L'l E> RAR.Y OF THE UNIVERSITY OF ILLINOIS AGRICULTURE NON CIRCULATING CHECK FOR UNBOUND COPY UNIVERSITY OF ILLINOIS Agricultural Experiment Station BULLETIN No. 308 THE ENERGY BASIS OF MEASURING MILK YIELD IN DAIRY COWS By W. L. GAINES URBANA, ILLINOIS, MAY, 1928 CONTENTS Page INTRODUCTION 403 ESTIMATION OF ENERGY VALUE 404 From the Fat and Solids-Not-Fat 404 From the Fat, Protein, and Lactose 410 By Direct Calorimetry 411 Summary of Estimates 413 Discussion of Estimates : 413 Interpretation of Formula 414 FAT PERCENTAGE AND FEED REQUIREMENTS 415 Data from Minnesota Station 415 Data from Copenhagen Station 418 FAT PERCENTAGE AND YIELD OF MILK 419 Correlation Between Fat Percentage and Milk Yield 419 Shorthorn Advanced Registry 419 Red Danish Advanced Registry 423 Red Danish Herd Records 425 Nature of the Relationship 427 SOME ILLUSTRATIVE APPLICATIONS 429 Lactation Curves 429 Nutrition Investigations 430 Economic Interpretation 431 Genetic Investigations 431 SIGNIFICANCE OF FAT PERCENTAGE 432 SUMMARY AND CONCLUSIONS 434 LITERATURE CITED . . .436 THE ENERGY BASIS OF MEASURING MILK YIELD IN DAIRY COWS a W. L. GAIXES, Chief in Milk Production INTRODUCTION The dairy cow is maintained primarily as a milk animal, as a source of human food, and as such her worth depends upon her milk produc- tion. The most obvious measure of the milk production of the cow is the yield of milk itself, in terms of weight or volume. It has come to be a somewhat prevalent practice to determine and record, by some systematic method, the weight of milk produced by in- dividual cows in dairy herds. Also, since the advent of the Babcock test, it is usual to determine the percentage fat content of the milk by some system of sample taking and testing. There have developed, then, two common measures of the performance of the cow at the pail: (1) the milk yield in pounds over some definite period of time; (2) the butterfat yield in pounds over the same period of time. The average fat percentage is readily derived from the total milk and fat yields and is likewise com- monly reported. Milk is highly variable in composition, particularly as between different cows and breeds. It always contains a large proportion of water. When we measure production of the cow on the basis of milk alone, we place the water of the milk on a par with the solids. The water of milk has no more food value than water from any other source, and what is more pertinent, it seems that the production of the water frac- tion of the milk requires no particular expenditure of energy on the part of the cow. It is clear, therefore, that milk yield alone is not an en- tirely satisfactory measure of production. When we measure production on the basis of fat alone, we ignore the other solids of the milk. These other solids have food value, and require the expenditure of energy on the part of the cow in their pro- duction. It is not quite proper to ignore them. Another measure of production that has been used to a very limited extent is based on the total solids of the milk. The solids of milk con- sist mainly of lactose, fat, protein, and ash. Measuring yield on the basis of total solids attaches equal importance to these several constit- uents according to their amount. Submitted for publication December 29, 1927. 403 404 BULLETIN No. 308 [May, In Bulletin 245 19 * of this Station it was proposed that the gross en- ergy value of the milk solids be used as a measure of the yield of dairy cows, the energy value to be estimated in terms of 4-percent milk from the milk and fat yields. Additional evidence on the subject has accum- ulated in the meantime, which seems to support the equity of the energy measure. Inasmuch as the idea seems to be of some general import to those concerned with the milk yields of dairy cows, it is purposed in this paper to submit the evidence as it appears at the present time. ESTIMATION OF ENERGY VALUE From the Fat and Solids-Not-Fat. Stocking and Brew 37 * have pre- sented indirect evidence concerning the energy value of milk, based on 4,220 calories 8 per pound of fat and 1,860 calories per pound of solids- not-fat. Their figures lead to the equation E = 49.64M(2.66+/) (1) where E is energy value in calories, M is the weight of milk in pounds, and / is the percentage fat content of the milk. Equation (1) is readily transformed to E' = AM + 15F (2) where E' is energy value in terms of pounds of average milk of 4-percent fat content, M is milk in pounds, and F is fat in pounds. b In equation (2) E' may be designated "4-percent milk," or " fat- corrected milk," or "F.C.M.," and we may write F.C.M. = AM + 15F (3) with the limitation only that the same unit of weight be used for each of the three terms. Equation (3) is in convenient form for computation from the pro- duction record as it is usually kept to show the yield of milk and fat by weight. Where the average fat percentage is reported it may be con- venient to employ the equivalent equation "Thruout this paper calorie refers to the large calorie, and 1,000 calories = 1 therm. b Utilizing the mathematical relation, M//100 = F, or Mf = 100F, we have total energy value of the entire quantity of milk E' = energy value of 1 pound of 4-percent milk 49.641T (2.66 +/) 2.Q6M + M/ 2.66M + 100F 49.64(2.66 + 4) 6.66 6.66 = .3994M + 15.015F or, in round numbers, as in equation (2), and this gives 1 pound of 4-percent milk = 49.64 (2.66 + 4) = 330.6 calories. It will be observed that the coefficient (49.64) of M in equation (1) cancels out in the transformation to the form of equation (2). That is to say, equation (2) is independent of the absolute value of this coefficient. 1928] ENERGY BASIS OF MEASURING MILK YIELD IN DAIRY Cows 405 F.C.M. = M(A+ .15/) (4) notation as before, using the same unit of weight for F.C.M. and M. Equation (4) is in useful form particularly for slide-rule computation, where one scale of the slide rule carries graduations of ( . 4 + . 