THE UNIVERSITY
OF ILLINOIS
LIBRARY
630.7 II6b
A6RI6ULTUBAL UIBABY
UNIVERSITY OF ILLINOIS
Agricultural Experiment Station
BULLETIN No. 245
RELATION BETWEEN PERCENTAGE
FAT CONTENT AND YIELD
OF MILK
Correction of Milk Yield for Fat Content
BY W. L. GAINES AND F. A. DAVIDSON
I
UKRANA, ILLINOIS, JUNE, 192.3
CONTENTS OF BULLETIN No. 245
PAGE
INTRODUCTION 577
SOURCE OF DATA 578
HYPOTHESIS 579
PRESENTATION 580
The Constant Energy Curve 581
The Logarithmic Curve 583
Comparisons 583
The Constant Fat Curve 583
Age Correction 583
DISCUSSION 584
The Coefficient of Correlation 584
Holstein Cow Testing Association Records 584
Jersey Cow Testing Association Records 585
Nature of Advanced Registry Selection 586
Jersey Register of Merit Long-Time Records 588
Jersey Register of Merit Seven-Day Records 589
Guernsey Advanced Register Records 589
Ayrshire Advanced Registry Records 589
Brown Swiss Register of Production Records 590
Holstein-Friesian Advanced Register Long-Time Records 591
Holstein-Friesian A. R. O. Seven-Day Records 592
Summary of Evidence 593
CORRECTION OF MILK YIELD FOR FAT CONTENT 594
Derivation of Formula 594
Application of Formula 594
SUMMARY 597
CONCLUSIONS 598
LITERATURE CITED 598
TABLES . ..599-621
RELATION BETWEEN PERCENTAGE FAT CONTENT AND YIELD OF MILK
Correction of Milk Yield for Fat Content
BY W. L. GAINES, CHIEF IN MILK PRODUCTION, AND F. A. DAVIDSON, FIRST ASSISTANT IN DAIRY HUSBANDRY
INTRODUCTION
Among dairymen, it is a matter of common observation that, in general, the milk yields of cows tend to vary inversely with the per- centage fat content of the milk. Various statistical investigations, by the method of correlation, support this observation. Such investiga- tions have shown the existence of a significant negative coefficient of correlation between the two variables, percentage fat content of the milk and yield of milk. The present study is a further analysis of this relation based on 23,302 records of the milk and fat production of cows. It purposes to show the nature of the relation between per- centage fat content of the milk and yield of milk ; and to formulate a method of correcting milk yield to equate for the influence of fat content.
The dairy cow occupies her position in our agriculture primarily as a producer of milk. Cows are highly variable in milk yield; and this variability is a large factor in the immediate economy of milk production, and of great import in the possible future dairy develop- ment of the cow. But variability in milk yield is affected by many factors, and if the milk yield of a cow is to be used as an indication of her position on the scale of merit with reference to immediate economy and future development, it is desirable to distinguish the factors affecting milk secretion, and to have a measure of the effect of each. The advanced registry* records of the dairy breeds usually list three such factors, each of which is very potent in its influence on milk yield; viz., time (length of record), percentage of fat, and age of cow.**
*The term advanced registry is used frequently, as here, in a general sense to apply to any of the breeds.
** Among other factors affecting milk yield the list following may be sug- gestive: food supply (amount, character) ; body food reserves (body fat, mineral store); growth of cow; size of cow; pregnancy preceding lactation (sex of fetus, sire of fetus, normal term, premature or delayed delivery, birth weight) ; pregnancy during time of lactation; ovariotomy; frequency of milking; char- acter of milking ; previous development (exercise and training of the mammary function at preceding lactations); physical exercise; comfort (temperature, flies, etc.). Undoubtedly some of these are of considerable importance, while others may have little or no influence. Of the many important factors it is remarkable that we have had an adequate measure of the influence of only one, that of age. It is hoped the data following will supply a measure for one other, that of percentage fat content of the milk.
577
578 BULLETIN No. 245 [June,
The age of a cow has long been recognized as a factor affecting the milk yield. The advanced registry system when first established in 1885 took account of this fact. Various data have been published from time to time showing the absolute or relative milk yields by cows at varying ages. Gowen1 has shown that the relation between these two variables — age and yield — may be closely expressed by a logarith- mic curve, and has given the equations for the curves for the Hoi- stein, Jersey, and Guernsey breeds. These equations have been found valuable in this laboratory in equating the milk yields of cows so as to make the yields directly comparable in so far as the age factor is concerned.*
SOURCE OF DATA
The data used in this study have been taken from the records of cow testing associations in Illinois (unpublished**) and the published records of the Holstein-Friesian Association, the American Jersey Cattle Club, the American Guernsey Cattle Club, the Ayrshire Breeders' Association, and the Brown Swiss Breeders' Association.
The records of the cow testing associations include only two breeds — Holstein and Jersey — in numbers large enough to be of value for present purposes. The Holstein records are of both grades and .pure- breds, located in commercial dairy herds in the whole-milk districts of Illinois. The records used are from those associations only that are known to have had competent and reliable testers in charge, and whose members sold whole milk at about the same price (price being a factor in the amount of feed given the cows, and consequently a factor in milk yield). Very little advanced registry testing was practiced.
The Jersey records are of both grades and pure-breds, obtained in one association over a period of five years. The number of cows in- volved is consequently less than the number of records used. Whole milk was sold, the market paying, however, in exact proportion to the fat content of the milk. The quality of the cows and the condi- tions under which the records were made were similar to those of the Holsteins. No advanced registry testing was practiced.
*The use of corrections is common in the physical sciences. When the chemist determines the volume of a gas, he corrects his measurement to certain standard conditions; he makes a correction for temperature, a second correction for barometric pressure, and a third correction for the tension of aqueous vapor. Biological corrections of the kind under consideration here are just as much needed and just as useful as those used in the physical sciences. In many cases it is impossible to standardize the cause of variation, and in such cases the only recourse is to standardize the effect thru the use of a correction factor. The determination of biological corrections is complicated by the multiplicity of re- actions occurring simultaneously in the living organism, and this condition may subject the determination to error and to the necessity of revision as addi- tional evidence accumulates.
**The writers acknowledge the courtesy of Professor C. S. Rhode of the Dairy Department, University of Illinois, in supplying part of these records.
W2S} RELATION BETWEEN FAT CONTENT AND MILK YIELD 579
The records of the breed associations are the well-known advanced registry records. They need no explanation here, but it may be in point to recall that they are made under a wide range of conditions, and that in some cases no expense in feed, care, and manipulation is spared in order to secure a maximum recorded production. The goal of advanced registry testing (except possibly the Ayrshire) is based on the fat record rather than on the milk record. Consequently, there is a stimulus toward any manipulation that increases the real or ap- parent fat percentage as well as the yield of milk.
It is very seldom that all the cows of a herd are included in the advanced registry system, whereas it is very rarely that they are not all included in the cow testing association system. As compared with the cow testing association records, the advanced registry rec- ords represent a higher capacity portion of the total population, pro- ducing under conditions nearer the optimum for maximum production.
HYPOTHESIS
Preliminary study suggested that the relation between the per- centage fat content of the milk and the yield of milk is simple and logical; namely, (1) the solids-not-fat, as well as the fat itself, are concerned in the relation; (2) the relation depends on the energy value of the fat and the solids-not-fat, rather than directly on the amount of solids present; (3) the energy value of the total solids of the milk is constant, if all factors which affect milk yield, other than the solids content, are compensated.
