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Principles and practice of agricultural analysis. Volume 3 (of 3), Agricultural products cover

Principles and practice of agricultural analysis. Volume 3 (of 3), Agricultural products

Chapter 55: FERMENTED BEVERAGES.
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About This Book

A practical laboratory manual that presents methods for sampling, drying, incinerating, and extracting organic agricultural materials and for analyzing their constituents. It surveys physical and chemical techniques used to determine carbohydrates—including density measurements, polarimetric and reducing-sugar assays—and addresses starch hydrolysis, oils and fats, and analyses of dairy and animal products. The text emphasizes sample preparation, apparatus design, procedural variations, sources of error, and calculation steps, supplying illustrated guidance and adaptable procedures to help analysts and students perform accurate compositional determinations.

Fig. 122.
Apparatus for Smoking.

In applying the test to the leaf it is important that the ignition be made with a fuse without flame, which maintains a uniform burning power. Any good slow burning fuse may be used and it is applied to the leaf in such a way that a hole may be burned in it, leaving its edges uniformly ignited. The number of seconds elapsing before the last spark is extinguished is noted. At the Connecticut Experiment Station a lighter, proposed by Nessler, is employed. It is prepared by digesting eighty grams of gum arabic in 120 cubic centimeters, and forty grams of gum tragacanth in a quarter of a liter of water for two days, mixing the mucilaginous masses and adding ten grams of potassium nitrate and about 350 grams of pulverized charcoal. The mixture is rolled, on a plate sprinkled with charcoal, into sticks a few inches in length and of the diameter of a cigar and dried at a gentle heat. These fuses burn slowly and without smoke and are well suited for lighting tobacco leaves. Several tests, at least six, should be made with each leaf. Leaves having a uniform burning power should be used as comparators and the number of seconds they burn be designated by 100. It is important that all the samples to be tested be exposed for a day or two to the same atmosphere in order that they may have, as nearly as possible, the same content of moisture. The burning tests, when possible, should be made both before and after fermentation. As a rule fermentation improves the burning quality of second rate leaves, but has little effect on leaves of the first quality.

613. Artificial Smoker.—For the purpose of comparing the burning properties of cigars, or of leaves rolled into cigar form, the artificial smoking apparatus devised by Penfield and modified in this laboratory is employed.[630] The construction of the apparatus is shown in the accompanying figure.

The lighted cigar is set in the tube at the left, so that air entering the test-tube must pass through the cigar. The test-tube contains enough water to seal the end of the tube carrying the cigar, and is connected with the aspirator on the right by the T tube, as shown. An arm of the T dips just beneath the surface of the liquid in the cup in the center. Water flows in a slow stream into the aspirator through the tube at the extreme right, forcing the air out through the arm of the T until the siphon begins to act. While the water is voided through the long arm of the siphon, air enters through the cigar, the liquid rising in the T. The action of the apparatus is automatic and intermittent. When the cigar is about one-third burned, it is removed without disturbing the ash cone, and the latter examined and compared with other samples as a standard. The sealing liquid of the long arm of the T may be mercury or water. In case mercury be used, care must be taken not to immerse the open end of the T more than one millimeter therein.

FERMENTED BEVERAGES.

614. Description.—Among fermented beverages are included those drinks, containing alcohol, prepared by fermenting the sugars or starches of fruits, cereals or other agricultural products. Wine and beer, in their various forms, and cider are the chief members of this class of bodies. Koumiss, although a fermented beverage, is not included in this classification, having been noticed under dairy products. The large number of artificial drinks, made by mixing alcohol with fruit and synthesized essences, is also excluded, although the methods of analysis which are used may be applied also to them.

Fermented beverages containing less than two per cent of alcohol are usually regarded as non-intoxicating drinks. Beers are of several varieties, and the term includes lager beer, ale, porter and stout. Distilled liquors are obtained by separating the alcohols and other volatile matters from the products of fermentation by distillation. It is not practicable here to attempt a description of the methods of preparing fermented drinks. Special works on this branch of the subject are easy of access.[631]

615. Important Constituents.—Alcohol is the most important constituent of fermented beverages. The solid matters, commonly called extract, which are obtained on evaporation are composed of dextrins, sugars, organic acids, nitrogenous bodies and mineral matters affording ash on combustion. Of these the dextrins and sugars form the chief part and the proteid bodies nearly ten per cent in the case of beers made of malt and hops. In beers the bitter principles derived from hops, while not important by reason of quantity, are of the utmost consequence from a gustatory and hygienic point of view. The ash of fermented beverages varies with their nature, or with the character of the water used in making the mash. In the manufacture of beer, water containing a considerable proportion of gypsum is often used, and this substance is sometimes added in the course of manufacture, especially of wine. The presence of common salt in the ash in any notable quantity is evidence of the addition of this condiment, either to improve the taste of the beverage or to increase the thirst of the drinker. In cider the organic acids, especially malic, are of importance.