15/) for various / values thru the range required (cf. Fig. 1. of Gaines 15 * and Fig. 3 of Gaines 16 *). It will be clear that equations (1), (2), (3), and (4) are merely differ- ent forms to express the same thing. The question arises, with what de- gree of accuracy may we estimate the energy value of the milk of vari- ous individual cows from the weight of milk and its fat percentage by the use of these equations? Five sets of data are available which show the percentages of fat and solids-not-fat for a considerable number of cows over part or all of a lactation period. The Minnesota Station 24 * has published the analyses of 543 samples of milk, each representing the milk yield for one week of 46 different cows in the Station herd. Various breeds and stages of lac- tation are represented. The solids were determined gravimetrically, the fat in part gravimetrically and in part by the Babcock method. The Connecticut Station 39 * has published 127 analyses, each representing a complete lactation period, for 50 cows of various dairy breeds in the Station herd. The Wisconsin Station 41 * has published analyses of the milk of 398 cows of various dairy breeds in the Wisconsin Cow Competi- tion of 1909-1911. For the most part the period covered was 365 days within the same lactation. The Holstein-Friesian Association 26 * has pub- lished analyses of the milk of 458 registered Holstein cows in their yearly advanced-registry work. The American Jersey Cattle Club 1 * has pub- lished analyses of the milk of 70 registered Jersey cows for 120 days at the flush of lactation in the contest at the 1904 St. Louis Exposition. Analyses in all cases, except the Minnesota data, were by the Babcock and lactometer method. By the use of Stocking's values it is possible to calculate the calories per pound of milk from the above analyses and then to determine the correlation between the fat percentage and energy value. The correla- tion surfaces and coefficients, together with the observed regressions and that of equation (1), give an index of the accuracy of the estimate by the equation. The correlation surfaces are given in Table 1 and the coefficients in Table 2. The mean energy values derived from Table 1 are given in Table 3, and are shown graphically in Fig. 1, together with the curve of equation (1). It is clear from Fig. 1 that the equation conforms quite closely to the observations. The equation is being tested here against data not identical with those from which it was derived. The good agreement 406 BULLETIN No. 308 [May, O 2 CO J3 4-( ^ is 0) .2 'E c ,2 S 03 ^ O p s 3 H o ^ |l-s all co -3 ^ -2 Q c3 c S O S Cv i -^ -S 5 CO ,H -^ -i C '5 S _ re CN 00 IN CO ^ _ IN "r: ^ - _~ 408 BULLETIN No. 308 [May, 1 IS&W oc - = - .OOCNOtO- ,= <" to o CO -CO CO rooi c o co-*t-co CO rt ^ 00 ~rt-Ci CN CO -1 CN NNCscjMNcocococoeoco 1 SjuNcoeocococococococo "S t- 1928] ENERGY BASIS OF MEASURING MILK YIELD IN DAIRY Cows 409 TABLE 2. COEFFICIENTS OF CORRELATION BETWEEN FAT PERCENTAGE AND ENERGY VALUE PER POUND OF MILK AND BETWEEN FAT PERCENTAGE AND SOLIDS-NOT-FAT PERCENTAGE (Energy value estimated on the basis of 4,220 calories per pound of fat and 1,860 calories per pound of solids-not-fat) Source of data Fat percentage and energy value Fat percentage and solids-not-fat percentage Minnesota Station .9882+ .0007 .801+ .007 Connecticut Station .9878+ .0015 .684+ .032 Wisconsin Station .9915+ .0006 .794+ .013 Holstein-Friesian Association .9152+ .0051 .533+ .023 American Jersey Cattle Club .9668+ .0053 .517+ .059 shown in Fig. 1 and the high coefficients of correlation of Table 2 may be taken to mean that the energy value of milk may be estimated with considerable accuracy from the fat percentage and weight of the milk. TABLE 3. MEAN ENERGY VALUES PER POUND OF MILK AT VARIOUS FAT PERCENTAGES (Computed on the basis of 4,220 calories per pound of fat and 1,860 calories per pound of solids-not-fat) Fat percentage Computed by equation CD" Source of data Minnesota Connecticut Wisconsin Holstein Jersey 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.6 6.8 7.0 7.2 cals. 261.1 271.0 281.0 290.9 300.8 310.7 320.7 330.6 340.5 350.5 360.4 370.3 380.2 390.2 400.1 410.0 420.0 429.9 439.8 449.7 459.7 469.6 479.5 489.5 cals. cals. cals. 265.0 280.0 279.7 291.5 300.8 312.5 320.3 331.4 340.6 349.7 362.5 370.3 379.6 389.2 398.3 408.5 417.2 427.0 436.7 445.0 cals. 255.0 276.4 280.4 291.9 302.0 313.2 322.5 331.7 341.0 355.0 cals. 265.0 275.4 290.0 296.0 305.0 315.0 329.6 342.3 352.5 361.6 371.2 382.2 390.1 399.6 409.2 419.1 426.7 439.2 451.4 458.0 471.0 480.0 480.0 270.0 275.0 292.8 298.3 313.0 321.7 330.7 344.2 350.3 360.9 365.0 379.4 383.8 395.0 407.5 418.3 430.0 445.0 448.3 285.0 297.5 305.9 317.3 326.4 340.0 345.0 355.0 367.2 370.0 378.3 "The gross energy value of one pound of milk at the various fat percentages (as will appear later) actually runs about 3 percent greater than the values given in this column. 410 BULLETIN Xo. 308 [May, JWI 400 4GB 440 420 400 -M) !-:; :?: ZCG 4C. i / co M o C inn. )na / s AA fl H -F */ " 4 rsex 4 X J3 61) CO -CO .CN^-HN-H . .~ . . . ^ "S * e o * 3 i w 8 f c .^H . .^H . -N -N CO "o 1 TK o percenl o :::::-:-:::::: c g ".2 is 00 w ^ . . .__ -coco a it o CO K rf o-a 30 CO ' !> < a 1-1 J3 || TO ^.s 3a" IN CO ( . -1 t| w "1 .So, o e . CM rt 1-1 -H i-i CO OS c a CO o a s $ ij 00 -H . -CM (Q s-i N J3 u. CO i-l -i-c CN Cl str ^ CN u 3 ie figures sf nutrien r-COU5^0-cM"5t>OS-CO5t-C- O S L- . 3 O a r- r vergenc* 1928} ENERGY BASIS OF MEASURING MILK YIELD IN DAIRY Cows 417 quirements excluded) per pound of milk yielded. The correlation sur- face is given in Table 4, and leads to the following constants: Mean Standard deviation Coefficient of correlation* Fat -percentage 4.399 .852 Nutrients for lactation per pound of milk .3463 pounds .0636 pounds .648 .033 The mean observed values of nutrients for lactation per pound of milk at the various fat-percentage classes are given in Fig. 4. The re- gression equation, y = .1334+ .0484/, derived from the above con- stants, shows that the production of 1 pound of 4-percent milk requires .34 \ Percentage rat Content of Milk. (1 ) FIG. 4. RELATION BETWEEN FAT PERCENTAGE AND NUTRIENTS FOR LACTATION PER POUND OF MILK DERIVED FROM HAECKER'S DATA The equation of the smooth curve is that of equation (3), in which 1 pound F.C.M. requires 327 pounds of nutrients for lactation, y = 327 (AM + .l5Mf) = .049(2.66 + /). The regression equation derived from the coefficient of corre- lation and standard deviations is y = .0484(2.76 + /) and gives a curve of slightly less slope than that of equation (3), but the difference is too small to be shown in the scale of the figure. "This coefficient has been computed by the use of four different groupings. As a matter of interest in statistical method the results are given below, in which / rep- resents fat percentage and y represents pounds of nutrients for lactation per pound of milk: Class interval, / 01 Class interval, y 001 Number of classes, / 349 Number of classes, y 317 Standard deviation, / 8571 Standard deviation, y 06380 SD, X SD, 05469 Coefficient of correlation 6386 It works out in this particular case that the coarser the grouping, the higher the coefficient of correlation. In the finest grouping the number of classes actually represented does not, of course, exceed the total number of observations, 140. .1 .01 36 34 .8596 .06404 .05505 .6411 .2 .02 18 16 .8520 .06363 .05422 .6479 .5 .03 8 11 .8806 .06479 .05705 .6596 418 BULLETIN No. 308 [May, . 