If the above is in fact the case, the physiological relation between the two variables fat percentage and milk yield is revealed, and a base is established from which to correct milk yield for the influence of fat content. If the percentage fat content of the milk is a factor affecting milk yield according to a definite physiological relation, and this relation can be expressed mathematically, the use of such mathe- matical expression in the correction of milk yield for fat content is justified from a physiological standpoint. Indeed, correction by such a method is preferable to the use of an expression describing the rela- tion found in the advanced registry data because advanced registry selection and practices may to some extent distort the true relation. For the purpose of the present study, the following hypothesis is therefore adopted:
The milk yield of cows with varying fat percentages is such that the total energy value of the milk is constant if the effects of all fac- tors other than composition are equalized.
That is, by way of further explanation, there are many things which influence the amount of milk that cows produce; for example, the fat percentage of the milk, length of record, the individuality of the cow, age, feed, and so forth. The influence of fat percentage
580 BULLETIN No. 245 [June,
(or rather, composition as measured by fat percentage) is the par- ticular factor now under study ; and the proposition of the hypothesis is that if the effects of each of the other factors are made equal for each cow, the energy value of the total milk produced by each cow will be the same — a constant. The influence of fat percentage on yield is, according to the hypothesis, a function of the energy value of the fat plus the energy value of the solids-not-fat present in the milk; and the influence is measured directly by the energy value of the solids. The milk yield must, by the hypothesis, be inversely pro- portional to the energy value of the solids per unit of milk.
Now, in order to subject the hypothesis to test it is necessary to meet the condition that all factors except composition be equalized. It is impossible to do this directly for all factors. Indirect methods, based on statistical principles must be used.
If we take a large number of cows, representative of the same breed, working under similar conditions, and separate them into classes on the basis of the percentage fat content of their milk, and deter- mine the average milk yield of each class, we may assume that, as between the averages so obtained, all factors in milk yield are equal- ized, except the one on which the classification is based. On statistical principles, which need not be elaborated here, this will be true, within a certain probability of error, except as to factors which are also cor- related with fat percentage. The factor solids-not-fat is such an ex- ception, and that is why it is treated together with the fat. What we really have to consider is the influence of composition on milk yield.
There are undoubtedly some other factors, such as the size of the cow, which are correlated with fat percentage, but the net effect of all such factors is regarded as being so small as to be negligible.
The hypothesis is concerned with the energy value of the milk solids, but the records used give only the amount of milk and the fat content. It is necessary, therefore, to estimate the energy value, and the method and justification for this will appear shortly.
It is on the principles outlined above that the hypothesis was sug- gested by study of the data. On the same principles the validity of the hypothesis is put to test in the following pages, representative data from all the records available being used.
PRESENTATION
The records used give the fat percentage to the closest second decimal, and the milk yield in pounds and tenths. Each group of records is arranged in a correlation table (see pages 599 to 621), class intervals of 0.1 for fat percentage and 1,000 pounds for milk yield (20 or 50 pounds for the seven-day records) being used. The coeffi-
192S] RELATION BETWEEN FAT CONTENT AND MILK YIELD 581
cients of correlation and other constants have been derived by standard methods and are given in Table 21. The mean milk yields of the several fat percentage classes have been computed from the corre- lation tables and are given in tabular form (pages 600 to 618) and in the accompanying graphs. Included with these latter data, in both tables and graphs, are two other sets of data : first, the corresponding milk yields calculated from a fitted curve of constant energy, and the deviations of the observed from the calculated values; second, the corresponding milk yields calculated from a fitted logarithmic curve, and the deviations of the observed from the calculated values.
The Constant Energy Curve. — It is well known that the solids- not-fat content of normal milk varies with the fat content in a very definite ratio. Gowen2 finds, in Holstein cows, a correlation of -f- .8991 ± .0071 between these two constituents ; indicating that the solids-not-fat content of milk may be determined with reasonable accuracy from the fat content. The energy value of milk fat and of solids-not-fat is> also definite and well established. Stocking and Brew3 working with extensive data compiled from various sources have prepared a table which shows these several relations.* From their table we derive :**
*Overman* also gives data which bear on this relation. He has compiled several thousand complete analyses of milk of stated known purity and studied them from the standpoint of the food value of milk of varying percentage fat content. His data cover a range of fat percentage from 3 to 7, and show a linear relation between fat percentage and food (energy) value per quart of milk. The curve is in excellent agreement With that of Stocking and Brew as to direction but somewhat lower (about 7 percent) in absolute values. The difference in absolute values is accounted for in large part by a variance in the energy values used by the two authorities for fat and solids-not-fat. ** Symbols are used as follows:
D = deviation of observed from calculated milk yield, in pounds.
E — energy of milk solids, in large calories.
ECM = milk yield corrected for energy value to 4 percent fat.
f = frequency.
F = milk fat, in pounds.
FCM — milk yield corrected for fat to 4 percent fat.
F-SCM = milk yield corrected for fat and solids to 4 percent fat.
M = milk, in pounds.
•»rci S(4-D) — S( — D)
ME — mean error, v ~ — : ±_1 '—
n
Me = milk yield, in pounds, calculated from constant energy curve. M, =. milk yield, in pounds, calculated from constant fat curve. M, = milk yield, in pounds, calculated from logarithmic curve. M0 — mean milk yield, in pounds, observed. n = number of values, r =i coefficient of correlation. -,
(y D2
EE = root mean square error, A ,'
\ n
S-N-F — solids-not-fat, in pounds. .
s-n-f =i percentage solids-not-fat content of milk. *P**£
t = percentage fat content of milk. .^
S = summation.
582 BULLETIN No. 245 [June,
s-n-f = 7.1 -f 0.4 t
E = 132.06 M -f 4964 F (and, since F = .01 Mt) = 132.06 M -f 49.64 Mt = 49.64 M (2.66 -f t)
By hypothesis, E is constant, say 49.64a (a being a constant the value of which is to be determined). Then, for the amount (pounds) of milk, Me, necessary to satisfy this value of E, we have:
49.64 Me (2.66 + 1) = 49.64a and,
M - a
= 2.66 -ft
This curve is arbitrarily so fitted to the observations that at values of t corresponding to those of the observations,
SM« = 3M.
Hence,
or,
and,
2Mn
a=-
* 2.66 -f t
The method of fitting causes the sum of the plus deviations and the sum of the minus deviations to be equal in value. It does not
2 (_I_J)) _ 2 ( _ D)
necessarily reduce either the mean error, — — , or the
2 D2 root mean-square error, ^/ - 1 to a minimum. However, the method
answers for present purposes. The constants are given in Table 22. The reader should bear in mind that the energy curve is an ex- pression of the hypothesis. While it is "fitted" to the observations, this "fitting" only adjusts the mean level of the curve to the mean level of the observations of milk yield. Its shape and general direc- tion are fixed and inflexible. If it conforms to the observations, that conformity is evidence that fat percentage affects milk yield and that the effect of fat percentage on milk yield is measured directly by the energy value of the milk solids. If the energy curve conforms to the observations, it is evidence in support of the validity of the hypothesis.
1923] RELATION BETWEEN FAT CONTENT AND MILK YIELD 583
The Logarithmic Curve. — In general, the data suggest that a curve of the type y = a-)-bx-(-c Iog10 (x-|-a) should be adapted to fit the observations. Further, this type of curve has been found appli- cable to the expression of many biological relations. Consequently, it has been used here, and has been fitted to each set of data by the method of -moments, using Miner's5 equations and tables. The con- stants for the several equations are given in Table 22. The logarithmic curve is used purely for purposes of comparison.