Glycerol is a product of fermentation and of the hydrolysis of the fats and oils in the substances fermented.

616. Specific Gravity.—In order to secure uniformity of expression, the specific gravity of fermented beverages is determined at about 15°.6, although that is a temperature much below the average found in American laboratories. The specific gravity may be determined by an alcoholometer, pyknometer or hydrostatic balance in harmony with the directions given in paragraphs 48-54 and 285. By reason of the extractive matters held in solution, fermented beverages are usually heavier than water, even if the content of alcohol be twenty per cent or more. On the other hand distilled liquors are lighter than water.

617. Determination of Alcohol.—The determination of the percentage of alcohol present in a solution is based on two general principles. On the one hand, and this is the base of the methods in common use, the alcohol is secured mixed only with water and its amount determined by ascertaining the specific gravity of the mixture. On the other hand the quantity of alcohol in a mixture may be determined by ascertaining the temperature of the vapors produced on boiling. This is the principle involved in the use of the ebullioscope. The latter method is not employed to any extent in this country.

Use of the Alcoholometer.—The alcoholometer usually employed is known by the name of Gay-Lussac, who first made practical use of it in the determination of alcohol. It is constructed in such a way as to read directly the volume of absolute alcohol contained in one hundred volumes of the liquid at a temperature of 15°.6. The instruments employed should be carefully calibrated and thoroughly cleaned by washing with absolute alcohol before use. The stem of the instrument must be kept free from any greasy substance, and this is secured by washing it with ether. After this last washing the analyst should be careful not to touch the stem of the instrument with his fingers. It is most convenient to make the determination exactly at 15°.6, but when made at other temperatures the reading of the instrument is corrected by tables which may be found in works especially devoted to the analysis of wines.[632]

In this country the alcoholometer is used to some extent, but the official method is based upon the determination of the specific gravity by an instrument constructed in every respect like the alcoholometer, but giving the specific gravity of the liquor at 15°.6 instead of its percentage by volume in alcohol. The reading of the instrument having been determined at a temperature of 15°.6, the corresponding percentage of alcohol by volume or by weight is taken directly from the table given further on.

Fig. 123. Metal Distilling Apparatus.

Methods of Distillation.—The metal apparatus employed in the laboratory of the Department of Agriculture, for the distillation of fermented beverages in order to determine the percentage of alcohol by the method given above, is shown in the accompanying figure. The apparatus consists of a retort of copper carried on supports in such a way as to permit an alcohol or bunsen lamp to be placed under it. It is connected with a block tin condenser and the distillate is received in a tall graduated cylinder placed under the condenser in such a way as to prevent the loss of any alcohol in the form of vapor. Exactly 300 cubic centimeters of the wine or fermented beverage are used for the distillation. Any acid which the wine contains is first saturated with calcium carbonate before placing in the retort. Exactly 100 cubic centimeters of distillate are collected and the volume of the distillate is completed to 300 cubic centimeters by the addition of recently distilled water.[633] The cylinder containing the distillate is brought to a temperature of 15°.6, the alcoholometer inserted and its reading taken with the usual precautions.

Official Method.—The alcoholometers employed in the official methods are calibrated to agree with those used by the officers of the Bureau of Internal Revenue. They are most conveniently constructed, carrying the thermometer scale in the same stem with that showing the specific gravity. It is highly important that the analyst assure himself of the exact calibration of the instrument before using it. Inasmuch as the volume of the distillate may not be suited in all cases to the use of a large alcoholometer, it is customary in this laboratory to determine the specific gravity by means of the hydrostatic balance, as described further on. Attention is also called to the fact that, in the official method, directions are not given to neutralize the free acid of the fermented beverage before the distillation. Since the Internal Revenue Bureau is concerned chiefly with the determination of alcohol in distilled liquors, this omission is of little consequence. Even in ordinary fermented beverages the percentage of volatile acids, (acetic etc.,) is so small as to make the error due to the failure to neutralize it of but little consequence. In order, however, to avoid every possibility of error, it is recommended that in all instances the free acids of the sample be neutralized before distillation. In this laboratory, the distillations are conducted in a glass apparatus shown in the accompanying figure. The manipulation is as follow:[634]

Fig. 124. Distilling Apparatus.