327 pounds of digestible nutrients for lactation (maintenance excluded). If we adjust equation (3) to this value, we have the smooth curve of Fig. 4. It is clear at once that, while the observed values of Fig. 4 are somewhat irregular, their trend is in the direction of the energy curve. The energy curve crosses the least-squares curve at / = 4, but its slope, .0491, is so nearly the same as that of the least-squares curve, .0484, as to make the two practically coincident in the scale of Fig. 4. The feed energy required for lactation is directly proportional to the energy value of the milk solids, a relationship which should be known as HAECKER 's LAW. Therefore, when we measure production in terms of F.C.M. by equation (3), we measure it also in terms of the nutrients required for lactation. By indirect, but altogether straightforward, methods it has been shown 13 * that, within the same breed, and so far as affected by the percentage fat content of the milk, the maintenance requirements per pound of milk are also proportional to the energy value of the milk solids per pound of milk. Data from Copenhagen Station. Frederiksen 11 * has presented data which indicate that the total feed consumption of dairy cows is propor- tional to the yield of F.C.M. , or 4-percent milk. His figures are of so much interest that they are given in Table 5, adapted to the present TABLE 5. PERCENTAGE FAT CONTENT OF MILK AND FEED CONSUMPTION PER POUND OF MILK Summary of ten years' (1909-1919) results of the Danish crossbreeding experi- ment, adapted from Frederiksen. The pertinent point of interest is the feed con- sumption per pound of F.C.M. This is remarkably constant, as measured in feed units. The Danish feed unit is 1 kilogram (2.2 pounds) of barley or its equivalent. Breed of cows Red Crossbred Jersey Danish Number of cows 368 350 353 Age of cows, in years 5.6 5.8 5.7 Live weight per cow, in pounds 1021 913 796 Percentage fat content of milk 3.60 4.28 5.34 Milk per cow per year, in pounds 7934 6389 5018 Fat per cow per year, in pounds 286 273 268 F.C.M. per cow per year, in pounds 7458 6657 6027 F.C.M. per pound live weight, in pounds. . . . 7 30 7 29 7.57 Feed units per cow per year . . 3079 2748 2484 Feed units per pound milk .388 .430 .495 Feed units per pound F.C.M .413 .413 .412 purpose. This table gives a summary of ten years' (1909-1919) results of an extensive breeding experiment conducted by the Counts Ahlefeldt- Laurvig in cooperation with the Copenhagen Experiment Station. Two pure breeds, the Red Danish and the Jersey, were used at the start in this experiment. These two breeds were intermated, creating a third 1928} ENERGY BASIS OF MEASURING MILK YIELD IN DAIRY Cows 419 breed class designated as crossbreds. The primary purpose of the in- vestigation was to determine the amount and economy of production of the three breed classes. Table 5 shows that the three breed classes differ markedly in weight, in milk yield, in the percentage of fat in the milk, in amount of feed con- sumed, and in amount of feed per unit of milk. The last line of the table shows, however, that the feed consumption per pound of F.C.M. is the same for each of the three breed classes. Therefore, when we measure production in terms of F.C.M., we also measure it in terms of total feed consumption, so far as the average results of these three groups of cows indicate. FAT PERCENTAGE AND YIELD OF MILK Correlation Between Fat Percentage and Milk Yield. Dairy liter- ature contains some confusion of thought relative to the relation between the richness of the milk and the amount of milk yielded by individual cows. In general it is recognized that these two variables show a small negative correlation. Some investigators have contended, however, that in certain breeds the correlation is zero. There are many factors which have a very great effect on milk yield, and this makes it difficult to de- termine precisely the relation between fat percentage and milk yield, independently of all other variables. Gaines and Davidson, 19 * studying the regression of milk yield on fat percentage as shown by a large number of yearly and 7-day records, reached the conclusion that milk yield is affected by the fat percentage (composition) of the milk, and that, "so far as affected by fat percentage, the milk yield is inversely proportional to the energy value of the milk solids per unit of milk. " That is, the energy yield is not affected by the fat percentage of the milk. Fig. 5 presents the method of attack and the results for one set of Holstein data. Concordant results were obtained also for the Ayrshire, Brown Swiss, Guernsey, and Jersey breeds. To the evidence from the records of these breeds may now be added similar evidence from the Milking Shorthorn and Red Danish breeds. Shorthorn Advanced Registry. The correlation surface for fat per- centage and milk yield for the Milking Shorthorns 2 * is given in Table 6. The coefficient of correlation works out at r = . 227 . 020. Fig. 6 shows graphically the mean milk yields at the various fat percentage classes, and the constant energy curve. The energy curve conforms "It is of interest to note that the energy yield of the three groups of cows is nearly proportional to their weight. Is this a general rule? (cf . footnote on page 597 of Gaines"*). 420 BULLETIN No. 308 [May, fl 215 U 29 3.1 3.3 3.5 3.7 3.9 41 43 45 47 49 5J 33 5.5 Percentage -Fat content or MilK (r) FIG. 5. RELATION BETWEEN FAT PERCENTAGE AND MILK YIELD: HOLSTEIN RECORDS This figure is based on 2,773 yearly records of milk yield and fat percentage of grade and purebred Holstein cows in Illinois cow-testing associations. The method of studying the records was to correlate the milk yield and fat percentage values, which gives, r = .229 .012. The correlation ratio for milk yield and fat percentage is, TJ = 242 .012. The difference between the two is, rf r 2 = .0061 .0020, statistical evidence that the regression of milk yield on fat per- centage deviates significantly from a straight line. The mean milk yields, indicated by the open circles, have been derived from the correlation table. Each circle represents the mean milk yield of a group of cows, each cow of the group lying within .05 of the fat percentage indi- cated by the base line scale. It appears that fat percentage is not correlated with any of the other important factors affecting milk yield (condition of the cow at calving is in certain cases a disturbing exception to this statement). Hence we may assume that all factors other than fat percentage which affect milk yield are equal or counterbalanced in each fat-percentage group, and that the differences in milk yield between groups are due to differences in fat per- centage. That is, inherent lactation capacity, size, age, feed supply, days in milk, etc., are assumed to average the same in each group, or advantages in some par- ticulars are counterbalanced by disadvantages in the other particulars. The ideal of this assumption will be realized only if the groups are large, and practically we may expect considerable irregularity in the observed yields, which in fact occurs. We are warranted in taking a smooth curve which represents the trend of the observed milk yields to represent the true relation between fat percentage (composition of the milk as measured by fat percentage) and milk yield. The constant energy curve, M = A/(2.Q6 + /), has been adjusted to the mean milk yields, thus: A = 2n M (2.66 + /)/2n, where M is the observed