Comparisons. — The graphs (Figs. 1 to 10) give a visual impression of how well the observations support the hypothesis: first, by com- paring the energy curve, which represents the hypothesis, with the observations themselves ; second, by comparing the energy curve with the fitted logarithmic curve. A further comparison with the logarith- mic curve is afforded by the tabular presentation (see pages 599 to 621) . Here a numerical expression of the fit of the energy curve is attempted by giving, for both curves, the mean error, and the root mean-square error. These errors are given also in the graphs. If the error of the energy curve is not greater than that of the logarithmic curve, then, so far as the logarithmic curve is a guide, the observations support the hypothesis. Likewise, an error for the energy curve greatly in excess of that for the logarithmic curve, shows a lack of support. The errors for the several sets of data are brought together in Table 23.
The Constant Fat Curve. — Since a fat standard is used as the basis of admission to the advanced registry, and since fat yield is quite generally used as a measure of a cow's production, it has seemed desirable to consider the yield of milk required for a constant yield
Q
of fat. The equation for the curve of constant fat is Mf =— , and
u
this curve has been fitted by determining a after the same manner as in the energy curve. The data are given only in summary form (Tables 22 and 23), except that for the purpose of illustration the curve is drawn into one of the graphs (Fig. 1).
Age Correction. — It has been found unnecessary to use an age- correction factor for the milk yields, except in two cases where a comparatively small number of records is used. For a limited num- ber of records it serves to smooth the data materially, and would prob- ably be useful in smoothing the values for the end and near-end fre- quencies in other cases. The two cases corrected are the Brown Swiss and the early Holstein seven-day records. The Brown Swiss records, as published, give the age only by groups. Yields are cor- rected to age of maximum yield by using Gowen's1 equation for the Holstein breed. The Holstein seven-day records have been corrected to the age of 8 years 9 months by using data given by Miner.5
584 BULLETIN No. 245 [June,
DISCUSSION
The Coefficient of Correlation. — Table 21 shows the correlation between fat percentage and milk yield to be negative in every case. The coefficient is not very high in any case but is significant in every case. The correlation for the Holstein and Jersey cow testing asso- ciations (r — — .198 ± .012 and — .212 ± .021, respectively) have the most meaning from the standpoint of the normal relation between percentage fat content and yield of milk because the populations they represent are the least selected of any of the groups.
Advanced registry selection (except the Ayrshire), by reason of the entrance requirements, tends to increase the negative correlation. This appears prominently in the case of the Jersey seven-day records, where r = — .506 ± .026. The entrance requirement in this class is twelve pounds of fat regardless of age. Inspection of the correlated distributions (Table 7) shows that a considerable part of the total population is cut off in the upper left portion (low fat percentage and low milk yield). The effect of this is to give a higher negative value to r than would be obtained from a distribution representative of the whole Jersey population (see also Fig. A). Exactly the same prin- ciple opesates, in lesser degree, in the other advanced registry groups, except in the Ayrshire. The Ayrshire standard is peculiar in that there is a minimum milk requirement besides the usual fat require- ment. The effect of the additional milk requirement is nil at values of t below 3.57^.29 (the value varying with age), but above that point the milk requirement tends to give a positive correlation. There are also other complications (see Roberts,6 page 73).
The low value of r is caused in part by the great variability in milk yield, due to the inherent quantitative differences in the function of milk secretion and to the extreme susceptibility of this function to environmental factors. Everyone knows, of course, that a knowledge of the percentage fat content of a cow's milk does not justify an estimate of her milk yield. But the fact of a significant correlation shows that there exists some definite relation between the fat per- centage and the mean milk yield of a number of cows. The nature of this relation is brought out more clearly by the graphs and tables for each group of records.
Holstein Cow Testing Association Records. — The data for these records are found in Tables 1 and 2, and Fig. 1. Survey of the graph shows that the energy curve is very nearly coincident with the logarithmic curve. Its mean error is one pound greater, and its root mean-square error six pounds less than for the logarithmic curve. If there is any choice between the two it would seem to be in favor of the energy curve, either on the basis of the magnitude of the errors or the general impression formed by study of the graph.
1923}
RELATION BETWEEN FAT CONTENT AND MILK YIELD
585
The curve of constant fat is added in Fig. 1 for the sake of illus- tration. It is quite obvious that fat yield is not an equitable measure of production within the classes represented. The fat curve has a mean error of 555 pounds and a root mean-square error of 775 pounds (Table 23), or nearly double that of the energy curve. It is not given in the data for the remaining records since it bears a similar relation to the energy curve in all cases.
?-
i.
»„
waf/M
osse*vATte4j *f
S3 SS S7
ffr COMTCHT Of MILK
FIG. 1. — RELATION BETWEEN FAT PERCENTAGE AND MILK YIELD: HOLSTEIN-
FRIESIAN Cow TESTING ASSOCIATION YEARLY RECORDS
2,773 records. Data from Table 2, page 600
The 2,773 records concerned here should be thoroly representative of the Holstein breed, under good conditions of management, in herds dependent primarily upon the sale of milk for their income. The majority of the cows were high grades.
It will be noted that while the general tendency of the observa- tions is plainly in the. direction of the energy curve, there are many rather wide deviations from it. Toward either end, where the fre- quencies are small, wide fluctuations are natural. But even with larger frequencies there are some apparently wide deviations. For example, the class at t — 3.345 shows a deviation of 132 pounds. Considering the 337 records of this class by themselves, the mean, 7,384, has a probable error of 79.6. From this we might expect a de- viation of 132 about once in five. For the other classes, having smaller frequencies, the chance of error in the mean would be still greater. Consequently, some irregularity in the observations is to be expected and is no reason for discrediting the data.
Jersey Cow Testing Association Records. — The data for these rec- ords appear in Tables 3 and 4, and Fig. 2. The observations are less regular in distribution than those in Fig. 1. The number of records is much smaller, 970, and the number of cows represented still smaller.
Again, the energy curve is practically coincident with the logar- ithmic curve. Its errors are greater by 6 pounds for the mean and
586
BULLETIN No. 245
[June,
1 pounds for the root. This is less than 2 percent, and considering the nature of the data is very close.
!•
c//>?, ter t T.A.
+6 4M S.O A* ** M S.e 6.0 ea «4 Ce SB
far CONTENT or MILK
FIG. 2. — RELATION BETWEEN FAT PERCENTAGE AND MILK YIELD: JERSEY
Cow TESTING ASSOCIATION YEARLY RECORDS
970 records. Data from Table 4, page 602
. The records of the Holstein and Jersey cow, testing associations are regarded as supporting the hypothesis remarkably well. No similar records for other breeds were available for study. We have to consider next the advanced registry records, but before doing so it is necessary first to discuss the nature of the selection effected by the requirements for admission to the advanced registry.
Nature of Advanced Registry Selection. — Fig. A is a diagram de- signed to illustrate the nature of advanced registry selection. It is intended to represent a correlation surface for fat percentage and milk yield for a very large number of cows under official test con- ditions. All cows above the line AB would be excluded by an entrance requirement of 360 pounds of fat, and all cows below the line could qualify. If the broken line represents the periphery of the popula- tion, and the population increases in density with some uniformity toward its center, then it is clear from the diagram that an increasing proportion of cows is eliminated as we go from higher to lower fat percentage. Since it is the poorest grades of cows that are eliminated, the qualitative effect must be to improve the mean grade of those left. And improvement would increase as we go from higher to lower fat percentage, because of the increasing proportion of the population eliminated.
