1/iBRARY OF THE UNIVERSITY: OF ILLINOIS' G30.7 UGb cop - 2. AGRICULTURE NOTICE: Return or renew all Library Materials! The Minimum Fee for each Lost Book is $50.00. The person charging this material is responsible for its return to the library from which it was withdrawn on or before the Latest Date stamped below. Theft, mutilation, and underlining of books are reasons for discipli- nary action and may result in dismissal from the University. To renew call Telephone Center, 333-8400 UNIVERSITY OF ILLINOIS LIBRARY AT URBANA-CHAMPAIGN LI61 O-1096 UNIVERSITY OF ILLINOIS Agricultural Experiment Station BULLETIN No. 282 THE ENERGY VALUE OF MILK AS RELATED TO COMPOSITION Formulas for the Computation of the Energy BY 0. R. OVERMAN AND F. P. SANMANN URBANA, ILLINOIS, DECEMBER, 1926 CONTENTS PAGES EXPERIMENTAL PART 207-208 STATISTICAL PART 212-214 APPLICATION 215-218 CONCLUSIONS 218 LITERATURE CITED. . . .218-219 THE ENERGY VALUE OF MILK AS RELATED TO COMPOSITION Formulas for the Computation of the Energy BY O. R. OVERMAN, Assistant Chief in Dairy Chemistry, and F. P. SANMANN, Associate in Dairy Manufactures A knowledge of the energy value a of milk or the number of calories of heat which can be produced by the complete combustion of a given quantity of milk is of interest and value both to students of human nutrition and to those of animal nutrition. Formulas have been devel- oped for the computation of this value. Gaines and Davidson, 1 work- ing from data compiled by Stocking and Brew, 2 have derived the form- ula E = 49.64 (2.66 + i), in which E is the energy of milk solids and t is the percentage of fat. This formula, which gives the energy value per pound of milk, is based on average analyses, and was used in esti- mating the energy yield of cows. Frederiksen 3 reports that Director A. C. Andersen gives the heat of combustion of milk to be equal to (percentage of fat X 113.5) + 290 calories per kilogram. The present investigation was begun for the purpose of determining the energy values of milks of different composition, and of comparing such determined values with corresponding energy values as computed from the composition of the milk. As the work progressed, the possi- bility of applying statistical methods to these results, for the purpose of deriving formulas by which the energy value of milk might be computed from its composition, was recognized. This treatment of the data resulted in the derivation of formulas based, first, upon the complete analysis of the milk; second, on the fat, protein, and lactose content; and third, on the fat alone. The details of the statistical methods by which these formulas were derived, and a discussion of the application of the formulas, are presented in the following pages. EXPERIMENTAL PART The milks studied were obtained from the purebred and experi- mental herds of the Dairy Department of the University of Illinois. "Where the terms energy value or calorie are used it is to be understood that the large calorie is the unit of heat involved. 207 208 BULLETIN No. 282 [December, The samples represent milk from Ayrshire, Guernsey, Holstein, and Jersey cows, and from cows in the Guernsey-Holstein crossbred experi- mental herd. At the beginning of the work a few samples were taken from single milkings of individual cows. Later, each sample was a com- posite made from all the milk produced by one cow during three days. Samples were taken at all stages during the normal lactation periods of the cows. The samples were preserved with formaldehyde, added in ap- proximately the proportions recommended by Palmer, 4 and were kept in half-gallon glass fruit jars fitted with glass lids and rubber rings. Determinations of percentages of fat, total protein, lactose, and total solids, and for specific gravity and energy value, were made for all samples studied. The specific