milk yield and n is the frequency at each fat percentage (/) class. This gives A = 43,668, which is simply the average energy yield shown by the 2,773 records, in units of 51 calories. The average energy yield is therefore 2,227 therms, or 6,550 pounds F.C.M. The constant energy curve, M = 43,668/(2.66 + /), shows the milk yield required to give this average energy value at the various fat per- centages. It describes the trend of the observed milk yields about as closely as could be expected of any simple smooth curve. We generalize, then, by saying that the milk yield changes with the fat percentage in such a manner that the energy yield remains constant, that is, the milk yield is inversely proportional to the calories per pound of milk. Perhaps the matter may be presented more clearly by considering the en- ergy yields directly, instead of the milk yields. The energy yields are repre- sented in the figure in terms of F.C.M. by the solid circles. They show, of course, the same sort of irregularity as the milk yields, but unlike the milk yields they show no consistent variation with the fat percentage. The correlation between the F.C.M. and fat percentage values is r = .010 .013. That is to say, the F.C.M. yields fluctuate independently of the fat percentage. 1928} ENERGY BASIS OF MEASURING MILK YIELD IN DAIRY Cows 421 P4 fc N c U i c a a: o z 2 a - -9 a 5 H < PB( 2 H H a 52 -fc O i J a M H o Y "3 S-o 3.2 ^^ * ei "a "o N^Hr5'CO' - oso5>oo5O' ^ 00 CO CO t- O5 (N O! 1-1 CO O iH N .... . i c*i ^^ co 1 1 * .... CC ^3 t- co U3 CO 1 * US rH !O TH IN fH -Nl-1 1-H -H C^ l-l -! 8 co t>- CD 00 t~ t O5 >O * IN i-H i-l iH X 58 in CO CJWTtl'-lOiOJNMi-l'-l -r- o IO ^ 1 us "3 o ri ' m a 05 s * "5 00 (O * V ^ CO * CO i CO IN CO -I < H V !* C! CO iOiO CO r 2 * ''' S lO J3 - I-H 1-C to S ^ , TOSCOOC-NCO rt 9 * ! CO .^-C005t-QOMO>^ "H .-H . . . . g 5 Tf o o & 1 2 i-l ttt 00 1>- 00 00 :O 00 5O CO N -" "-if* te s I-H IN CO 1* N (N -H " I o S o . .^^ N O i Ou,0 S WOr ( .-<^ l COO^iMi-lOO'i * o 3 IN cc c * | ^ '^ 8 * i * a> *o CO 01 00 -HW * 1-1 CO CO CO t- 00 CO .lOCO-H r- ! CO -r e t^ BO 8 CO "3 p M to CO . rt I-H co * IN in co oi oo co M t^ * * m -n-c -i-c 'C ercenta Ui CO ININ'-i-HCD-*NOCOOO^iOOCO(N(M .1- .... i 1 a ^ * p a CO "o CO -COi-H -K3CVIM b- 00 00 >O "O CO QlOO 1 H 1928} ENERGY BASIS OF MEASURING MILK YIELD IN DAIRY Cows 427 principal interest is the regression of milk yield on fat percentage as shown in Fig. 8. The average energy yield of the 511 records is 2,375 therms, or 6,985 pounds, F.C.M. The constant energy curve of Fig. 8 represents this value thruout, and, except for some deviations at either fat percentage extreme, it conforms reasonably well with the observed milk yields. Nature of the Relationship. Milk secretion, as it has become quan- titatively developed in the dairy cow, requires a very great expenditure of energy. It seems reasonable to suppose that on the average a 3-per- cent cow should do as much work as, and no more than, a 4-percent cow, or a 5-percent cow, if all factors such as size and age are equalized. It seems reasonable further that the work performed by the cow in milk secretion should be proportional to the product of that work as measured in terms of calorific value. 3 Haecker's work and the results of the Copenhagen experiment confirm the latter proposition. The nature of the relationship between fat percentage and milk yield seems to indicate that the energy required in milk secretion is a limiting factor in the amount of milk secreted, and the amount of energy devoted to milk secretion is independent of the particular proportions in which the several milk constituents are elaborated. On the basis of such a physiological interpretation we should expect to find no exceptions so far as any particular breed of cows is con- cerned. In this connection the negative correlation between fat percentage and milk yield found above for the Red Danish breed is of special in- terest because of the fact that Ellinger 9 * has reported a correlation of r = .055 .044 for this breed in the Count Ahlefeldt herd. He dealt, however, with only the first ten weeks of the lactation and it seems 8 In some cases glandular activity is partly manifest in a difference in the osmot- ic pressure of the secretion and the osmotic pressure of the blood. The urine, for example, may be of much higher osmotic pressure than the blood and in such case the kidney has expended energy and performed work in this particular (cf. Baylis, 5 * pages 339-343). A striking characteristic of the milk of the cow (and probably all mammals) is that its osmotic pressure is the same as that of the blood which nour- ishes the gland; and the osmotic pressure of the blood in health varies only within very narrow limits. In milk secretion there is no balance of osmotic energy with which to reckon, unless it requires energy on the part of the cell to maintain, for in- stance, a lower concentration of sodium chlorid in the milk than exists in the blood. If the quantity of water in the milk is determined by osmotic forces (as seems likely) without net expenditure of energy, then it seems clear enough that the water of the milk should be ignored in any quantitative measure of milk yield for biological study of dairy capacity. To do otherwise places undue emphasis on the lactose of the milk (cf. 12 . " 28 - 29 38 *). 428 BULLETIN No. 308 [May, that his peculiar result is in some way connected with this early stage of lactation, since as shown above, the usual negative correlation ob- tains when dealing with the yearly records in the same breed and herd. 8 Some other investigators have reported practically zero correlation, or even positive correlation, between fat percentage and milk yield, but so far as the writer has observed, there was always some plausible reason to believe that extraneous fac- tors were entering in to disturb the true relation. For example, in certain Holstein records special feeding and management practices may render the records unsuitable to reveal the true relationship. This is especially the case in the later 7-day records made shortly after calving (cf. Fig. 4 of Gaines 18 *). Langmack 30 * has published an extensive series of correlations between fat per- centage and milk yield for the separate lactation periods of the same cow. If we could have the same cow produce alternately, for certain periods, milk of a prescribed fat percentage, with other conditions remaining constant, we would have a direct way of measuring the influence of fat percentage (composition of the milk) on the yield of milk. Unfortunately this is a condition impossible of experimental control, and hence we must depend on the indirect evidence of some such statistical device as that of Fig. 5. In Langmack's procedure there is some fluctuation in fat percentage from one lactation to another. But the age of the cow is certainly changing, and, for immature ages, her weight (size) also. Age and weight are both powerful factors