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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 valuea 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. Frederiksen3 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 0
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 PARTa
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 3.955 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
values6 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-
aln 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 20°C.
F = determined calories per quart.
Fu — computed calories per quart (metabolizable).
FT = computed calories per quart (total).
1926]
THE ENERGY VALUE OF MILK
213
gression equation of F, based upon the other variables, is F = MF +
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
rAB = .7923 ± .0172
rAC = .1837 + .0448
rAD = .9640 ± .0033
rAE= .5657 ± .0315
rAV = .9813 ± .0017
rBC = .0426 + .0462
rBD = .8653 ± .0116
r». = .6842 ± .0246
r_. = .8525 ± .0127
rcl) = .3025 ± .0421
rCE = .4687 + .0361
rcf = .2274 + .0439
rDB = .6965 ± .0238
rD. = .9862 ± .0013
rEF = .6419 ± .0272
rAF = .9838 ± .0015
•y
(/3 for six variables)
0fA = .46132
£„ = .06696
|8,c = .00745
£„ = .48542
PfK = .00063
(0 for variables A, B, C, and F
e,A = .7925
0M = .2215
Prc = -0723
The regression equation81 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: MA = 4.2686, MF =
763.036, aA = .969632, a, = 111.7665, rAr = .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 FM, 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 R2 = j3FA • rAF -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 R2 —
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 <sF, or 11.28 percent of the standard deviation of F. In the case
of Formula 4 the standard error of estimate is aF • ABC = <sF \/l — R^
= cF Vl - ,9830 = .1304, or 13.04 percent of the standard devi-
atior of F.
For Formulas 2a and 3 the" standard errors of estimate are, re-
spectively, cF • A =aF Vl - I*AF = °F Vl - (.9867)2 = .1626 oF,
or 16.26 percent of the standard deviation of F, and <sFM • A = aFM
- (.9838)2 = .1793 aFM, or 17.93 percent of the
standard deviation of FM-
The differences were found between the determined energy values
(Cohmn F, Table 1) and the total computed values given in the columns
heaced Total, Formula 1, Formula 2, and Formula 4, respectively;
and also between the computed metabolizable energy and Formula 3.
The means, standard deviations, and limits at odds of 30:1 and at odds
of 100:1 for these five sets of differences are given in Table 3.
"Using for Formula 2 the statistical values given in the preceding footnote,
pags 213.
1926}
THE ENERGY VALUE OF MILK
215
APPLICATION
The regression equations give a convenient method for use in com-
puting the energy value of a quart of milk if the percentage composition
of the milk is known. If A, B, C, D, and E are known, Formula 1 may
be used. When A, B, and C are known, Formula 4 is to be used, and
Formula 2 when A only is known. To compute the metabolizable
energy value of a quart of milk when A only is known, Formula 3 is to
be used.
Table 3, giving means, standard deviations, and limits within which
the results computed by the various formulas will lie, gives a measure
of the reliability of the computed values.
TABLE 3. — MEANS AND STANDARD DEVIATIONS OP THE DIFFERENCES AND LIMITS
Differ-
ences
Number
of differ-
ences
Mean
Standard
deviation
Limits at
odds of
30:1
Limits at
odds of
100:1
cals.
cals.
cals.
cals.
Fl-F*
F2l-F**
F*T-F
212
212
212
212
212
212
+ .1416
-.0071
- .4437
-.4436
- .3702
+6.3584
5.7081 + .1870
18.1755 ± .5953
18.2448 + .5976
14.9076 + .4882
8.3356 + .2730
8.5812 + .2811
± 12.2153
± 38.9056
+ 39.0439
± 31.9023
± 17.8382
± 18.3638
± 14.7269
± 46.8928
+ 47.0267
+ 38.4616
+ 21.5058
± 22.1395
F = calories per quart, determined. Fa = calories per quart, computed by Form-
F2l
calories per quart, computed by Form-
ula 1.
calories per quart, computed by Form-
ula 2.
= calories per quart, computed from re-
gression equation obtained from grouped
data.
ula 3.
Ft = calories per quart, computed by Form-
ula 4.
FM = calories per quart metabolizable.
FT := calories per quart, computed from energy
value of constituents.
*The mean and the standard deviation of the differences Fz — F were determined
without grouping the data into classes; all other means and standard deviations in
this table were determined from grouped data.
**The values FZl were obtained by the use of the regression equation given in the
footnote on page 213. The standard deviations and limits for F2 — F and for F2j — F
show that the results obtained by grouping are only slightly different from those
obtained without grouping.
Formula 1 gives results which at odds of 30:1* will lie within
+ 12.2153 calories per quart of the determined value. These limits
are within about + 2 percent of the determined values for milk with
low fat content, and within +1.25 percent for milk with high fat
content.
•The mean of each group of differences ± 2.14 times the corresponding standard
deviation gives limits such that the chances are 30:1 that any single difference de-
termined in the same way will fall within them. For odds of 100:1 the standard devi-
ation is to be multiplied by ± 2.58.
The constants + 2.14 and ± 2.58 were determined from the equation given on
page 28 of Karl Pearson's Tables for Statisticians and Biometricians.
216 BULLETIN No. 282 [December,
Formula 2 gives results which at odds of 30:1 will lie within ±
38.8956 calories per quart of the determined value, or within about
+ 6.5 percent for milk with low fat content, and ± 3.9 percent for milk
with high fat content.
Formula 3 gives values which at odds of 30:1 will lie within ±
31.9023 calories per quart of the computed metabolizable energy value,
or within about + 6 percent of the computed value for milk with low
fat content, and ± 3.4 percent for milk with high fat content.
Formula 4 gives values which at odds of 30:1 will lie within ±
17.8382 calories per quart of the determined value, or within about
+ 3.4 percent for milk with low fat content, and + 2 percent for milk
with high fat content.
The mean and standard deviation of the differences between the
total energy per quart as computed and as determined show that for
the values for fat, for protein, and for lactose, as used in this work, the
computed values are, on the average, 6.3584 calories per quart higher
than the determined values. They also show that if 6.3584 calories are
substracted from the computed values, the chances are 30:1 that such
values will then lie within + 18.3638 calories per quart of the deter-
mined values.a
The standard errors of estimate show that the standard deviations
of computed values from determined values are, for Formula 1, 11.28
percent of the standard deviation of F; for Formulas 2 and 4, 16.26
percent and 13.04 percent, respectively, of the standard deviation of F;
and for Formula 3 the standard deviation of values computed by the
formula, from those obtained by the use of the metabolizable energy
value of the constituents (FM), is 17.93 percent of the standard devia-
tion of FM>
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 Andersen3 (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
<o
<§*»
l_
/
s
/
/
2
/
s
//.
/
/
<
2
/
<
X'
' /
/
C^STO
<n
A
/ /
/
/
2 810
<o
°,8o
£
/ /
V-
2
750
r*o
650
440
430
too
570
/•
f/
/
A
/>
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 Abderhalden5
and by Hammarsten5 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.
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