gravity was determined with a specific-gravity balance of the chainomatic type. The percentage of fat was determined by the Roese-Gottlieb method, using about 5 grams of the sample. Total protein was determined by the Official Kjeldahl method. Lactose was determined by the Official Optical method, mercuric nitrate being used as the precipitant. A Schmidt-Haensch saccharimeter was used for all polarizations. Total solids were determined by the Official method. A Parr adiabatic oxygen-bomb calorimeter was used for all determinations of energy value. The water equivalent of the calorimeter was carefully determined by several combustions of weighed quantities of pure benzoic acid. About 10 grams of the milk sample were accurately weighed into an Illium combustion capsule and dried on a water bath. The dried samples were kept in a desiccator until the combustion could be made. Combustions were made in oxygen under a pressure of 25 to 30 atmos- pheres. Temperature changes were read to thousandths of a degree centigrade on a standardized Beckmann thermometer. The rise in temperature was corrected in every case for stem emergence and for the setting of the Beckmann thermometer. The total energy change in the combustion was then computed by multiplying the rise in temperature in degrees by the water equivalent of the calorimeter. This value was then corrected for the heat liberated by the combustion of the iron fuse wire and the heat liberated in the formation of nitric acid during the com- bustion. A total of 212 samples of milk were so studied. All analytical results are tabulated in the first six columns of Table 1, arranged down the column in the order of increasing fat percentages. These results in each case are the means of closely corresponding duplicate determinations. 1926} THE ENERGY VALUE OF MILK 209 TABLE 1. ANALYSES OF 212 MILK SAMPLES WITH COMPUTED AND DETERMINED ENERGY VALUES Calories per quart Fat Pro- Lactose Total solids Specific Computed gravi y Deter- mined Meta- Form- Form- Form- Form- Total boliz- ula ula ula ula A B C D E F able 1 2 3 4 perct. perct. perct. perct. cals. cals. 2.68 2.93 4.72 10.96 1.0298 580.4 585.8 533.3 582.2 582.4 536.8 583.6 2.72 3.27 3.92 10.58 1.0291 565.8 577.1 518.5 577.7 586.9 541.0 584.3 2.76 2.86 4.89 11.13 1.0310 589.2 596.3 544.8 591.3 591.5 545.2 591.6 2.82 2.72 5.05 11.07 1.0312 585.3 600.3 541.2 589.5 598.3 551.5 593.7 2.85 2.91 4.81 11.04 1.0317 591.1 604.6 551.9 593.7 601.7 554.7 600.3 2.86 2.66 4.78 11.18 1.0301 592.0 589.5 541.0 595.5 602.8 555.8 586.9 2.94 3.10 4.60 11.48 1.0319 618.9 615.3 559.2 618.8 611.9 564.2 613.2 2.94 3.18 4.82 11.55 1 . 0329 622.6 628.8 571.4 622.3 611.9 564.2 623.4 2.94 2.92 4.46 11.10 1.0310 607.3 599.4 .546.2 601.8 611.9 564.2 599.7 2.94 3.03 4.80 11.20 1.0306 602.9 618.4 563.5 606.5 611.9 564.2 614.8 2.96 3.06 4.70 11.15 1.0316 604.8 618.6 563.1 606.5 614.2 566.3 615.5 2.98 2.88 4.48 11.09 1.0316 603.0 601.9 549.3 602.9 616.5 568.4 601.7 2.98 3.02 4.84 11.37 1.0321 606.6 623.8 569.1 614.8 616.5 568.4 618.9 2.99 2.82 4.71 11.08 1.0310 595.0 607.9 556.4 601.4 617.6 569.4 605.5 2.99 2.94 4.62 11.25 1.0313 606.2 611.3 557.8 610.1 617.6 569.4 609.6 3.01 2.97 5.16 11.71 1.0318 625.2 635.9 582.1 627.6 619.9 571.6 627.5 3.02 2.97 4.75 11.48 1.0319 623.8 621.1 567.0 620.5 621.0 572.6 617.4 3.04 3.13 4.84 11.56 1.0317 614.0 635.1 578.4 627.0 623.3 574.7 630.3 3.04 3.16 5.01 11.90 1.0325 638.1 644.0 586.7 639.9 623.3 574.7 636.5 3.04 3.18 4.92 11.76 1.0326 639.0 641.5 585.7 635.2 623.3 574.7 635.2 3.06 3.15 5.11 12.23 1 . 0353 659.7 650.7 593.5 653.2 625.6 576.8 640.4 3.08 2.87 5.21 11.68 1.0318 624.4 638.6 586.3 628.4 627.9 578.9 629.7 3.09 2.91 4.96 11.66 1 . 0324 630.9 632.4 579.3 629.5 629.0 580.0 626.1 3.10 2.92 5.03 11.50 1 . 