The proportion of a total population that would fail to qualify for the advanced registry is uncertain. Roberts13 refers to 98 Ayrshires which were tested and failed to qualify (with an entrance require- ment of 214.3 to 322 pounds of fat, according to age) presumably comparable with 1,091 that did qualify. Since the poorest cows are probably not tested at- all, it would seem that advanced registry re- quirements would exclude at least 10 percent of the total population if all were tested.
19*8]
RELATION BETWEEN FAT CONTENT AND MILK YIELD
587
tr CoM-rttrr tr MILK
*/*> I
B-
FIG. A. — ILLUSTRATING THE NATURE OF THE SELECTION EFFECTED BY A
CONSTANT FAT PRODUCTION REQUIREMENT
The broken line is intended to represent the periphery of a very large cow population. The line AB is drawn thru the points correspond- ing to 360 pounds of fat. Note that selection is more severe at low fat percentages than at higher fat percentages. The figure is purely dia- grammatic.
On the basis of energy yield, the nature of advanced registry selec- tion is shown clearly by Table A. The table shows that selection be- comes increasingly more severe in going from higher to lower fat percentages. It is therefore to be expected that the mean energy yield shown by advanced registry records will be greater at lower values of t than at higher values of t. Since the energy curve is ad- justed to the mean of the observations, there will be a tendency toward plus deviations at the left end of the graphs, and a less marked tendency toward minus deviations at the right, assuming the energy
TABLE A. — ILLUSTRATING THE NATURE OF THE SELECTION EFFECTED IN ADVANCED REGISTRY BY A FIXED FAT ENTRANCE REQUIREMENT
(Note increasing increment in E in going from higher to lower fat percentages)
|
t |
F |
M |
E |
Increment in E |
|
000 omitted |
||||
|
8.0 7.0 6.0 5.0 4.0 3.0 2.0 |
360 360 360 360 360 360 360 |
4 500 5 143 6 000 7 200 9 000 12 000 18 000 |
2 381 2 466 2 579 2 738 2 976 3 372 4 164 |
85 113 159 238 396 792 |
588
BULLETIN No. 245
[June,
curve to represent the true relation for the unselected population. Bearing this in mind, we may now consider the advanced registry data in relation to the hypothesis.
Jersey Register of Merit Long-Time Records. — The data for this group are given in Tables 5 and 6, and Fig. 3. Considering the graph, it will be seen that the energy curve does not conform closely to the logarithmic curve. That the energy curve does not go thru the observations quite so well as the logarithmic curve is shown both by inspection and by the errors. The logarithmic curve, of course, is
4.4 4.9 4JB
S.O &» 9.4 SS S» t.O At 8.4 9.9 9.6
fAr CONTC.NT or MILK
7.0 7-t 7.4 79
FIG. 3. — EELATION BETWEEN FAT PERCENTAGE AND MILK YIELD: JERSEY
REGISTER OF MERIT LONG-TIME RECORDS
8,038 records. Data from Table 6, page 604. (One observation at t •=. 8.145. M0 =: 4500 is omitted in the graph.)
determined solely by the observations on the selected advanced reg- istry population; whereas the energy curve can be expected to con- form to observations only on a random sample of the population. In how far is the selection effected by the entrance requirements an ex- planation of the difference between the two curves (accepting the logarithmic curve as representing the observations) ? Without at- tempting to answer quantitatively, it is apparent that the effect of selection would be to produce a difference similar to that actually found. Think of the energy curve as placed slightly lower on the graph so that the two curves coincide at the right-hand end. Com- pare, now, the curved wedge-shaped surface between the two, with the curved wedge-shaped surface of the population excluded by the entrance requirements as illustrated in Fig. A. It would seem quite possible that the differential selection of the entrance requirements is entirely responsible for the deviations of the logarithmic curve, or observations, from the energy curve.
192S]
RELATION BETWEEN FAT CONTENT AND MILK YIELD
589
Jersey Register of Merit Seven-Day Records. — The data for this group are given in Tables 7 and 8, and Fig. 4. Judged by the errors, the energy curve fits nearly as well as the logarithmic curve. Visual impression from the graph, however, is favorable to the logarithmic curve. It will be noted that the difference between the two is similar to that found in the case of the long-time records.
|
<36t |
• |
t/fA |
ser |
/fM |
7-i |
1AY |
||||||||||||||||
|
S *<U0 |
<£* |
0 ^> |
•n ° |
0 0 |
OSSt UX. |
'JHW earn |
ma * |
Me. n.4 |
*c 0.0 |
|||||||||||||
|
5 JW |
*W |
<o |
*> |
"™ |
entz |
w |
10.4 |
ISJ |
||||||||||||||
|
!» Q *H |
e* |
o |
o |
^TT |
o |
0 |
||||||||||||||||
|
D1""0" |
--w 0 |
o |
o •«•••» |
— «_ |
||||||||||||||||||
|
*** 180 |
o |
— ^. |
**. |
•»-« |
*~^ |
|||||||||||||||||
|
o |
far CONTENT of MILK
FIG. 4. — RELATION BETWEEN FAT PERCENTAGE AND MILK YIELD: JERSEY
REGISTER OF MERIT SEVEN-DAY RECORDS 367 records. Data from Table 8, page 606
Guernsey Advanced Register Records. — The data for this group are given in Table 9 and Fig. 5. The relation between the two curves, as shown in the graph, is very similar to that noted and discussed for the Jersey long-time records.
J« Jfl ¥.0 4t +4 +.» 46 S.O S.l 3.4 ft 5.8 «O 61 9.4 t.t 9» 7.0
FIG. 5. — RELATION BETWEEN FAT PERCENTAGE AND MILK YIELD: GUERNSEY
ADVANCED REGISTER RECORDS 3,564 records. Data from Table 9, page 607
Ayrshire Advanced Registry Records. — The data for this group are given in Table 10 and Fig. 6. The observations show, from left to right, first a descending tendency and then an ascending tendency.
590
BULLETIN No. 245
[June,
The logarithmic curve is not fitted to the whole data because the type used is not adapted. As previously pointed out, the Ayrshire entrance requirements are peculiar. At values of t above 3.57-4.29, selection becomes more severe, and consequently the mean energy yield of the right-hand end groups is increased. Making allowance for this, the Ayrshire data differ from the energy curve in a manner similar to that for the Jersey and Guernsey, and in accordance with expectation.
|
Y/fLff Of MtLK-CWT. s_l_st_L_i_; |
6YRSH/KC aaactvent |
j.m. •a MI |
»e. |
|||||||||||
|
\ |
^~ |
t»*t f*e» |
u*rt V |
147 113 |
191 H7 |
|||||||||
|
^ |
V |
° |
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^ |
% |
|||||||||||||
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— |
•*^ |
•**-. |
^ |
0 |
||||||||||
U 5* J-2 3.4 At 55 4* 4.2 ** 4.6 44 &0 Si £4 &*
nir COMTCMT of MILK
FIG. 6. — RELATION BETWEEN FAT PERCENTAGE AND MILK YIELD: AYRSHIRE
ADVANCED REGISTRY RECORDS 1,091 records. Data from Table 10, page 608
Brown Swiss Register of Production Records (Age-Corrected). — The data for this group are given in Tables 11, 12 , and 13 and Fig. 7. The age-correction factor applied here is that for the Holstein breed (for lack of better data) and may be subject to some error. The graph shows a great deal of irregularity in the observations, which is pos- sibly due to the small number of records, 311. The general trend of the observations is in conformity with the energy curve, but the data are hardly satisfactory for the purpose of fitting a curve.
o o taaa umo HMf.