One hundred cubic centimeters of the liquor are placed in a flask of from 250 to 300 cubic centimeters capacity, fifty cubic centimeters of water added, the flask attached to a vertical condenser by means of a bent bulb tube, 100 cubic centimeters distilled and the specific gravity of the distillate determined. The distillate is also weighed, or its weight calculated from the specific gravity. The corresponding percentage of alcohol by weight is obtained from the appended table, and this figure multiplied by the weight of the distillate, and the result divided by the weight of the sample, gives the per cent of alcohol by weight contained therein.

The percentage of alcohol by volume of the liquor is the same as that of the distillate, and is obtained directly from the appended table.

In distilled liquors about thirty grams are diluted to 150 cubic centimeters, 100 cubic centimeters distilled and the per cent of alcohol by weight determined as above.

The percentage of alcohol by volume in the distillate is obtained from the appended table. This figure divided by the number expressing the volume in cubic centimeters of the liquor taken for the determination (calculated from the specific gravity), and the result multiplied by 100 gives the per cent of alcohol by volume in the original liquor.

618. Determining the Specific Gravity of the Distillate.—The specific gravity of the distillate may be determined by the pyknometer, alcoholometer, hydrostatic balance or in any accurate way. The volume of the distillate is not always large enough to be conveniently used with an alcoholometer, especially the large ones employed by the Bureau of Internal Revenue. In the laboratory of the Agricultural Department, it is customary to determine the density of the distillate by the hydrostatic balance shown in paragraph 285. The specific gravity is in each case determined at 15°.6, referred to water of the same temperature, or if at a different temperature calculated thereto.

619. Table for Use with Hydrostatic Plummet.—It is more convenient to determine the density of the alcoholic distillate at room temperature than to reduce it to the standard for which the plummet is graduated. In the case of a plummet which displaces exactly five grams, or multiple thereof, of distilled water at 15°.6, the corrections for temperatures between 12°.2 and 30° are found in the following table, prepared by Bigelow.[635]

If the weight of the alcoholic solution displaced be 4.96075 grams the apparent specific gravity 0.99215 and the temperature of observation 25°.4, the correction, which is additive, as given in the table is 0.00191 and the true specific gravity is 0.99406 and the percentage of alcohol by volume 4.08.

When the plummet does not exactly displace five grams of water at 15°.6, but nearly so, the table may still be used.

For example, suppose the weight of water displaced be 4.9868 instead of five grams. The apparent specific gravity of the water by this plummet is 0.99736 and the difference between this and the true specific gravity is 0.00264, which is a constant correction to be added to the specific gravity as determined in each case.

Correction Table for Specific Gravity.

Below 15°.6 Subtract; Above 15°.6 Add.

  Temp.     Correction.    Temp.     Correction.    Temp.     Correction. 
12.2 0.00047 18.2 0.00043 24.2 0.00163
12.4 0.00044 18.4 0.00046 24.4 0.00167
12.6 0.00042 18.6 0.00050 24.6 0.00172
12.8 0.00039 18.8 0.00053 24.8 0.00176
13.0 0.00037 19.0 0.00057 25.0 0.00181
13.2 0.00634 19.2 0.00061 25.2 0.00186
13.4 0.00032 19.4 0.00065 25.4 0.00191
13.6 0.00029 19.6 0.00068 25.6 0.00195
13.8 0.00027 19.8 0.00072 25.8 0.00200
14.0 0.00024 20.0 0.00076 26.0 0.00205
14.2 0.00021 20.2 0.00080 26.2 0.00210
14.4 0.00018 20.4 0.00084 26.4 0.00215
14.6 0.00015 20.6 0.00087 26.6 0.00220
14.8 0.00012 20.8 0.00091 26.8 0.00225
15.0 0.00009 21.0 0.00095 27.0 0.00230
15.2 0.00006 21.2 0.00099 27.2 0.00235
15.4 0.00003 21.4 0.00103 27.4 0.00240
15.6 0.00000 21.6 0.00107 27.6 0.00246
15.8 0.00003 21.8 0.00111 27.8 0.00251
16.0 0.00006 22.0 0.00115 28.0 0.00256
16.2 0.00009 22.2 0.00119 28.2 0.00261
16.4 0.00012 22.4 0.00123 28.4 0.00267
16.6 0.00016 22.6 0.00128 28.6 0.00272
16.8 0.00019 22.8 0.00132 28.8 0.00278
17.0 0.00022 23.0 0.00136 29.0 0.00283
17.2 0.00025 23.2 0.00140 29.2 0.00288
17.4 0.00029 23.4 0.00145 29.4 0.00294
17.6 0.00032 23.6 0.00149 29.6 0.00299
17.8 0.00036 23.8 0.00154 29.8 0.00306
18.0 0.00039 24.0 0.00158 30.0 0.00311