0308 621.4 635.5 582.4 623.9 630.1 581.0 629.4 3.10 3.00 4.96 11.88 1.0325 643.4 638.4 583.7 639.8 630.1 581.0 631.9 3.12 2.88 5.10 11.79 1.0321 653.7 638.9 586.0 635.1 632.4 583.1 631.0 3.12 3.12 4.93 11.70 1.0333 634.4 646.3 589.5 636.2 632.4 583.1 639.4 3.14 2.90 4.75 11.49 1.0316 633.0 627.7 574.6 626.1 634.7 585.2 624.5 3.14 2.91 4.64 11.39 1.0314 631.1 624.0 570.6 622.7 634.7 585.2 622.1 3.16 2.98 5.08 11.56 1.0312 623.8 646.5 592.2 630.2 637.0 587.3 639.5 3.17 3.11 4.48 11.72 1.0313 635.8 631.6 574.8 640.5 638.1 588.4 631.4 3.18 2.89 4.85 11.55 1 . 0298 628.6 633.6 580.6 629.9 639.2 589.4 630.3 3.18 3.03 5.02 11.82 1.0312 634.2 648.8 593.5 642.1 639.2 589.4 642.4 3.18 3.11 4.88 11.74 1 . 0329 637.4 649.0 592.2 640.8 639.2 589. 4 643.0 3.19 3.05 4.74 11.63 1 . 0302 632.8 639.4 583.7 636.4 640.4 590.5 636.9 3.20 2.88 4.84 11.42 1 . 0294 625.1 634.2 581.4 625.9 641.5 591.6 631.3 3.20 3.26 4.78 11.80 1 . 0327 644.7 655.1 595.8 646.9 641.5 591.6 650.3 3.22 3.00 4.74 11.77 1.0313 638.7 641.9 587.0 642.4 643.8 593.7 636.9 3.22 3.18 4.48 11.70 1.0315 651.3 639.4 582.0 643.6 643.8 593.7 639.7 3.25 2.83 5.18 11.96 1.0317 646.3 650.5 598.4 647.4 647.2 596.8 642.2 3.29 3.00 4.94 11.94 1.0310 647.4 653.8 598.8 652.1 651.7 601.0 648.6 3.32 3.09 5.17 12.30 1.0323 667.8 671.2 614.7 668.2 655.1 604.2 662.4 3.35 2.88 5.26 12.01 1.0319 652.1 665.4 612.4 655.1 658.6 607.3 656.1 3.37 3.20 5.03 12.14 1.0317 671.3 676.1 617 6 667.0 660.8 609.5 669.1 3.39 3.07 4.69 11.68 1.0315 652.8 657.4 600.8 649.4 663.1 611.6 654.8 3.41 2.90 5.24 12.17 1 . 0329 669.6 671.8 61S.3 664.8 665.4 613.7 662.1 3.42 3.11 4.94 11.90 1 . 0322 670.0 672.5 615.2 659.3 666.5 614.7 666.4 3.42 3.38 4.83 12.34 1.0316 682.7 682.8 621.1 680.7 666 5 614.7 678.1 3.43 3.13 5.27 12.64 1 . 0327 693.1 687.5 630.1 687.3 667.7 615.8 C77.2 3.45 3.06 4.58 11.66 1.0314 653.3 658.0 601.4 652.0 670.0 617.9 656.7 3.46 3.14 5.15 12.24 1.0318 679.9 685.6 627.9 674.2 671.1 618.9 677.2 3.47 3.48 4.77 12.37 1 . 0322 684.1 691.0 627.4 686.3 672.2 620.0 686.4 3.49 3.02 4.98 12.32 .0322 678.1 675.3 619.4 677.3 674.5 622.1 668.9 3.50 3.10 4.87 12.04 .0310 671.7 675.6 618.4 668.8 675.6 623.1 671.2 3.50 3.64 5.26 12.87 .0351 704.0 723.6 657.3 708.2 675.6 623.1 710.9 3.51 2.98 5.14 12.26 .0319 676.3 680.8 635.4 675.0 676.8 624.2 672.8 3.52 2.90 5.26 12.22 .0320 670.1 682.0 628.2 672.4 677.9 625 2 672.6 3.52 3.01 4.86 12.10 .0333 676.1 673.5 617.6 670.8 677.9 625.2 667.9 3.52 3.12 4.90 12.10 .0322 673.0 680.5 622.8 672.5 677.9 625.2 674.9 3.56 2.94 5.21 12.20 .0312 676.3 685.4 630.8 674.5 682.4 629.5 677.0 3.56 3.55 5.16 12.97 .0338 703.4 719.2 654.3 713.9 682.4 629.5 708.8 3.58 3.22 5.14 12.58 .0325 694.4 700.9 641.6 694.8 684.7 631.6 692.2 3.59 3.10 5.39 12.72 1 . 0326 703.4 704.9 647 6 698.0 685.9 632.6 693.3 3.60 3.05 4.82 12.24 1.0308 677.8 679.7 623.2 681 687.0 633.7 676.2 3.60 3.08 5.05 12.16 1.0310 678.4 690.4 633.4 677.8 687.0 633.7 684.0 3.60 3.52 4.73 12.57 1.0331 698.3 704.0 639.4 701.5 687.0 633.7 699.3 3.61 3.12 5.31 12.66 1 . 0322 697.2 704.4 646.8 697.3 688.1 634.7 694.0 210 BULLETIN No. 282 [December, TABLE 1. ANALYSES OF 212 MILK SAMPLES WITH COMPUTED AND DETERMINED ENERGY VALUES (Continued) Calories per quart Fat Pro- Lactose Total Specific Computed VG1D SOllGS gravity Deter- mined Meta- Form- Form- Form- Form- Total boliz- ula ula ula ula A B C D E F able 1 2 3 4 perct. perct. perct. perct. cals. cals. 3.62 2.93 5.10 12.18 1 . 0324 692.8 686.7 632.1 677.1 689.3 635.8 679.0 3.62 3.25 5.24 12.51 1 . 0325 696.3 710.1 650.2 694.5 689.3 635.8 700.1 3.64 3.06 4.50 12.06 1 . 0308 675.6 671.5 614.8 677.3 691.5 637.9 671.8 3.64 3.14 4.83 12.10 1 . 0333 674.4 690.5 632.1 679.4 691.5 637. S 685.0 3.64 3.62 5.16 12.84 1.0348 708.6 731.0 664.7 714.4 691.5 637.9 719.9 3.68 3.08 4.56 11.85 1.0313 649.1 679.0 621.5 671.7 696.1 642.1 678.1 3.70 3.00 4.99 12.16 1.0329 684.1 694.0 637.9 682.0 698.4 644.2 687.1 3.70 3.50 4.81 12.77 1 . 