwoloboff method (Section 11,12) and convert the other portion into the 3 5-dinitrobenzoate (Section III, 27) and determine the m.p. 

Meihylamine hydrochloride method. Place 100 g. of 24 per cent, methyl-amine solution (6) in a tared 500 ml. flask and add concentrated hydrochloric acid (about 78 ml.) until the solution is acid to methyl red. Add water to bring the total weight to 250 g., then introduce lSO g. of urea, and boil the solution gently under reflux for two and three-quarter hours, and then vigorously for 15 minutes. Cool the solution to room temperature, dissolve 55 g. of 95 per cent, sodium nitrite in it, and cool to 0°. Prepare a mixture of 300 g. of crushed ice and 50 g. of concentrated sulphuric acid in a 1500 ml. beaker surrounded by a bath of ice and salt, and add the cold methylurea - nitrite solution slowly and with mechanical stirring and at such a rate (about 1 hour) that the temperature does not rise above 0°. It is recommended that the stem of the funnel containii the methylurea - nitrite solution dip below the surface of the acid solution. The nitrosomethylurea rises to the surface as a crystalline foamy precipitate. Filter at once at the pump, and drain well. Stir the crystals into a paste with about 50 ml. of cold water, suck as dry as possible, and dry in a vacuum desiccator to constant weight. The yield is 55 g. (5). 

Illustration showing the method of coning and quartering as a means of reducing a gross sample for subsampling, (a) The gross sample is first piled into a cone and... 

The oxidation of carbohydrates is the oldest method for oxahc acid manufacture. The reaction was discovered by Scheele in 1776, but was not successfully developed as a commercial process until the second quarter of the twentieth century. Technical advances in the manufacture of nitric acid, particularly in the recovery of nitrogen oxides in a form suitable for recycle, enabled its successful development. Thus 150 t of oxahc acid per month was produced from sugar by I. G. Earben (Germany) by the end of World War II. 

The desugarization by-product is normally sold as a low value molasses. Pulse method systems also produce a relatively high value betaine-rich (at least 50% on soHds) fraction. The concentrated betaine-rich by-product is used as a custom animal feed, whose European markets are well estabUshed and may provide a future opportunity in the U.S. feed industry. Beet sugar molasses contains from 3 to 6% betaine, by weight, about three-quarters of which may be recoverable as a potential by-product ( 40 50% purity). 

It would not be unusual for some action plans to take a long time to complete. When extended implementation time is necessary, a follow-up mechanism should be used to document progress and show that an effort is being made to resolve the issues. Periodic (i.e., quarterly, semiannually) progress reports should be used as a follow-up method to ensure implementation. Future audits of the facility should include confirmation of the implementation of previous audit action plans. 

The zero in the eontrol-to-output eharaeteristie eaused by the ESR of the output filter eapaeitor ean be found by two methods if the value of the aetual ESR is known from the eapaeitor s data sheet, then the loeation of the zero ean be ealeulated, if not, it ean be grossly estimated. Using four aluminum eleetrolytie eapaeitors in parallel should eut the total ESR to one-quarter that exhibited by eaeh. I will estimate the zero to be at 10 KHz. 

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