The table is only accurate when the distillate does not contain over seven nor less than three per cent of alcohol. If the distillate contain more than seven per cent of alcohol it is diluted and the compensating correction made.

620. Calculating Results.—The specific gravity of the alcoholic distillate having been determined by any approved method and corrected to a temperature of 15°.6, the corresponding per cents of alcohol by volume and by weight are found by consulting the following table.[636] If, for example, the corrected specific gravity be exactly that given in any figure of the table the corresponding per cents are directly read. If the specific gravity found fall between two numbers in the table the corresponding per cents are determined by interpolation.

Table Showing Percentage of Alcohol
by Weight and by Volume.

Specific
gravity at
  15°.6./15°.6.  
Per cent
alcohol
  by volume.  
Per cent
alcohol
  by weight.  
1.00000 0.00 0.00
0.99992 .05 .04
984 .10 .08
976 .15 .12
968 .20 .16
961 .25 .20
953 .30 .24
945 .35 .28
937 .40 .32
930 .45 .36
.99923 0.50 0.40
915 .55 .44
907 .60 .48
900 .65 .52
892 .70 .56
884 .75 .60
877 .80 .64
869 .85 .67
861 .90 .71
854 .95 .75
.99849 1.00 0.79
842 .05 .83
834 .10 .87
827 .15 .91
819 .20 .95
812 .25 .99
805 .30 1.03
797 .35 .07
790 .40 .11
782 .45 .15
.99775 1.50 1.19
768 .55 .23
760 .60 .27
753 .65 .31
745 .70 .35
738 .75 .39
731 .80 .43
723 .85 .47
716 .90 .51
708 .95 .55
.99701 2.00 1.59
694 .05 .63
687 .10 .67
679 .15 .71
672 .20 .75
665 .25 .79
658 .30 .83
651 .35 .87
643 .40 .91
636 .45 .95
0.99629 2.50 1.99
622 .55 2.03
615 .60 .07
607 .65 .11
600 .70 .15
593 .75 .19
586 .80 .23
579 .85 .27
571 .90 .31
564 .95 .35
.99557 3.00 2.39
550 .05 .43
543 .10 .47
536 .15 .51
529 .20 .55
522 .25 .59
515 .30 .64
508 .35 .68
501 .40 .72
494 .45 .76
.99487 3.50 2.80
480 .55 .84
473 .60 .88
466 .65 .92
459 .70 .96
452 .75 3.00
445 .80 .04
438 .85 .08
431 .90 .12
424 .95 .16
.99417 4.00 3.20
410 .05 .24
403 .10 .28
397 .15 .32
390 .20 .36
383 .25 .40
376 .30 .44
369 .35 .48
363 .40 .52
356 .45 .56
.99349 4.50 3.60
342 .55 .64
335 .60 .68
329 .65 .72
322 .70 .76
315 .75 .80
308 .80 .84
301 .85 .88
295 .90 .92
288 .95 .96
0.99281 5.00 4.00
274 .05 .04
268 .10 .08
261 .15 .12
255 .20 .16
248 .25 .20
241 .30 .24
235 .35 .28
228 .40 .32
222 .45 .36
.99215 5.50 4.40
208 .55 .44
202 .60 .48
195 .65 .52
189 .70 .56
182 .75 .60
175 .80 .64
169 .85 .68
162 .90 .72
156 .95 .76
.99149 6.00 4.80
143 .05 .84
136 .10 .87
130 .15 .92
123 .20 .96
117 .25 5.00
111 .30 .05
104 .35 .09
098 .40 .13
091 .45 .17
.99085 6.50 5.21
079 .55 .25
072 .60 .29
066 .65 .33
059 .70 .37
053 .75 .41