0322 711.9 714.5 650.0 713.8 698.4 644.2 709.4 3.71 2.84 5.34 12.33 1 . 0328 689.6 699.3 646.2 685.4 699.5 645.3 688.7 3.71 3.23 4.79 12.48 1 . 0328 699.8 699.9 639.9 699.0 699.5 645.3 695.2 3.72 3.08 4.85 12.29 1.0317 681.9 694.6 636.6 689.7 700.6 646.3 689.5 3.72 3.11 5.02 12.36 1.03H 693.6 702.0 644.2 692.9 700.6 646.3 695.7 3.75 3.17 4.99 12.38 1 . 0308 695.5 706 . 5 647.6 695.7 704.1 649.5 700.9 3.77 2.99 4.95 12.40 1.0324 700.8 697.8 641.8 694.8 706.3 651.6 691.8 3.78 3.10 4.50 12.12 1.0310 683.1 686.6 628.5 687.7 707.5 652.6 686.7 3.80 3.15 4.76 12.32 1 . 0329 693.9 702.4 643.6 696.5 709.7 654.7 698.2 3.82 2.79 5.02 12.20 1.0331 681.8 694.4 641.6 686.4 712.0 656.8 687.4 3.86 3.02 4.50 12.28 1.0311 691.8 689.4 632.5 696.6 716.6 661.0 689.6 3.86 3.36 5.41 13.21 1 . 0338 731.5 745.3 683.1 735.0 716.6 661.0 732.4 3.89 3.42 4.74 12.70 1.0314 718.2 723.9 660.3 720.0 720.0 664.2 720.4 3.89 3.64 5.07 13.06 1.0336 738.9 750.4 683.2 736.5 720.0 664.2 741.2 3.91 3.43 5.24 13.23 1 . 0332 739.5 746.7 683.2 740.0 722.3 666.3 736.2 3.92 2.99 4.42 12.24 1 . 0308 694.6 689.8 633.3 698.0 723.4 667.4 691.3 3.93 3.14 5.16 12.96 1.0342 724.5 730.0 671.1 726.4 724.5 668.4 720.1 3 94 3.37 5.02 12.78 1 . 0329 718.2 737.4 674.7 724.2 725.7 669.5 729.8 3.96 3.47 4.01 12.24 1.0314 698.4 704.7 639.9 709.1 727.9 671.6 710.0 3.97 3.71 5.15 13.36 1.0351 754.8 765.7 697.2 753.1 729.1 672.6 754.4 3.98 3.00 4.88 12.36 1.0313 706.4 713.8 657.2 704.6 730.0 673.7 709.6 3.98 3.16 4.88 12.49 1.0331 708.1 724.1 664.6 712.3 730.0 673.7 718.2 3.99 3.57 4.58 12.83 1.0314 727.4 735.0 668.7 733.1 731.4 674.7 733.4 4.02 3.29 5.22 13.26 1.0339 745.5 748.6* 687.1 744.8 734.8 677.9 738.0 4.02 3.66 4.50 12.84 1.0318 723.7 740.0 672.0 736.8 734.8 677.9 738.8 4.04 3.62 5.44 13.54 1.0355 760.1 778.6 711.5 761.3 737.0 680.0 763.6 4.05 3.41 5.12 13.26 1.0328 751.4 753.4 689.8 748.5 738.2 681.0 744.6 4.07 4.32 4.98 13.97 1 . 0365 790.5 803.4 724.2 792.0 740.4 683.2 792.0 4.08 3.34 5.17 13.17 1.0319 743.9 753.4 691.0 745.4 741.6 684.2 744.8 4.09 3.05 5.17 12.84 1 . 0306 725.0 737.2 679.7 728.6 742.7 685.3 730.0 4.10 3.74 4.71 13.06 1 . 0308 749.4 758.9 689.7 750.1 743.9 686.3 756.1 4.12 3.41 3.96 12.14 1.0306 711.0 713.3 649.2 712.9 746.1 688.4 719.9 4.13 3.16 5.18 12.95 1.0330 738.6 749.0 689.5 736.8 747.3 689.5 739.9 4.16 3.06 5.01 12.84 1.0312 726.7 738.4 680.4 732.9 750.7 692.6 732.6 4.16 3.34 4.84 12.99 1.0317 748.6 747.8 685.0 743.7 750.7 692.6 743.3 4.16 3.36 5.36 13.42 1.0336 757.4 770.3 707.4 759.0 750.7 692.6 758.2 4.17 3.67 5.07 13.36 1.0335 765.9 777.3 709.0 763.1 751.8 693.7 768.2 4.18 3.70 4.76 13.47 1.0322 773.0 766.9 699.0 769.1 753.0 694.7 762.5 4.20 3.21 5.07 13.30 1 . 0332 753.4 754.1 693.4 754.8 755.2 696.8 746.0 4.25 3.62 5.46 13.80 1.0341 792.1 797.2 729.8 782.1 760.9 702.1 783.2 4.28 3.71 4.99 13.66 1.0341 782.0 786.8 717.5 781.2 764.3 705.3 778.2 4.32 3.39 4.68 13.19 1 . 0328 743.7 759.6 695.5 761.0 768.9 709.5 756.2 4.32 4.08 4.81 13 96 1 . 0338 799.9 803.9 728.3 801.2 768.9 709.5 797.1 4.38 3.14 4.94 12.92 1.0328 748.4 761.1 701.2 749.1 775.7 715.8 755.0 4.38 3.76 4.91 13.70 1 . 0327 792.6 794.5 724.2 788.9 775.7 715.8 787.9 4.39 3.71 5.41 14.06 1.0350 803.4 813.7 743.1 801.0 776.8 716.8 799.4 4.41 3.22 5.18 13.35 1.0325 762.8 777.3 716.1 767.7 779.1 719.0 768.5 4.41 3.68 5.10 13.91 1 . 0334 797.0 800.6 731.6 796.7 779.1 719.0 791.3 4.42 3.24 5.29 13.55 1 . 0324 779.7 783.5 722.0 775.8 780.3 720.0 773.4 4.42 3.29 5.01 13.31 1.0311 768.7 774.5 712.1 768.2 780.3 720.0 768.7 4.45 3.72 4.78 13.74 1 . 0326 794.8 793.5 723.6 793.8 783.7 723.2 788.6 4.46 3.36 4.86 13.32 1.0312 760.8 776.3 712.6 772.3 784.8 724.2 772.1 4.46 3.50 5.06 13.78 1.0338 792.7 793.8 727.7 791.6 784.8 724.2 785.0 4.47 3.94 4.77 13.90 1 0328 807.3 807.3 733.7 804.6 785.9 725.3 802.1 4.48 3.48 5.32 13.70 1 . 0336 791.0 804.4 738.7 788.5 787.1 726.3 792.7 4.50 3.32 5.28 13.50 1 . 