^S>
28 3.0 iJt 0* 9.9 J.fl 4.0 +t +4 48 4.9 Sit
ntr COMTKHT of MILK
FIG. 7. — RELATION BETWEEN FAT PERCENTAGE AND MILK YIELD: BROWN
Swiss REGISTER OF PRODUCTION RECORDS 311 records, age-corrected. Data from Table 13, page 611
1923]
RELATION BETWEEN FAT CONTENT AND MILK YIELD
591
Hoist ein-Friesian Advanced Register Long-Time Records. — The data for this group are given in Tables 14, 15, 16, and 17, and in Figs. 8 and 9. Considering Fig. 8, which is based on Vols. 24 to 30, the records are seen to be exceptional. The center of the group shows some tendency to conform to the energy curve. But the right-hand portion is very remarkable. As the data stand, they do not support the hypothesis.* That the conditions of official testing were responsi-
|
2* |
* |
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|
at tea 200 19* /«< 179 l-l SJN *"> |
o o |
teta 0830 |
fW MOM* |
1.R.V 9 Mt. |
»u * 1£ |
-so |
|||||||
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o |
tffC CMUH |
U*t Y" |
**» <**s |
•to/ set |
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|
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if a jo A! 34 a.e 9.9 .& +t 44 *e
FXr COKTCMT Of Mil*
FIG. 8. — RELATION BETWEEN FAT PERCENTAGE AND MILK YIELD : HOLSTEIN-
FRIESIAN ADVANCED REGISTER LONG-TIME RECORDS 5,266 records, 1912-1919. Data from Table 15, page 613 (cf. Figs. 1, 9, 10).
ble for the exceptional results shown is indicated by the fact that Hoi- stein cows, under the conditions of the cow testing association ( Fig. 1 ) , showed an entirely consistent behavior in their records. Eckles7 has shown experimentally that the condition of the cow at freshening materially affects milk secretion, qualitatively, the fat percentage being increased by a fat condition of the cow. It is commonly be- lieved that the Holstein cow is especially susceptible to this influence. It may be offered in explanation that a part of the advanced registry
*It may be noted that the energy basis is, nevertheless, a more equitable basis of comparison than the fat basis, as shown by the errors, Table 23.
592
BULLETIN No. 245
Holstein cows, having normally a somewhat low value of t and a high value of M, were in high condition at freshening, and thereby the value of t was greatly increased while the value of M was not de- creased. Such a condition might distort the data to produce the effect observed.
Because of the exceptional nature of the above records, which may be called "modern," the earlier records of Vols. 18 to 24 are con- sidered. They are the first 1,003 long-time official records of the breed. The data (Fig. 9) show a somewhat similar tendency, but in lesser degree. It will be seen that judged by the logarithmic curve, the energy curve does not fit well; but judged by the observations themselves, it fits fairly well. This view is supported by the errors, which are not much greater for the energy curve than for the logarithmic curve.
|
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0 0 |
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A* tf it 30 42 **
Ktr COMTEMT Of MILK
FIG. 9. — RELATION BETWEEN FAT PERCENTAGE AND MILK YIELD: HOLSTEIN-
FRIESIAN ADVANCED REGISTER LONG-TIME RECORDS 1,033 records, 1906-1913. Data from Table 17, page 615. These are the first 1,003 long-time official records of the breed. Note the partial disappearance of the discordantly high milk yields shown at the higher fat percentages in Fig. 8.
Holstein-Friesian AM.O. Seven-Day Records (Age-Corrected). — The data for this group are given in Tables 18, 19, and 20, and Fig. 10. The records represent the first 277 cows admitted (1894-1898) to the Holstein-Friesian advanced registry under the system of official tests. The graph shows a slight tendency of the data in the direction noted for the long-time records. While there is not the closest agreement between the energy curve and the logarithmic curve, yet it is evident that the energy curve goes thru the observations strikingly well. Its mean error is less than that of the logarithmic curve, but its root error is somewhat greater.*
*It should be noted that the "modern" seven-day records do not support the hypothesis at all. They show, in fact, a tendency to constant milk yield. Refer- ence is had to those seven-day records made shortly after calving. For records made some time after calving, the energy relation may hold. The seven-day rec- ords are being studied further from this standpoint.
1923]
RELATION BETWEEN FAT CONTENT AND MILK YIELD
593
While the "modern" Holstein advanced registry records do not support the hypothesis, the early records, both long-time and seven- day, are regarded as supporting it very satisfactorily.
sn
540
i.i 12 zs a i» 31
VOLSTEIN ,t.R.O.
9asetnn»aM£.
r-aiK /u.
37 9.9 41 4* 4.S 4.7 +9
FIG. 10. — RELATION BETWEEN FAT PERCENTAGE AND MILK YIELD: HOLSTEIN-
FRIESIAN ADVANCED REGISTER SEVEN-DAY RECORDS 277 records, 1894-1898, age-corrected. Data from Table 20, page 618. These are the records of the first 277 cows of the breed admitted to the advanced register under the present system of official supervision. Note the practically complete disappearance of the discordantly high milk yields at the higher fat percentages shown in Fig. 8.
Summary of Evidence. — The coefficient of correlation (Table 21) indicates the presence of a definite relation between percentage fat content and yield of milk. As brought out further by the mean milk yields and by the fitted curves and their errors (as shown in the graphs and tables) this relation is in excellent conformity with that expressed in the hypothesis for all the records except the "modern" Holstein advanced registry records.
It is therefore held that the hypothesis is verified by the evidence at hand.*
*The hypothesis of this paper has a bearing, on the problems of inheritance of the characters fat percentage and milk yield. The low value of r as found in correlating the two variables has given rise to the notion that the genetic factors responsible for the two characters are independently transmitted and capable of combination in any way. Such may be the fact. But we must re- member that to secure the simultaneous development of high fat percentage and high milk yield would involve an extraordinary expenditure of energy. The hypothesis suggests that a high energy yield is no more certain of attainment with a high fat percentage than with a low fat percentage; and that there is no more likelihood of securing a super-dairy breed by crossing a high fat per- centage breed with a high milk yielding breed than there is within either breed itself, so far as the direct influence of the genetic factors determining the two characters in question is concerned.
An alternative explanation of the relation between fat percentage and milk yield deserves consideration. If the mean fat percentage of the various milk
594 BULLETIN No. 245 [June,
CORRECTION OF MILK YIELD FOR FAT CONTENT
Derivation of Formula. — The principal product of the dairy cow is her mammary product — milk, — variable in quantity and chemical composition. Composition itself, as measured by fat percentage, is a factor having a certain definite influence on quantity. It is desirable to express the mammary product in terms of milk of some certain standard composition, and this is readily possible because of the nature of the influence of composition on yield. The choice of the standard composition to be used is not predetermined, except that it be the normal composition of milk of some particular fat percentage. For the Holstein breed the choice might be the mean of the breed, say milk of 3.4 percent fat; for the Jersey breed, likewise, 5.4 percent fat. For general convenience and utility, it is better to have a single standard for all cows, and normal milk of 4.0 percent fat has been chosen as being near a mean and most convenient of use.