047 .80 .45
040 .85 .49
034 .90 .53
027 .95 .57
.99021 7.00 5.61
015 .05 .65
009 .10 .69
002 .15 .73
.98996 .20 .77
990 .25 .81
984 .30 .86
978 .35 .90
971 .40 .94
965 .45 .98
0.98959 7.50 6.02
953 .55 .06
947 .60 .10
940 .65 .14
934 .70 .18
928 .75 .22
922 .80 .26
916 .85 .30
909 .90 .34
903 .95 .38
.98897 8.00 6.42
891 .05 .46
885 .10 .50
879 .15 .54
873 .20 .58
867 .25 .62
861 .30 .67
855 .35 .71
849 .40 .75
843 .45 .79
.98837 8.50 6.83
831 .55 .87
825 .60 .91
819 .65 .95
813 .70 .99
807 .75 7.03
801 .80 .07
795 .85 .11
789 .90 .15
783 .95 .19
.98777 9.00 7.23
771 .05 .27
765 .10 .31
754 .20 .39
748 .25 .43
742 .30 .48
736 .35 .52
724 .45 .60
.98719 9.50 7.64
713 .55 .68
707 .60 .72
701 .65 .76
695 .70 .80
689 .75 .84
683 .80 .88
678 .85 .92
672 .90 .96
666 .95 8.00
0.98660 10.00 8.04
654 .05 .08
649 .10 .12
643 .15 .16
637 .20 .20
632 .25 .24
626 .30 .28
620 .35 .33
614 .40 .37
609 .45 .41
.98603 10.50 8.45
597 .55 .49
592 .60 .53
586 .65 .57
580 .70 .61
575 .75 .65
569 .80 .70
563 .85 .74
557 .90 .78
552 .95 .82
.98546 11.00 8.86
540 .05 .90
535 .10 .94
529 .15 .98
524 .20 9.02
518 .25 .07
513 .30 .11
507 .35 .15
502 .40 .19
496 .45 .23
.98491 11.50 9.27
485 .55 .31
479 .60 .35
474 .65 .39
468 .70 .43
463 .75 .47
457 .80 .51
452 .85 .55
446 .90 .59
441 .95 .63
.98435 12.00 9.67
430 .05 .71
424 .10 .75
419 .15 .79
413 .20 .83
408 .25 .87
402 .30 .92
397 .35 .96
391 .40 10.00
386 .45 .04
0.98381 12.50 10.08
375 .55 .12
370 .60 .16
364 .65 .20
359 .70 .24
353 .75 .28
348 .80 .33
342 .85 .37
337 .90 .41
331 .95 .45
.98326 13.00 10.49
321 .05 .53
315 .10 .57
310 .15 .61
305 .20 .65
299 .25 .69
294 .30 .74
289 .35 .78
283 .40 .82
278 .45 .86
.98273 13.50 10.90
267 .55 .94
262 .60 .98
256 .65 11.02
251 .70 .06
246 .75 .14
240 .80 .15
235 .85 .19
230 .90 .23
224 .95 .27
.98219 14.00 11.31
214 .05 .35
209 .10 .39
203 .15 .43
198 .20 .47
193 .25 .52
188 .30 .56
182 .35 .60
177 .40 .64
172 .45 .68
.98167 14.50 11.72
161 .55 .76
156 .60 .80
151 .65 .84
146 .70 .88
140 .75 .93
135 .80 .97
130 .85 12.01
125 .90 .05
119 .95 .09
0.98114 15.00 12.13
108 .05 .17
104 .10 .21
099 .15 .25
093 .20 .29
088 .25 .33
083 .30 .38
078 .35 .42
073 .40 .46
068 .45 .50
.98063 15.50 12.54
057 .55 .58
052 .60 .62
047 .65 .66
042 .70 .70
037 .75 .75
032 .80 .79
026 .85 .83
021 .90 .87
016 .95 .91
.98011 16.00 12.95
005 .05 .99
001 .10 13.03
.97996 .15 .08
991 .20 .12
986 .25 .16
980 .30 .20
975 .35 .24
970 .40 .29
965 .45 .33
.97960 16.50 13.37
955 .55 .41
950 .60 .45
945 .65 .49
940 .70 .53
935 .75 .57
929 .80 .62
924 .85 .66
919 .90 .70
914 .95 .74
.97909 17.00 13.78
904 .05 .82
899 .10 .86
894 .15 .90
889 .20 .94
884 .25 .98
879 .30 14.03