0337 775.2 795.0 731.9 779.6 789.4 728.4 784.2 4.52 3.22 4.41 12.94 1.0311 756.8 756.5 694.8 760.0 791.6 730.5 757.9 4.52 3.33 4.82 13.38 1.0315 773.8 778.7 715.3 777.3 791.6 730.5 774.8 4.52 3.40 5.00 13.35 1.0313 767.4 789 4 725.0 776.9 791.6 730.5 783.4 4.53 3.56 5.24 13.84 1 . 0334 798.1 810.1 743.0 798.0 792.8 731.6 799.4 1926} THE ENERGY VALUE OF MILK 211 TABLE 1. ANALYSES OP 212 MILK SAMPLES WITH COMPUTED AND DETERMINED ENERGY VALUES (Continued) Calories per quart Fat Pro- t ci 11 Lactose Total solids Specific Computed gravi y Deter- mined Meta- Form- Form- Form- Form- Total boliz- ula ula ula ula A B C D E F able 1 2 3 4 perct. perct. perct. perct. cals. rah. 4.55 3.85 4 92 13.87 1.0340 803.6 816.2 744.0 805.9 795.0 733.7 808.4 4.55 3.97 5.38 14.69 1.0355 845.7 842.0 767.8 837.8 795.0 733.7 827.2 4.58 3.80 4.96 13.82 1.0325 807.3 816.5 745.2 804.5 798.5 736.9 809.5 4.60 3.41 3.91 12.71 1 . 0307 747.7 754.7 689.4 760.0 800.7 739.0 762.1 4.62 2.96 4.60 13.03 1.0322 769.1 759.1 701.6 763.9 803.0 741.1 757.9 4.63 3.54 5.26 14.06 1 . 0337 809.8 819.1 752.0 811.2 804.1 742.1 808.0 4.64 3.36 5.41 14.18 1.0331 812.8 815.2 751.3 812.9 805.3 743.2 803.1 4.65 3.80 4.62 13.73 1.0313 807.8 808.8 737.2 805.7 806.4 744.2 806.8 4.67 3.68 3.64 12.83 1 . 0297 773.0 764.9 694.9 773.3 807.7 746.3 775.9 4.68 3.80 4.69 14.09 1.0304 827.3 813.5 741.9 820.7 809.8 747.4 811.4 4.74 4.38 4.72 14.74 1.0344 858.3 855.6 773.9 858.1 816.7 753.7 849.1 4.74 4.04 5.02 14.47 1.0351 845.8 848.8 772.9 841.5 816.7 753.7 838.7 4.75 3.46 5.42 14.14 1.0338 821.7 831.7 765.8 818.9 817.8 754.7 818.8 4.76 4.08 5.02 14.41 1 . 0330 834.3 851.1 774.6 840.8 818.9 755.8 842.6 4.82 3.36 5.54 14.42 1 . 0320 842.3 835.6 771.4 831.1 825.7 762.1 822.9 4.87 3.91 4.59 14.19 1 . 0326 843.7 834.6 760.6 836.7 831.4 767.4 831.9 4.88 3.58 5.24 14.06 1 . 0332 822.5 842.6 774.4 825.1 832.6 768.4 832.3 4.88 3.70 5.24 14.20 1 . 0344 826.9 850.4 780.0 832.5 832.6 768.4 838.8 4.88 4.10 5.06 14.66 1 . 0346 856.8 864.9 788.8 856.9 832.6 768.4 855.7 4.94 3.54 5.59 14.58 1.0348 842.5 860.7 793.0 846.4 839.4 774.8 844.9 4.94 4.12 4.75 14.33 1 . 0340 842.6 859.9 782.2 848.8 839.4 774 8 853.9 4.96 3.23 5.08 13.78 1.0319 808.7 823.1 760.5 813.4 841.7 776.9 816.2 4.96 3.93 4.88 14.58 1.0338 860.4 856.1 781.5 855.8 841.7 776.9 848.9 4.97 3.48 5.37 14.30 1.0329 836.7 850.0 783.3 837.0 842.8 777.9 838.5 4.98 4.26 5.08 14.83 1 . 0358 874.7 885.7 805.6 871.3 843.9 779.0 874.0 5.05 4.09 4.76 14.51 1.0331 856.4 867.9 790.5 860.8 851.9 785.3 862.5 5.07 3.84 4.79 14.38 1 . 0330 853.9 856.8 783.5 852.8 854.2 788.4 851.6 5.07 4.04 5.09 14.60 1.0334 868.9 880.7 804.2 863.6 854.2 788.4 870.4 5.10 4.01 4.89 14.76 1.0337 872.9 873.5 797.3 871.3 857.6 791.6 866.2 5.10 4.02 4.86 14.61 1 . 0328 871.6 872.0 795.8 865.8 857.6 791.6 865.9 5.11 4.02 4.90 14.67 1.0320 870.0 873.8 797.6 868.5 858.7 792.7 867.9 5.19 4.18 4.82 14.83 1 . 0338 881.8 888.4 809.2 881.7 867.8 801.1 881.7 5.21 3.56 4.96 14.19 1.0321 847.1 859.6 790.9 847.9 870.1 803.2 853.6 5.21 3.59 5.17 15.04 1 . 0345 883.6 871.4 802.1 880.1 870.1 803.2 860.9 5.21 4.22 4.88 14.89 1 . 0346 881.6 895.5 815.5 885.5 870.1 803.2 887.3 5.22 3.70 5.22 14.65 1 . 0340 867.0 880.0 808.9 867.5 871.2 804.2 869.1 5.22 4.28 4.96 15.10 1 . 0349 899.1 903.1 822.1 894.8 871.2 804.2 893.6 5.23 3.82 5.16 14.64 1 . 0340 870.0 885.3 812.1 869.8 872.4 805.3 874.9 5.23 4.45 4.78 15.16 1 . 0353 897.9 906.9 822.9 900.9 872.4 805.3 898.9 5.25 3.68 5.25 14.72 1 . 0338 869.6 882.6 811.7 871.3 874.7 807.4 871.5 5.27 3.91 5.34 14.90 1 . 0345 881.9 901.3 826.6 882.7 876. 9 809.5 888.2 5.28 3.66 4.97 14.64 1 . 0329 880.2 872.5 802.0 870.2 878.1 810.6 865.7 5.28 4.07 5.15 15.24 1 . 0352 901.0 904.4 826.8 899.3 878.1 810.6 892.7 5.34 3.45 5.59 14.75 1 . 0346 879.7 891.7 824.6 872.5 884.9 816.9 876.3 5.34 4.13 4.90 15.04 1 . 