The problem is now to equate the milk yield at varying fat per- centages to the standard of a milk having a fat content of 4.0 percent. The equation takes the form,
Fat corrected yield Enersv vield
of milk (pounds), FCM = g gy %' -, , , nr/ ^--
Energy of 1 pound of 4.0% milk
132.06 M + 4964 F
330.62 = .4 M -f 15 F
Application of Formula. — It will be recalled that the "modern" Holstein advanced registry records do not support the proposition on which this formula is based. There may be some doubt as to whether the formula may equitably be applied to this class of records. The
yield classes be determined, it is found that there is a decrease in fat percent- age from lower to higher milk yields. 'On the basis of this, Gowen1 (p. 95) has offered, in explanation of the relation between fat percentage and milk yield, the proposition that a higher milk yield requires a greater expenditure of energy (in total) than a lower milk yield, and that the fat or fat precursors of the milk are drawn on to meet this energy requirement, thus reducing, to some extent, the proportion of fat' in the milk at the higher milk yields. According to Gowen's view, milk yield is cause and fat percentage is effect (milk yield, however, affecting fat percentage only to a minor degree) ; whereas, according to the view of the present paper, fat percentage (together with the correlated solids-not-fat percentage) is cause and milk yield is effect (fat percentage being, however, only one of many factors affecting milk yield). Both views have in common the recognition of an energy requirement in explanation of the relation between the two variables. To the writers, it does not seem reasonable to suppose that the fat or fat precursors of the milk should be the sole source of the energy required in milk secretion: whereas, it does seem reasonable to suppose that the energy requirement should be a determining factor in the amount of milk secreted, and that the energy requirement should be in proportion to the energy content of the solids of the milk secreted.
M8S} RELATION BETWEEN FAT CONTENT AND MILK YIELD 595
only apparent reason that it might not be so applied would be that the composition of the milk of advanced registry Holstein cows (under the particular conditions surrounding the production of their records) is different from that of other cows (or Holstein cows under ordinary conditions), where the fat percentage is the same. There is no evi- dence that it is different, but on the other hand there is some evidence* that it is not different. In the judgment of the writers, the discordant results noted are due to subjecting part of the population to unusual conditions and the discord would disappear if the whole population were subjected to the same condition. The formula is therefore re- garded as applicable to the class of records in question.
The proposition on which the formula is based is supported by the use of mean milk yields of groups. The question arises, is it applicable to individuals? The relation E = 132.06 M -f- 4964 F is naturally subject to some variation, and to that extent there is the probability of error in applying the formula to the individual. That such error would not be great is indicated by two facts : first, the fat itself rep- resents more than half the energy of the milk (except when t < 3.8) ; second, the solids-not-fat, which are responsible for the remainder of the energy, are closely correlated with the fat (r = +.9). Hence, the formula may be applied to the individual with the prob- ability of only slight injustice.**
The recommendation is therefore made that for comparative pur- poses in considering the milk production of cows, the yield of milk be corrected by the formula .4 M -|- 15 F ; where M = milk yield, in pounds, and F = fat yield, in pounds.***
* Unpublished data, Illinois Agricultural Experiment Station.
**It would be more accurate to determine the energy value calorimetrically. The greater accuracy is not regarded as a sufficient offset to the difficulties in- volved in the calorimetric determination to warrant its use, ordinarily. If the energy value is determined directly the equation would take the form:
E C M = — = .3025 E
330.62
Where both the solids and fat are determined, the equation might take the form:
F-S C M = 4220 F + 1860 S-N-F ^^ p «. ^ g.N.p 330.62
***As to the equity of this correction, further evidence, of a different sort, is to be had from the feed required for the production of milk of different fat percentages. On this, a great deal of experimental work is summarized and generalized in the feeding standards for milk production. Table B analyzes several standards on the basis of the energy value of the milk solids. It will be noted from the table that the feed required per unit energy of milk is practically a constant for the varying fat percentages (except with the Eckles standard). In point of feed required, the evidence of the feeding standards supports the equity of the correction formula.
596
BULLETIN No. 245
[June,
The results of experimental work in milk production are generally stated in terms of milk and of fat. There are often economic condi- tions that make it desirable to lay stress on one or the other of these terms. In other cases, where a physiological comparison is desired, it may be desirable to have a single expression to cover both terms, and for such purpose the above formula should be of value. To illustrate specifically, take the results of grading up from scrub cows
TABLE B. — RELATION BETWEEN PERCENTAGE FAT CONTENT OP MILK AND FEED REQUIRED TER UNIT ENERGY OF THE MILK SOLIDS
(The table shows the relative values of the feed required by various feeding
standards as given in Larson and Putney,8 at the several fat percentages
indicated. Four-percent miUc is taken as 100 for each standard.
The energy of the milk solids is estimated by the
formula given in the text.)
|
Feeding |
Fat |
contem |
of milk |
|||||||
|
standard |
2.5% |
3.0% |
3.5% |
4.0% |
4.5% |
5.0% |
5.5% |
6.0% |
6.5% |
7.0% |
|
Haecker |
98 |
99 |
100 |
101 |
101 |
101 |
101 |
102 |
||
|
Savage |
95 |
97 |
99 |
100 |
101 |
101 |
101 , |
101 |
101 |
100 |
|
Henry and Morrison. . . . |
96 |
97 |
99 |
100 |
101 |
101 |
101 |
101 |
101 |
101 |
|
Eckles |
102 |
101 |
100 |
102 |
104 |
109 |
115 |
121 |
||
|
Armsby |
91 |
92 |
96 |
100 |
100 |
103 |
103 |
103 |
105 |
105 |
We may now develop a point of some practical interest, namely, the relative feed cost of producing milk as affected by the percentage fat content. Table B shows the nutrients required for milk production (exclusive of maintenance) at different fat percentages to be in proportion to the energy value of the milk. We have seen above that the energy yield of cows is constant, so far as it is affected by the fat percentage of their milk. Therefore, the nutrients required for maintenance, per unit energy of the milk produced, are a constant so far as they are affected by percentage fat content (disregarding any correlation between fat percentage and size of cow). It follows, then, that the relative feed cost of producing milks of different fat percentages is substantially in accordance with the equation:
Feed cost per cwt. milk = X (.4 -(- ,15t),
where X is the feed cost per cwt. of 4.0-percent milk. To illustrate, if the feed cost of 4.0-percent milk is $2.00 per cwt., then the corresponding cost of 3.0- percent milk is $2.00 [.4 -j- (.15) (3)] =$1.70; and, of 5.0-percent milk, $2.00 [.4 -{-(.15) (5)] =$2. 30; and so forth. Or, to put it perhaps more simply, a difference of 1 in the percentage fat content of the milk corresponds to a differ- ence in feed cost which is equal to 15 percent of the feed cost of 4.0-percent milk. It is plain, at this point, that the argument of this paper is essentially that the energy value of the milk solids is an equitable basis of comparison of the production of cows. That the energy value should be expressed in terms of aver- age milk of 4.0-percent fat content is purely a matter of convenience and desire to retain the term ' ' milk. ' ' It was stated near the outset that the relation between fat percentage and milk yield is "simple and logical." The reason for the statement is seen now, since the laws of energetics may be expected to be involved in the secretion of milk, as they are in other life activities. Apparently, the water of the milk represents no expenditure of energy on the part of the mammary gland. The osmotic pressure of the milk and the blood are the same, so that there is no balance of osmotic energy with which to reckon. Consequently, the energy relation goes back entirely to the solids of the milk.