affecting pro- ductive capacity, and hence it is not permissible to attribute changes in milk yield from lactation to lactation as due entirely, or even to any important extent, to dif- ferences in fat percentage. About two-thirds of Langmack's coefficients were nega- tive and one-third positive. The negative correlation is in accord with the known pronounced tendency for milk yield to increase with age (in cows under 8 or 9 years of age, which constitute the great majority of the population), and the slight tend- ency for the fat percentage to decrease with age. The positive correlations indicate, however, that a considerable proportion of the individual cows have a slight tend- ency for the fat percentage to increase with age. It would not be proper to interpret Langmack's positive correlations as conflicting with the theory that, so far as affected by the fat percentage (composition) of the milk, the milk yield is inversely propor- tional to the energy value per pound of milk. Neither do his negative correlations lend any support to the theory. Since this paper was prepared there has come to hand Missouri Research Bulle- tin 105, by Samuel Brody, entitled "Growth and Development with Special Reference to Domestic Animals: X, The Relation Between the Course of Growth and the Course of Senescence with Special Reference to Age Changes in Milk Secretion." On the relation between fat percentage and milk yield Brody uses the equation M = Cf~ k in which M and / are in the present notation and C and k are constants. This is a very interesting form of expression and undoubted!} 7 capable of describing the re- lation with accuracy. Just what biological meaning may be attached to the constants is not clear. 1928] ENEBGY BASIS OF MEASURING MILK YIELD IN DAIRY Cows 429 SOME ILLUSTRATIVE APPLICATIONS Lactation Curves. An illustration of the application of energy values to the lactation curves of farrow Guernsey cows, has been pre- sented heretofore (Fig. I 20 *). It was there shown that the energy lacta- tion curve is more regular than the milk or fat lactation curves. Sim- ilar material is presented here in Fig. 9 taken from Ellinger's 10 * data on the Red Danish breed. a It is evident from the graph and from the numerical values given in the legend, that the energy lactation curve is much more regular than the milk or fat lactation curves. Time after Calving - Weeks (t) FIG. 9. LACTATION CURVES OF RED DANISH Cows This figure shows for the first lactation periods of Red Danish cows the rate of milk yield (M'), the rate of F.C.M. yield (F.C.M/), and the rate of fat yield (F') in pounds per day with advance in lactation. The curves are of the exponential type, rate oj yield = Ae -*. They have been fitted by the method of least squares, excluding the first observation. (For details of method of fitting cf. Games 15 ' 20 *). The equations are: M' = 28.25e ~ - 017 "' ; F.C.M.' = 25.55e ~- 01468 ; and F' X 25 = 23.78e " - 01468 '. The relative root-mean square errors \veighted by I/A are: F.C.M., 100; F, 487, and M, 476. The F.C.M. observa- tions thus agree much more closely with their smooth curve than do the fat or milk observations with theirs. The constant of proportionality, k, shows the rate of decrease per week in the rate of yield. The rate of decrease per month would be 4.345fc. The rate of decrease in energy yield is therefore 6.38 percent per month. This figure is for young cows; for older, higher-yielding cows the rate of decrease would un- doubtedly be considerably greater (cf. Fig. 28 of Gaines 16 *). If we choose to regard the cow as a machine, the energy lactation curve may be translated directly as representing the horsepower de- livered by the machine. This point of view may be justified by the fact, as above pointed out, that the feed energy required for lactation is proportional to the milk energy. On the basis that 1 pound of "The writer is indebted to Dr. Ellinger for the numerical data, which were pre- sented only graphically in the reference given. 430 BULLETIN No. 308 [May, F.C.M. = 340 calories, and on the basis of the mechanical equivalent of heat that 1 calorie = 3,084 foot-pounds, we have 1 pound F.C.M. = 1,048,560 foot-pounds and 1 pound F.C.M. per day = .022 horse- power. Accordingly, in Fig. 9 we would have a maximum power out- put of .533 (= 24.23 X .022) horsepower, which gradually declines with time, finally reaching zero with the cessation of lactation. This interpretation may serve to indicate the broad nature of the energy measure. It clearly puts the performance of the cow on a dy- namical basis. Nutrition Investigations. Hansson 25 * says, "Die beste Grundlage zur Berechnung des Nahrungsbedarfs der Kiihe bei der Produktion von Milch mit verschiedenem Fettgehalte ist der Kalorienwert der Milch je Kilogramm. " (The best basis of reckoning the food requirement of cows for the production of milk of different fat content is the calorific value of the milk per kilogram.) The advantage of measuring milk yield on an en- ergy basis for nutritional studies seems to be so plain as to require no extended discussion. For very refined investigations it would be de- sirable to have direct determinations of the energy value of the milk by the calorimeter. For the usual feeding trials equation (3), page 404 or the equivalent calorie formula, page 414 would seem to be amply accu- rate. 8 "It may be of interest to take any of the dairy feeding standards and compute the nutrients required at various fat percentages for one pound F.C.M. The re- sults will be found substantially constant. Haecker's data as above analyzed lead to the formula, Pounds of digestible nutrients for lactation = .327 F.C.M. His standard for maintenance is, Pounds digestible nutrients for maintenance per year = 2 . 893 W, where W is li ve weight of the cow in pounds. It is of interest to compare the observed feed consumption of Table 5 (1 feed unit = 1 kilogram of barley = 1.75 pounds of digestible nutrients) with the requirements computed by Haecker's formulas: Red Danish Crossbred Jersey Pounds digestible nutrients consumed, observed 5,388 4,809 4,347 Pounds digestible nutrients required, computed 5,393 4,818 4,274 This is a rather remarkable agreement between theory and observation. Since this paper was prepared there has come to hand Wisconsin Research Bulletin 79, by M. J. B. Ezekiel, P. E. McNall, and F. B. Morrison, entitled "Prac- tices Responsible for Variations in Physical Requirements and Economic Costs of Milk Production on Wisconsin Dairy Farms." Fig. 6 of this Wisconsin bulletin presents three sets of data from farm records from the states of Wisconsin, Virginia, and Pennsylvania, showing the relation between fat percentage and the yield and feed cost of the milk. The three sets of data are not in the closest agreement among them- selves, a result possibly of the difficulty of accurately evaluating all the factors in- volved, particularly pasture. The results from the Wisconsin farms agree fairly