0350 905.2 903.4 824.5 896.6 884.9 816.9 894.7 5.36 4.24 4.81 15.05 1 . 0337 898.9 906.6 826.0 900.0 887.2 819.0 900.1 5.42 3.95 5.14 15.08 1 . 0360 902.2 910.6 834.7 898.7 894.0 825.3 898.6 5.44 4.06 5.14 15.37 1 . 0358 921.5 918.5 840.6 912.6 896.3 827.4 906.4 5.49 4.78 4.45 15.68 1 . 0356 950.7 936.3 846.1 940.6 902.0 832.7 931.6 5.50 3.71 5.04 14.70 1.0321 887.3 897.2 825.3 884.7 903.1 833.7 890.2 5.50 3.79 5.00 14.72 1 . 0328 886.2 900.7 827.5 886.9 903.1 833.7 893.5 5.50 3.90 5.08 15.06 1 . 0340 909.0 911.0 835.9 901.4 903.1 833.7 901.6 5.52 3.90 5.07 15.00 1 . 0349 898.7 913.3 838.0 900.3 905.4 835.8 903.1 5.62 3.87 4.95 14.98 1.0337 902.8 914.9 839.9 904.6 916.7 846.3 907.3 5.62 4.21 4.84 15.30 1 . 0359 913.8 931.6 850.7 922.7 916.7 846.3 922.9 5.66 3.62 5.25 15.02 1.0326 909.0 915.2 844.5 903.2 921.2 850 6 905.4 5.66 4.21 5.14 15.59 1 . 0355 951.9 946.4 865.7 935.0 921.2 850.6 934.5 5.72 3.83 5.20 15.28 1.0351 927.4 932.6 858.1 920.0 928.1 856.9 920.9 5.76 3.52 4.84 14.98 1 . 0336 916.8 903.6 834.2 906.5 932.7 861.1 898.1 5.76 4.08 5.33 15.57 1 . 0367 924.0 956.8 877.9 936.9 932.7 861.1 941.6 5.79 4 00 5.18 15.47 1 . 0342 928.5 946.8 869.4 933.7 936.1 864.2 936.0 5.86 3.73 4.96 15.04 1 . 0328 911.0 928.3 855.2 917.2 944.0 871.6 921.8 5.87 4.19 4.90 15.70 1 . 0339 951.9 953.6 872.7 950.5 945.2 872.7 946.0 5.88 3.84 4.97 15.61 ] . 0323 944.7 936.2 861.3 941.6 946.3 873.7 929.8 5.88 4.10 4.94 15.54 1 . 0357 940.8 952.7 873.1 943.4 946.3 873.7 943.1 5.90 3.98 5.34 15.86 1.0361 957.7 963.7 886.2 953.6 948.6 875.8 949.1 5.94 4.26 5.26 16.03 1 . 0355 963 6 979.3 897.0 966.9 953 1 SSI 1.0 9I>5.S 212 BULLETIN No. 282 [December, TABLE 1. ANALYSES OF 212 MILK SAMPLES WITH COMPUTED AND DETERMINED ENERGY VALUES (Concluded) Calories per quart Fat Pro- Lactose Total Specific Computed Deter- mined Meta- Form- Form- Form- Form- Total boliz- ula ula ula ula A B C D E F able 1 2 3 4 perct. perct. perct. perct. cals. cals. 5.94 4.32 5.00 15.97 1.0342 964.2 971.3 888.1 966.3 953.1 880.0 962.1 5.96 4.05 4.66 15.33 1.0336 950.2 944.3 865.5 939.5 955.4 882.1 940.2 5.98 3.88 4.90 15.43 1 . 0342 937.0 946.5 870.5 941.0 957.8 884.3 939.2 5.99 4.12 5.26 15.98 1.0353 962.6 975.7 895.8 965.3 958.8 885.3 962.7 6.00 3.69 5.18 15.33 1.0323 935.0 946.7 874.2 934.3 960.0 886.4 938.2 6.04 4.31 5.14 16.08 1.0349 981.0 985.9 902.6 975.2 964.5 890.6 974.4 6.05 4.83 4.14 15.87 1 . 0352 988.7 977.4 884.9 979.1 965.6 891.6 976.8 6.16 3.69 4.86 15.16 1.0326 939.7 949.1 876.0 937.2 978.2 903.2 944.1 6.42 3.95 5.24 16.27 1.0351 992.7 1004.2 926.1 996.3 1007.7 903.6 992.0 6.56 4.34 5.02 16.58 1 . 0338 1020.2 1028.8 943.9 1022.3 1023.6 945.3 1020.0 7.59 3.23 5.00 16.69 1.0314 1070.7 1056.6 988.1 1062.6 1140.8 1053 . 8 1052.6 STATISTICAL PART a The total computed calories per quart for each of the 212 samples tabulated in Table 1, were obtained with a computing machine by com- pleting the following computations: total calories per quart = (A X 9.23 + B X 5.71 + C X 3.95) (946.36 X E) * 100. In this expression the values 9.23, 5.71, and 3.95 5 are large calories of heat evolved by the complete combustion of one gram of butterfat, one gram of protein, and one gram of lactose, respectively; 946.36 is the volume of one quart in milliliters. The metabolizable calories per quart given in the eighth column in Table 1 were obtained by completing the indicated computation: [A X 9.00 + (B + C) 4.00] [946.36 X E] -4- 100. In this expression the values 6 9.00 and 4.00 are the metabolizable energy values, in large calories, of one gram of butterfat and one gram of protein and carbo- hydrate, respectively. The means, standard deviations, coefficients of correlations, and partial regression coefficients of the analytical results in columns A to F inclusive are given in Table 2. The partial regression coefficients were computed by the method given by Wallace and Snedecor. 