19SS]
RELATION BETWEEN FAT CONTENT AND MILK YIELD
597
by the use of dairy bred bulls as reported in Bulletin 188 of the Iowa Agricultural Experiment Station. The daughters of the Holstein bull used showed a milk production equal to 190 percent of that of the dams, and a fat production equal to 159 percent. The average production of the dams was 3,894 pounds FCM and of the daughters, 6,602 pounds FCM. The production of the daughters, on this basis, is 170 percent of that of the dams; and we may say that the dairy- bred bull has increased the dairy capacity of the first generation by 70 percent when compared with the stock with which he was mated (age is not taken into account here).
The formula should be of especial value in comparing the pro- duction of cows having a considerable difference in the percentage fat content of their milk. Table C has been prepared from the pub- lished records of five dairy breeds in order to show the relation be- tween the highest milk and highest fat records in each breed. Deci- mals are omitted from the milk and fat records.* Suppose it is de- sired to compare the records of the first two cows in the table. Cow B.P. has a recorded fat production 100 pounds greater than cow S.P.P. ; but the latter has more milk by 10,364 pounds. Which is the better record ? From the physiological standpoint of work performed, and reduced to terms of 4.0-percent milk, S.P.P. has the better record by 2,645 pounds. In like manner, comparison may be made between the breeds, if desired.
TABLE C. — HIGHEST MILK AND HIGHEST FAT RECORDS OF FIVE BREEDS
(August, 1922)
|
Name and Number |
Milk Ibs. |
Fat Ibs. |
Fat % |
FCM* Ibs. |
FCM* relative values |
|
Segis Pietertje Prospect HFHB 221846. . Bella Pontiac, CHB 46321 |
37 381 27 017 |
1 159 1 259 |
3.10 4.66 |
32 337 29 692 |
100 92 |
|
Murne Cowen, AGCC 195977 |
24 (HIS |
1 098 |
4.57 |
26 073 |
81 |
|
Countess Prue, AGCC 43785 |
18 627 |
1 103 |
5.92 |
23 996 |
74 |
|
Garclaugh May Mischief, ABA 27944.. . Lily of Willowmore, ABA 22269 |
25 329 22 596 |
895 956 |
3.53 4.23 |
23 557 23 378 |
73 72 |
|
Fauvic's Star, AJCC 313018 |
20 616 |
1 006 |
4.88 |
23 336 |
72 |
|
Lad's Iota. AJCC 350672 |
18 632 |
1 048 |
5.63 |
23 173 |
72 |
|
Hawthorn Dairy Maid, BSBA 6753 |
22 623 |
927 |
4.10 |
22 954 |
71 |
*Milk yield corrected for fat to 4.0-percent fat.
SUMMARY
The relation between percentage fat content and yield of milk is shown by analysis of ten groups of cow records, comprizing 23,302 records in all. Accordant results are shown by nine groups:
*The writers feel that the extensive printing of meaningless decimals in data of this nature as practiced by Agricultural Experiment Stations and Breed Associations, is without justification.
598 BULLETIN No. 245 [June,
970 Jersey Cow Testing Association yearly records
8,038 Jersey Register of Merit long-time records
367 Jersey Register of Merit seven-day records
3,564 Guernsey Advanced Register long-time records
1,091 Ayrshire Advanced Registry long-time records
311 Brown-Swiss Register of Production long-time records
2,773 Holstein Cow Testing Association yearly records
277 Holstein-Friesian Advanced Register seven-day records (Vols. 1-9)
1,003 Holstein-Friesian Advanced Register long-time records (Vols. 18-24)
Discordant results are shown by one group : 5,266 Holstein-Friesian Advanced Register long-time records (Vols. 24-30)
The relation supported by the majority of the data is made the basis of a correction formula for milk yield designed to equate for the influence of fat percentage on yield.
CONCLUSIONS
The percentage fat content of the milk is a factor affecting milk yield. 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 value of the milk solids, in the total milk yield, is a constant. For a group of comparable cows, the relation be- tween fat percentage and milk yield is expressed by the equation
o
M — — — — — — ; where M is the average milk yield (in pounds), t is
fat percentage, and a is a constant determined in value by the pro- ductive level of the particular group. As corollaries : F = .Ola — .0266a , .06036a .03376a
2156+T' where F is fat, S-N-F is solids-not-fat, S is solids (all, in pounds)
and a is the same constant as above.
The milk yields of cows may be corrected for the influence of fat content to the physiological equivalent of 4.0-percent (fat) milk by the equation, F C M = .4M -f 15F ; where F C M is "fat corrected milk," M is the actual milk yield, and F is the actual fat yield (all, in pounds).
LITERATURE CITED
1. GOWEN, JOHN W. Report of Progress on Animal Husbandry Investiga- tions in 1919. Maine Agr. Exp. Sta. Bui. 283. 1919.
2. GOWEN, JOHN W. Variations and Mode of Secretion of Milk Solids. Jour. Agr. Research, 16, 3, 79-102. 1919.
3. STOCKING, W. A., AND BREW, J. D. Milk — The Essential Food. The Dairymen's League News, Jan. 10, 1920.
4. OVERMAN, O. R. Food Values and Dairy Products. 111. Agr. Exp. Sta. Circ. 235. 1919.
5. MINER, JOHN RICE. Fitting Logarithmic Curves by the Method of Mo- ments. Jour. Agr. Research, 3, 5, 411. 1915.
6. ROBERTS, ELMER. Correlation Between the Percentage of Fat in Cow's Milk and the Yield. Jour. Agr. Research, 14, 2, 67. 1918.
7. ECKLES, C. H. Influence of Fatness of Cow at Parturition on Percent of Fat in the Milk. Mo. Agr. Exp. Sta. Bui. 100. 1912.