well with the proposition that feed cost in nutrients is proportional to the energy value of the milk. 192S\ ENERGY BASIS OF MEASURING MILK YIELD IN DAIRY Cows 431 Economic Interpretation. Certain economic aspects of equation (3) have been presented in detail elsewhere 13 - 17 * and it is sufficient here to say that the cost of producing milk, so far as affected by the fat per- centage of the milk, is proportional to the energy value of the milk. There is a growing disposition on the part of whole-milk buyers to ad- just the price of milk according to its fat test, and there seems to be a tendency for this adjustment to align more or less closely with the en- ergy value of the milk (cf. Fig. 2 of Gaines 13 *). Genetic Investigations. A possible use of energy yield in genetical analysis may be illustrated by a hypothetical case. Suppose we have two pure races of cattle, one of which has a genetic capacity of an annual yield of 10,000 pounds of 3.5-percent milk, and the other 7,551 pounds of 5.5-percent milk. If these two races are hybridized, we might an- ticipate obtaining a certain proportion of F 2 segregates which had a capacity of 10,000 pounds of 5 . 5-percent milk. But if we take the en- ergy yield as the measure of production, we find the two races have the same capacity, namely, 9,250 pounds F.C.M., and consequently we should expect all the F 2 generation to be of the 9,250-pound class, as- suming that the capacity of 9,250 pounds F.C.M. of the two original pure races was determined by similar factors. While we are speculating, let us consider a still wider divergence in the orginal stock. The reindeer produces milk containing 22 per- cent of fat. 4 * It is not extraordinaiy to conceive of a Holstein cow pro- ducing in 365 days 20,000 pounds of 3.3-percent milk. Many cows have exceeded that performance. Suppose such a race is crossed with the rein- deer (assuming for the sake of the argument that such a cross would be fertile) should we obtain in the F 2 generation an occasional female segregate producing 20,000 pounds of 22-percent milk in 365 days under favorable environmental conditions? Considered from the energy viewpoint, we should expect nothing of the kind, for the reindeer's energy-yield capacity is a mere fraction of that of the Holstein, and we should be lucky, therefore, to recover in F 2 even the original capacity of the Holstein ancestor.* Various breeding operations have been entered into at various times by various people with the idea of obtaining an improved dairy cow as a high-milk and high-fat-percentage segregate, on the basis that milk yield and fat percentage are not correlated. The above noted crossing of the Red Danish and Jersey breeds is an example, and much wider The foregoing speculation assumes inheritance and segregation in accordance with Mendelian principles. The actual inheritance of milk yield and composition of the milk is a very complicated affair, necessitating, on the Mendelian interpreta- tion, the assumption of multiple factors (cf. ' " 12 - 22 - "- 35 - 43 *). 432 BULLETIN No. 308 [May, crosses have been made, as mating a zebu male with Holstein females. The results of such crossings do not appear to promise the realization of increased capacity by such methods. To a certain extent, therefore, these hybridizing results may be regarded as experimental evidence that the energy yield is a more fundamental measure of performance than is the milk yield. An experiment to demonstrate the possibility of improving the dairy production of the daughters of scrub cows by the use of purebred dairy bulls, has been carried out at the Iowa Experiment Station. In one case the average of three lactations of a certain scrub cow and six lactations of a certain daughter of the cow by a Holstein bull are given 31 * as: M F f F.C.M. Dam 3,874 .6 192 .62 4 .97 4,439 Daughter 6,955 .5 266 .25 3 .83 6,776 Daughter/dam 1 .795 1 .382 .771 1 .526 The daughter's production shows thus an increase of 80 percent in milk and 38 percent in fat over and above that of the dam. The actual in- crease in work accomplished (F.C.M. yield) by the daughter is 53 per- cent. This may appeal to the reason as being a better expression of the improvement effected by the sire. a The dairyman who is selling whole milk at a fixed price per hun- dredweight may argue that he is concerned only with the increase in milk yield. Likewise, the one who is selling cream may argue that he is con- cerned only with the increase in fat yield. But if the biologically im- portant measure of activity of the mammary gland is the energy value of the milk solids, as seems to be sufficiently evident from the citations of the foregoing pages, then what the dairyman needs first of all is a high- energy-yielding (hard-working) cow. b If economic conditions are such that milk has money value only according to weight, then he will nat- urally want that high-energy-yielding cow which gives milk with a mini- mum energy value per pound, that is the cow with low fat percentage. If economic conditions are such that only the fat of the milk has money value, then he will want that high-energy-yielding cow which devotes the largest part of the energy of lactation to the production of fat. This is the cow with high fat percentage, as is clearly shown in Fig. 3. SIGNIFICANCE OF FAT PERCENTAGE The percent of fat in milk has been very extensively determined be- cause of economic reasons, and has become a very familiar characteristic a lt should be noted that this ratio method is not a good way of measuring the potential dairy capacity of the sire (cf. Yapp 42 *). b High yield is essential to efficiency of production (cf. Fig. 29 of Gaines 16 *). 1928} ENERGY BASIS OF MEASURING MILK YIELD IN DAIRY Cows 433 of breeds and individuals. Fat percentage is a universally used measure of the chemical quality of milk. Many investigators seem to regard the fat yield of a cow as being due to the milk yield and fat percentage. Thus Winters 40 * cites the rec- ords of two purebred full sisters: M F f F.C.M. No. 1 8,735.2 401.55 4.60 9,517 No. 2 8,345.5 479.30 5.73 10,528 and says of them: "Sister number 1 has a greater production of milk, but number 2 has a greater production of fat, due to the greater percent of fat in her milk. This is a case of physiological variation where the quantitative variation favored one sister but the qualitative favored the other one. " The quoted statement seems to involve the same sort of conception as is involved in the idea of securing a high-milk and high- fat-percentage cow by the crossbreeding methods mentioned in the pre- vious section. The italics are the present writer's. From a biological standpoint it is not proper to regard fat yield, at a given milk yield, as "due to" fat percentage. Fat yield is the direct result of the rate of fat secretion by the milk secreting cells and the time over which secretion continues. Likewise, milk yield is the result of the rate of milk secretion. In one case we