7 From the results given in Table 2, regression equations were de- veloped by substitution in the general regression equations. The re- a ln the statistical part, the following symbols are used: A = percentage of fat in the sample. B = percentage of protein in the sample. C = percentage of sugar (lactose) in the sample. D = percentage of total solids in the sample. E = specific gravity of the sample at 20C. F = determined calories per quart. F u computed calories per quart (metabolizable). F T = computed calories per quart (total). 1926] THE ENERGY VALUE OF MILK 213 gression equation of F, based upon the other variables, is F = M F + aF aF aF aF (D MD) + @FE . ~^ (E ME). Substituting the values given in Table 2, and simplifying, this equation becomes, F! = 52.78A + 16.415 + 37.87D + 46.91E - 2.75C - 57.70 calories per quart (Formula 1). TABLE 2. MEANS, STANDARD DEVIATIONS, COEFFICIENTS OF CORRELATIONS AND PARTIAL REGRESSION COEFFICIENTS DERIVED FROM ANALYSES OF 212 MILK SAMPLES SHOWN IN TABLE 1 Column Means Standard deviations Coefficients of correlations A B C D E F F 1 it 4.2717 .0452 3.4620 + .0211 4.9519 + .0140 13.3000 .0663 1 .0328 .00007 763.02 5.17 704.386 4.839 .9761 + .0320 .4558 + .0149 .3021 .0099 1.4316 .0469 .0015 + .00005 111.681 + 3.658 104.463 +3.422 r AB = .7923 .0172 r AC = .1837 + .0448 r AD = .9640 .0033 r AE = .5657 .0315 r AV = .9813 .0017 r BC = .0426 + .0462 r BD = .8653 .0116 r. = .6842 .0246 r_. = .8525 .0127 r cl) = .3025 .0421 r CE = .4687 + .0361 r cf = .2274 + .0439 r DB = .6965 .0238 r D . = .9862 .0013 r EF = .6419 .0272 r AF = .9838 .0015 y (/3 for six variables) fA = .46132 = .06696 |8, c = .00745 = .48542 P fK = .00063 (0 for variables A, B, C, and F e, A = .7925 M = .2215 P rc = -0723 The regression equation 81 of F on A is F = MF + MA) ; which becomes, aF = 113.7334 (A + 2.4404) calories per quart (Formula 2). "As the regression equation of F on A is most likely to be of practical value, it was determined, without grouping, from the data given in columns A and F, Tible 1, by the method set forth by Wallace and Snedecor. 7 The means, the standard deviations, and the coefficient of correlation are as follows: M A = 4.2686, M F = 763.036, a A = .969632, a, = 111.7665, r Ar = .9867. It is interesting to observe that the regression equation of F on A, based en the statistical values obtained by grouping the data into classes given in Table 2, is Fz = 112.276 (A + 2.524). In this case the slope of the line constructed by plotting the estimated F's against their corresponding percentages of fat is less than the slope of the line obtained when the equation derived without grouping into classes is used. The other regression equations are derived from the statistical values obtainei by grouping the data. 214 BULLETIN No. 282 [December, The correlation coefficient of A and F M , the metabolizable energy value (Table 1, eighth column), was computed. The regression equation in this case becomes, 7^3 = 105.287 (A + 2.4185) calories per quart (metabolizable) (Formula 3). The regression equation for F, based on A, B, and C, computed from the data given in Table 2, becomes, 7^4 = 90.67A + 54.275 + 26.73C + 55.44 calories per quart (Formula 4). These formulas may be used for estimating the energy value of a quart of milk. The values of the 212 samples used in this investiga- tion, ranging in fat percentage from 2.68 to 7.59, so computed, are in- cluded in Table 1 in the columns headed by the respective formula numbers. The multiple correlation coefficients may be computed by substi- tuting the values from Table 2 in the equation, 7 R 2 = j3 FA r AF -f $ FB - fsf + (etc.). In the case of the six variables this becomes R\ \/-98726 = .9936; and for the four variables, A, B, C, and F, it becomes R 2 V.9830 = .9915. ) The standard error of estimate in the energy