874 .35 .07
869 .40 .11
864 .45 .15
0.97859 17.50 14.19
853 .55 .23
848 .60 .27
843 .65 .31
838 .70 .35
833 .75 .40
828 .80 .44
823 .85 .48
818 .90 .52
813 .95 .56
.97808 18.00 14.60
803 .05 .64
798 .10 .68
793 .15 .73
788 .20 .77
783 .25 .81
778 .30 .85
773 .35 .89
768 .40 .94
763 .45 .98
.97758 18.50 15.02
753 .55 .06
748 .60 .10
743 .65 .14
738 .70 .18
733 .75 .22
728 .80 .27
723 .85 .31
718 .90 .35
713 .95 .39
.97708 19.00 15.43
703 .05 .47
698 .10 .51
693 .15 .55
688 .20 .59
683 .25 .63
678 .30 .68
673 .35 .72
668 .40 .76
663 .45 .80
.97658 19.50 15.84
653 .55 .88
648 .60 .93
643 .65 .97
638 .70 16.01
633 .75 .05
628 .80 .09
623 .85 .14
618 .90 .18
613 .95 .22
0.97608 20.00 16.26
603 .05 .30
598 .10 .34
593 .15 .38
588 .20 .42
583 .25 .46
578 .30 .51
573 .35 .58
568 .40 .59
563 .45 .63
.97558 20.50 16.67
552 .55 .71
547 .60 .75
542 .65 .80
537 .70 .84
532 .75 .88
527 .80 .92
522 .85 .96
517 .90 17.01
512 .95 .05
.97507 21.00 17.09
502 .05 .13
497 .10 .17
492 .15 .22
487 .20 .26
482 .25 .30
477 .30 .34
472 .35 .38
467 .40 .43
462 .45 .47
.97457 21.50 17.51
451 .55 .55
446 .60 .59
441 .65 .63
436 .70 .67
431 .75 .71
426 .80 .76
421 .85 .80
416 .90 .84
411 .95 .88
.97406 22.00 17.92
401 .05 .96
396 .10 18.00
391 .15 .05
386 .20 .09
381 .25 .13
375 .30 .17
370 .35 .21
365 .40 .26
360 .45 .30
0.97355 22.50 18.34
350 .55 .38
345 .60 .42
340 .65 .47
335 .70 .51
330 .75 .55
324 .80 .59
319 .85 .63
314 .90 .68
309 .95 .72
.97304 23.00 18.76
299 .05 .80
294 .10 .84
289 .15 .88
283 .20 .92
278 .25 .96
273 .30 19.01
268 .35 .05
263 .40 .09
258 .45 .13
.97253 23.50 19.17
247 .55 .21
242 .60 .25
237 .65 .30
232 .70 .34
227 .75 .38
222 .80 .42
216 .85 .46
211 .90 .51
206 .95 .55
.97201 24.00 19.59
196 .05 .63
191 .10 .67
185 .15 .72
180 .20 .76
175 .25 .80
170 .30 .84
165 .35 .88
159 .40 .93
154 .45 .97
.97149 24.50 20.01
144 .55 .05
139 .60 .09
133 .65 .14
128 .70 .18
123 .75 .22
118 .80 .26
113 .85 .30
107 .90 .35
102 .95 .39
0.97097 25.00 20.43
092 .05 .47
086 .10 .51
081 .15 .56
076 .20 .60
071 .25 .64
065 .30 .68
060 .35 .72
055 .40 .77
049 .45 .81
.97014 25.50 20.85
039 .55 .89
033 .60 .93
028 .65 .98
023 .70 21.02
018 .75 .06
012 .80 .10
007 .85 .14
001 .90 .19
.96996 .95 .23
.96991 26.00 21.27
986 .05 .31
980 .10 .35
975 .15 .40
969 .20 .44
964 .25 .48
959 .30 .52
953 .35 .56
949 .40 .61
942 .45 .65
.96937 26.50 21.69
932 .55 .73
926 .60 .77
921 .65 .82
915 .70 .86
910 .75 .90
905 .80 .94
899 .85 .98
894 .90 22.03
888 .95 .07
.96883 27.00 22.11
877 .05 .15
872 .10 .20
866 .15 .24
861 .20 .28
855 .25 .33
850 .30 .37
844 .35 .41
839 .40 .45
833 .45 .50
0.96828 27.50 22.54
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