are considering a parti- cular part of the activity of the mammary gland, namely, its elabora- tion of milk fat; in the other case we are considering the entire mass of the secretory product. Obviously fat percentage is merely a mathemat- ical expression of the ratio (X 100) of the average rate of fat secretion to the average rate of milk secretion. At a given rate of milk yield fat percentage is due to the rate of fat yield ; certainly the rate of fat yield is not, in any biological sense, due to the fat percentage. The criticism is offered, not so much for the special case quoted, as for its bearing on the general point of view. While the determination of fat percentage has been stimulated pri- marily by economic forces, it so happens, fortunately, that it is a very good biological measure of the properties of the entire and normal milk of the cow. There is a high correlation between fat percentage and both protein and water percentage, 14 *(r = .812 and .916, respectively) while, roughly, the percentage of lactose and ash may be regarded as constant. We have noted from Overman and Sanmann's 33 - 34 * work that fat percentage is very highly correlated with energy value per unit of milk (r = .9814). From the milk yield and fat percentage we have warrant, therefore, to estimate energy yield. The energy yield affords an inclusive, and fundamentally well- grounded measure of the amount of work performed by the cow in 434 BULLETIN No. 308 [May, milk secretion. The fat percentage gives a reliable index of the di- rection in which the work is performed, that is, the relative extent to which it is directed toward the elaboration of fat, of protein, and of lactose, as shown in Fig. 3. Energy yield may be regarded as the primary variable in dairy production, expressing the quantity of production. Fat percentage may be regarded as a secondary variable, expressing the kind of production. SUMMARY AND CONCLUSIONS The performance of the dairy cow at the pail is commonly measured by one or both of two expressions milk yield and fat yield. In Bul- letin 245 of this Station (1923) it was suggested that the energy yield, that is, the gross energy value of the milk, is a better measure of yield than either the milk or the fat. This paper is intended to bring the evidence on the subject up to date. It is based largely on prior perti- nent literature. Energy yield may be estimated with a reasonable degree of accu- racy from the milk yield and fat percentage. The correlation between fat percentage and energy value per unit of milk is of the order, r = .98 to .99. The formula used in Bulletin 245 was F.C.M. = AM + 15F, where F.C.M. ("fat-corrected milk") is gross energy value in terms of normal average cows' milk of 4-percent fat content, M is actual milk and F is fat, all in the same unit of weight. Evidence since accumula- ted quite fully substantiates the accuracy of this formula, but indicates that the energy value of 1 pound of 4-percent milk is about 340 large calories (instead of 330.6, as previously given). The corresponding cal- orie formula becomes E = 51M (2 % +/), where E is energy in large calories, M is milk in pounds, and / is fat percentage. Use of the F.C.M. formula is continued because of facility of computation and with the idea that the expression of energy yield in calories might be reserved for refined experimental work, where the energy value is determined by direct calorimetry. The F.C.M. formula appears to be sufficiently ac- curate for ordinary work. The nutrients required for lactation (maintenance excluded) per pound of milk are directly proportional to the energy value of the milk as computed by the above formula. The correlation between fat per- centage and nutrients for lactation per pound of milk is r = .648. It seems probable that the total feed consumption is also closely propor- tional to the energy value of the milk. This relation means practically, in terms of money, that the cost of milk production is proportional to the energy value of the milk. In nutritional work the energy value 1928} ENERGY BASIS OF MEASURING MILK YIELD IN DAIRY Cows 435 of the milk affords a comprehensive and well-grounded expression of yield. It was previously concluded that in so far as milk yield is affected by the composition of the milk, the yield is inversely proportional to the energy value per unit of milk, that is, the energy yield is not affect- ed by the fat percentage of the milk. This conclusion is here supported by additional evidence from the records of the Milking Shorthorn and Red Danish breeds. The correlation between fat percentage and milk yield is of the order, r = .2 to .4; but between fat percentage and energy yield, r = 0. As between different cows a certain amount of variability in milk yield is due to differences hi the composition of the milk. This source of variability is eliminated when the yield is measured on the energy basis. Energy yields are directly comparable so far as fat percentage of the milk is concerned. The lactation curve (rate of yield with time after calving) is more regular when expressed in terms of energy than in terms of milk or fat. Utilizing the mechanical equivalent of heat (1 calorie = 3084 foot-pounds) the energy lactation curve may be translated directly in terms of power: 1 pound F.C.M. per day = .022 horsepower. Measuring milk yield on an energy basis puts the performance of the cow on a dynamical basis. Considering milk yield on an energy basis exposes the fallacy of attempting to breed increased dairy capacity by hybridizing a high- milk, low-fat-percentage race with a low-milk, high-fat-percentage race, in the expectation of obtaining a high-milk, high-fat-percentage, F 2 segregate. The results of several crossbreeding experiments do not promise improvement in energy yield capacity, and this may be taken as experimental evidence that energy yield is a more fundamental meas- ure of performance than is milk yield. The biological significance of fat percentage is as a measure of the relative rates of secretion of the fat as a part and of the milk as a whole. At a given milk yield the fat yield is not, in any biological sense, due to or caused by the fat percentage. Fat percentage is a good index of the composition of the milk and of its energy value. Energy yield may be regarded as the primary measure of yield, showing the amount of work done in milk secretion. This work may be done in different directions, that is, to variable degrees in the elabo- ration of fat, protein and lactose. Fat percentage may be regarded as a secondary measure of yield, showing the direction in which the work is done. From a biological point of view the essential measures of perform- ance of the cow at the pail are the energy yield and fat percentage. 436 BULLETIN No. 308 [May, LITERATURE CITED 1. AMERICAN JERSEY CATTLE CLUB. The dairy cow demonstration at the Louisiana Purchase Exposition, St. Louis, Mo., U. S. A., 1904. 1905. 