values computed by the use of Formula 1 is cF - ABCDE = aF \/l - R? = cF \/l - .98726 = .1128 For the purpose of comparing results obtained by their use, with results obtained by using Formula 2 of this work, the formulas of Gaines and Davidson and of Andersen were changed to the basis of the average weight of a quart of milk (977.4 grams). These formulas thus become, E = 106.9643 (2.66 + t) calories per quart, and E = 110.9349 (per- centage of fat + 2.555) calories per quart, respectively. If the values given by Frederiksen asfound by Andersen 3 (butterfat, 9.11 calories per gram; milk protein, 5.86 calories; and lactose, 3.76 calories per gram) are used, the results are as follows: mean of the differences between the determined energy value per quart and the value computed by Andersen's constants, 2.8302 calories; standard deviation of these differences, 8.5485 calories. That is, the energy of a quart of milk computed in this way is on the average 2.8302 calories less than the determined energy. At odds of 30:1, the limits within which computed values may be expected to fall are + 18.2938; and at odds of 100:1, the limits are 22.0551. This work of Andersen's was not at hand when the statistical study shown in the tables was made. 1926} THE ENERGY VALUE OF MILK 217 IHO MB / X / / /, x / / V f / t / f? y , / / o 540 t?5ZO Mea.n determined i/a-lue Values computed from formula. 2 Valuta computed from Andersen's form. Values, computed 'rom Ga-ines' a.nd Da-vidson's forjnulaL >// / // 2 / P 1.80 3.1O 3.+0 3.70 -J-OO 4-.3O 4.tO +.30 J.2O 55O 5.60 4.1O M-0 Percent a.es of Ta.t 7.30 7.40 DETERMINED AND COMPUTED ENERGY VALUES OF MILK The energy value of milk of a given fat content, computed by formula, corre- sponds very closely to the value determined in the calorimeter. The results as computed by each formula are compared graphically with each other and with the mean determined results in the accom- panying figure. These graphs show that the energy values computed by the formulas correspond very closely with the determined values 218 BULLETIN No. 282 CONCLUSIONS 1. The heat of combustion of a quart of milk may be computed in one of the following ways: a. If the percentages of fat, protein, lactose and total solids, and the specific gravity are known, the formula F = 52.78A + 16.411? -f- 37.87D + 46.9 IE - 2.75C - 57.70 should be used. b. If the percentages of fat, protein, and lactose are known, the formula F = 90.67A + 54.275 + 26.73(7 + 55.44 should be used. c. If only the percentage of fat is known, the formula F = 113.7334 (A + 2.4404) should be used. d. If only the percentage of fat is known and the metabolizable energy is wanted, the formula FM = 105.287 (A + 2.4185) should be used. 2. The true heats of combustion per gram of butterfat, milk pro- tein, and lactose probably lie between the values given by Abderhalden 5 and by Hammarsten 5 and those given by Frederiksen as found by Andersen. 3 LITERATURE CITED 1. GAINES, W. L., AND DAVIDSON, F. A. Relation between percentage fat content and yield of milk. 111. Agr. Exp. Sta. Bui. 245. 1923. 2. STOCKING, W. A., AND BREW, J. D. Milk, the essential food. Dairymen's League News. Jan. 10, 1920. 3. iFREDERIKSEN, LARS. Second Communication from the Experiment Station, Div. of Anim. Husb., Roy. Vet. and Agr. Col. Copenhagen, Denmark. 1925. 4. PALMER, L. S. The preservation of milk for chemical analysis. Mo. Agr. Exp. Sta. Res. Bui. 34, 29. 1919. 5. ABDERHALDEN, EMIL. Text-book of physiological chemistry, 1st ed., 333. 1908. HAMMARSTEN-MANDEL. Text-book of physiological chemistry, 6th ed., 829. 1912. 6. SHERMAN, H. C. Chemistry of food and nutrition. 3d ed. 1926. 7. WALLACE, H. W., AND SNEDECOR, GEORGE W. Correlation and machine calculation. la. State Col. of Agr. and Mech. Arts. Official Publication 23, No. 35, 28-33. 1925. UNIVERSITY OF ILLINOIS-URBANA