2. AMERICAN SHORTHORN BREEDERS' ASSOCIATION. Milking Shorthorn Year Book 5-7. 1920-1922. 3. ANDERSEN, A. C. Unders0gelser over Komaelkens Sammensaetning. (Investi- gations on the composition of cow's milk.) Nord. Jordbrugsforsk. 4/7: 133-145, (Beret. Nord. Jordbrugsforsk. For. 3d. Kong. Oslo, Juni, 1926.) 1926. 4. BARTHEL, CHR., AND BERGMAN, A. M. Renntiermilch und Renntierkiise. (Rein- deer milk and reindeer cheese.) Ztschr. Untersuch. Nahr. u. Genussmtl. 26, 238-241. 1913. 5. BAYLIS, W. M. Principles of general physiology. Longmans, Green and Co. 1920. 6. BECK, N. F0rste-fjortende Meddelelse fra Fors0gslaboratoriet om Resultaterne fra sammenlignende Fors0g med forskellige Kvaegracer paa Tranekjaer, 1905-1906 1918-1919. (First-fourteenth communication from the experi- mental laboratories on the results of cooperative experiments with vari- ous breeds of cattle at Tranekjaer, 1905-19061918-1919.) Andelsbog- trykkeriet i Odense, 1906-1920. (For Brody reference, see page 438.) 7. CASTLE, W. E. Inheritance of quantity and quality of milk production in dairy cattle. Nat. Acad. Sci. Proc. 5, 428-434. 1919. 8. COLE, L. J. The Wisconsin experiment in cross-breeding cattle. Cattle breeding: Proceedings of the Scottish Cattle Breeding Conference. 1924. 315-327. Oliver and Boyd. 1925. 9. ELLINGER, TAGE. The variation and inheritance of milk characters. Nat. Acad. Sci. Proc. 9, 111-116. 1923. 10. . Causes of variations in milk secretion and their bearing on prac- tical breeding methods. Proc. of the World's Dairy Congress 1923, 2, 1396-1401. 1924. (For Ezekiel reference see page 438.) 11. FREDERICKSEN, LARS. Forel0bige Oplysninger om nogle Fors0g med Malkek0er i Vinteren 1923-1924. Plan for nogle Fors0g med Malkek0er i Vinteren 1924-1925. (Preliminary information on some experiments with milk cows in the winter of 1923-1924. Plan for some experiments with milk cows in the winter of 1924-1925.) Meddel. Fors0gslab. Husdyrbrug. K. Vet. og Landboh0jskole (Denmark), 2. 1925. 12. GAINES, W. L. Inheritance of fat content of milk in dairy cattle. Amer. Soc. Anim. Prod. Proc. 1922, 29-32. 1923. 13. . Feed cost of milk production as affected by the percentage fat content of the milk. Jour. Agr. Res. 29, 593-601. 1924. 14. . Relative rates of secretion of various milk constituents. Jour. Dairy Sci. 8, 486-496. 1925. 15. . Measures of persistency of lactation. Jour. Agr. Res. 34, 373- 383. 1927. 16. . Persistency of lactation in dairy cows. Ill.-Agr. Exp. Sta. Bui. 288. 1927. 1928] ENERGY BASIS OF MEASURING MILK YIELD IN DAIRY Cows 437 17. . A price differential for whole milk. 111. Agr. Exp. Sta. Circ. 318. 1927. 18. . The deferred short-time test as a measure of the performance of dairy cows. Jour. Agr. Res. 35, 237-249. 1927. 19. and DAVIDSON, F. A. Relation between percentage fat content and yield of milk. 111. Agr. Exp. Sta. Bui. 245. 1923. 20. . Rate of milk secretion as affected by advance in lactation and gestation. 111. Agr. Exp. Sta. Bui. 272. 1926. 21. GOWEN, JOHN W. Studies in inheritance of certain characters of crosses be- tween dairy and beef breeds of cattle. Jour. Agr. Res. 15, 1-57. 1918. 22. - . Inheritance in crosses of dairy and beef breeds of cattle. II On the transmission of milk yield to the first generation. Jour. Heredity 11. 300-316. 1920. 23. . Inheritance in crosses of dairy and beef breeds of cattle. Ill Transmission of butterfat percentage to the first generation. Jour. Heredity 11, 365-376. 1920. 24. HAECKER, T. L. Investigations in milk production. Minn. Agr. Exp. Sta. Bui. 140. 1914. 25. HANSSON, NILS. Fiitterung der Haustiere. (Feeding domestic animals.) Verlag von Theodor Steinkopff, Dresden. 1926. 26. Holstein-Friesian Association of America. Holstein-Friesian Advanced Reg- ister Year Book 21-26. 1910-1915. 27. JACKSON, L. C., and ROTHERA, A. C. H. Milk: its milk sugar, conductivity, and depression of freezing point. Biochem. Jour. 8, 1-27. 1914. 28. VAN DER LAAN, H. F. Het osmotisch Evenwicht tusschen Bloed en Melk. (The osmotic equilibrium between blood and milk.) Chem. Weekbl. 12, 522-541. 1915. 29. . Das osmotische Gleichgewicht zwischen Blut, Milch und Galle (The osmotic equilibrium between blood, milk and bile). Biochem. ztschr. 71, 289-305. 1915. 30. LANGMACK, P. V. F. P. Anden Beretning om Unders0gelse af de enkelte Koers Maelk. (Second report on the investigation of the milk of indi- vidual cows.) Beret. Fors0gslab. K. Vet. og Landboh0jskole (Denmark) 107. 1921. 31. MCCANDLISH, A. C., GILLETTE, L. S., and KILDEE, H. H. Influence of environ- ment and breeding in increasing dairy production, II. Iowa Agr. Exp. Sta. Bui. 188. 1919. 32. OVERMAN, O. R., DAVIDSON, F. A., and SANMANN, F. P. Relation of solids in milk to fat and specific gravity of the milk. 111. Agr. Exp. Sta. Bui. 263. 1925. 33. and SANMANN, F. P. The energy value of milk as related to composition. 111. Agr. Exp. Sta. Bui. 282. 1926. 34. . Valeur du lait en calories. (Value of milk in calories.) Le Lait. 7, 149-161. 1927. 35. VON PATOW, C. F. Studien iiber die Vererbung der Milchergiebigkeit an Hand von fiinfzigjahrigen Probemelkaufzeichnungen. (Studies on the inheritance of milk yield on the basis of 50-years' milk records.) Zeitschr. f. Tierziicht, u. Ziichtungsbiol. 4, 253-329. 1925. 438 BULLETIN No. 308 36. SAMVIRKENDE DANSKE LANDBOFORENINGER. Stambog over K0er af R0d Dansk Malkerace. (Cooperating Danish Agricultural Societies. Herdbook of cows of the Red Danish dairy breed.) 1-4. 1921-1924. 37. STOCKING, W. A., and BREW, J. D. Milk the essential food. The Dairymen's League News. Jan. 10, 1920. 38. TAYLOR, WILLIAM, and HUSBAND, A. D. The effect on the percentage compo- sition of the milk of (a) variations in the daily volume and (b) vari- ations in the nature of the diet. Jour. Agr. Sci. 12, 111-124. 1922. 39. WHITE, G. C., and JUDKINS, H. F. Variations in the fat, solids-not-fat, and total solids in cow's milk. Conn. (Storrs) Agr. Exp. Sta. Bui. 94. 1918. 40. WINTERS, L. M. Animal breeding. Wiley and Sons. 1925. 41. WOLL, F. W. Studies in dairy production. Wis. Agr. Exp. Sta. Res. Bui. 26 1912. 42. YAPP, W. W. Transmitting ability of dairy sires. Amer. Soc. Anim. Prod. Proc. 1924, 90-92. 1925. 43. . The inheritance of percent fat content and other constituents of milk in dairy cattle. Cattle breeding: Proceedings of the Scottish Cattle Breeding Conference. 1924, 328-334. Oliver and Boyd. 1925. 44. BRODY, SAMUEL. Growth and development with special reference to domestic animals. X. The relation between the course of growth and the course of senescence with special reference to age changes in milk secretion. Mo. Agr. Exp. Sta. Res. Bui. 105. 1927." 45. EZEKIEL, M. J. B., McNALL, P. E., and MORRISON, F. B. Practices responsible for variations in physical requirements and economic "costs of milk pro- duction on Wisconsin dairy farms. Wis. Agr. Exp. Sta. Res. Bui. 79. 1927." "The last two references were added to the list just before the manuscript was printed, and therefore are not in alphabetical order. UNIVERSITY OF ILLINOIS-URBANA