8. LARSON, C. W., AND PUTNEY, F. S. Dairy Cattle Feeding and Manage- ment. 1917.
19SS}
RELATION BETWEEN FAT CONTENT AND MILK YIELD
599
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600
BULLETIN No. 245
TABLE 2. — COMPARISON OP MEAN MILK YIELDS AS OBSERVED, AND AS CALCU- LATED FROM FITTED LOGARITHMIC AND CONSTANT ENERGY CURVES
Grade and Pure-Bred Holstein Cow Testing Association Records (See Table 1)
|
t |
f |
M0 |
M, |
D |
Me |
D |
|
2.545 |
3 |
8 500 |
8 483 |
+ 17 |
8 366 |
+ 134 |
|
2.645 |
10 |
7 400 |
8 276 |
- 876 |
8 209 |
- 809 |
|
2.745 |
17 |
8 147 |
8 089 |
+ 58 |
8 057 |
+ 90 |
|
2.845 |
36 |
7 778 |
7 919 |
- 141 |
, 7 910 |
- 132 |
|
2.945 |
86 |
8 023 |
7 761 |
+ 262 |
7 769 |
+ 254 |
|
3.045 |
139 |
7 608 |
7 615 |
- 7 |
7 633 |
- 25 |
|
3.145 |
202 |
7 718 |
7 478 |
+ 240 |
7 502 |
+ 216 |
|
3.245 |
238 |
7 277 |
7 348 |
- 71 |
7 375 |
- 98 |
|
3.345 |
337 |
7 384 |
7 225 |
+ 159 |
7 252 |
+ 132 |
|
3.445 |
322 |
7 220 |
7 107 |
+ 113 |
7 133 |
+ 87 |
|
3.545 |
283 |
7 058 |
6 994 |
+ 64 |
7 018 |
+ 40 |
|
3.645 |
256 |
6 871 |
6 886 |
- 15 |
6 907 |
- 36 |
|
3.745 |
218 |
6 610 |
6 781 |
- 171 |
6 799 |
- 189 |
|
3.845 |
169 |
6 808 |
6 680 |
+ 128 |
6 695 |
+ 113 |
|
3.945 |
140 |
6 529 |
6 582 |
- 53 |
6 593 |
- 64 |
|
4.045 |
99 |
6 389 |
6 487 |
- 98 |
6 495 |
- 106 |
|
4.145 |
65 |
6 654 |
6 394 |
+ 260 |
6 399 |
+ 255 |
|
4.245 |
47 |
6 117 |
6 304 |
- 187 |
6 307 |
- 190 |
|
4.345 |
36 |
6 194 |
6 216 |
- 22 |
6 217 |
- 23 |
|
4.445 |
20 |
6 100 |
6 130 |
- 30 |
6 129 |
- 29 |
|
4.545 |
16 |
5 438 |
6 045 |
- 607 |
6 044 |
- 606 |
|
4.645 |
14 |
5 929 |
5 963 |
- 34 |
5 961 |
- 32 |
|
4.745 |
7 |
5 929 |
5 882 |
+ 47 |
5 881 |
+ 48 |
|
4.845 |
5 |
4 900 |
5 802 |
- 902 |
5 802 |
- 902 |
|
4.945 |
4 |
6 750 |
5 724 |
+ 1026 |
5 726 |
+ 1024 |
|
5.045 |
1 |
6 500 |
5 647 |
+ 853 |
5 652 |
+ 848 |
|
5.245 |
1 |
5 500* |
||||
|
5.445 |
2 |
6 500* |
||||
|
Mean error |
248 |
249 |
||||
|
Root mean-square error |
397 |
391 |
*Excluded in fitting curves and computing errors.
1923]
RELATION BETWEEN FAT CONTENT AND MILK YIELD
601
TABLE 3. — CORRELATION OF THE VARIABLES PERCENTAGE FAT CONTENT AND YIELD OF MILK
Data from Jersey (Grade and Pure-Bred) Cow Testing Association Yearly Records
Percentage fat content of milk; class mid-points (add .045)
|
3.6 |
3 7 |
3 8 |
s q |
4 0 |
4 1 |
4 ?, |
4 3 |
4 4 |
4 5 |
4 6 |
4.7 |
4 8 |
4 q |
5 0 |
5 1 |
5 ?, |
||
|
^ |
||||||||||||||||||
|
25 |
1 |
1 |
1 |
J2 |
||||||||||||||
|
35 |
1 |
1 |
4 |
4 |
2 |
2 |
7 |
7 |
7 |
7 |
1? |
13 |
11 |
J2 |
||||
|
45 |
2 |
3 |
3 |
3 |
6 |
q |
q |
13 |
13 |
13 |
15 |
16 |
17 |
•O |
||||
|
55 |
2 |
i |
4 |
5 |
8 |
10 |
?3 |
13 |
20 |
20 |
?q |
17 |
17 |
14 |
CD |
|||
|
65 75 |
I |
3 1 |
3 |
2 a |
4 |
2 ?, |
9 6 |
8 4 |
12 8 |
12 6 |
7 4 |
13 11 |
11 7 |
17 7 |
6 1 |
9 3 |
g |
|
|
85 |
1 |
1 |
1 |
1 |
2 |
3 |
2 |
1 |
2 |
o |
||||||||
|
95 |
1 |
2 |
1 |
1 |
U |
|||||||||||||
|
Total |
2 |
1 |
7 |
7 |
12 |
16 |
20 |
35 |
46 |
46 |
59 |
54 |
66 |
69 |
71 |
54 |
55 |
|
Yield of milk (cwt.); class mid-points |
5.3 |
5.4 |
5.5 2 3 17 18 8 3 2 1 |
5.6 3 6 8 16 5 2 |
5.7 |
5.8 |
5.9 |
6.0 1 4 9 2 1 |
6.1 |
6.2 |
6.3 |
6.4 |
6.5 |
6.6 |
6.7 |
6.8 |
Total |
|
|
25 35 45 55 65 75 85 95 |
2 6 8 6 7 |
I 8 9 10 11 |
1 7 3 9 1 |
13 141 226 311 177 74 21 7 |
||||||||||||||
|
12 14 18 7 3 2 |
14 14 24 14 2 2 |
2 1 |
1 |
|||||||||||||||
|
1 3 2 |
3 1 |
1 |
2 |
1 1 |
1 |
|||||||||||||
|
1 |
1 |
|||||||||||||||||
|
1 |
||||||||||||||||||
|
1 |
||||||||||||||||||
|
40 |
29 |
21 |
17 |
3 |
||||||||||||||
|
Total |
56 |
70 |
54 |
41 |
6 |
4 |
2 |
2 |
2 |
2 |
1 |
970 |
602
BULLETIN No. 245
[June,
TABLE 4. — COMPARISON OF MEAN MILK YIELDS AS OBSERVED, AND AS CALCU- LATED FROM FITTED LOGARITHMIC AND CONSTANT ENERGY CURVES
Grade and Pure-Bred Jersey Cow Testing Association Records (See Table 3)
|
t |
f |
M0 |
M, |
D |
Me |
D |
|
3.645 |
2 |
4 541* |
||||
|
3.745 |
1 |
6 515 |
6 554 |
- 39 |
6 469 |
+ 46 |
|
3.845 |
7 |
6 785 |
6 385 |
+ 400 |
6 369 |
+ 416 |
|
3.945 |
7 |
6 928 |
6 249 |
+ 679 |
6 273 |
+ 655 |
|
4 . 045 |
12 |
5 583 |
6 133 |
- 550 |
6 179 |
- 596 |
|
4.145 |
16 |
6 124 |
6 030 |
+ 94 |
6 088 |
+ 36 |
|
4.245 |
20 |
5 400 |
5 937 |
- 537 |
6 000 |
- 600 |
|
4.345 |
35 |
5 700 |
5 851 |
- 151 |
5 915 |
- 215 |
|
4.445 |
46 |
5 565 |
5 770 |
- 205 |
5 832 |
- 267 |
|
4.545 |
46 |
5 980 |
5 694 |
+ 286 |
5 750 |
+ 230 |
|
4.645 |
59 |
5 568 |
5 621 |
- 53 |
5 672 |
- 104 |
|
4 . 745 |
54 |
5 444 |
5 552 |
- 108 |
5 595 |
- 151 |
|
4.845 |
66 |
5 712 |
5 485 |
+ 227 |
5 520 |
+ 192 |
|
4.945 |
69 |
5 572 |
5 420 |
+ 152 |
5 448 |
+ 124 |
|
5.045 |
71 |
5 430 |
5 356 |
+ 74 |
5 377 |
+ 53 |
|
5.145 |
54 |
4 815 |
5 295 |
- 480 |
5 308 |
- 493 |
|
5.245 |
55 |
4 827 |
5 235 |
- 408 |
5 241 |
- 414 |
|
5.345 |
56 |
5 160 |
5 176 |
- 16 |
5 176 |
- 16 |
|
5.445 |
70 |
5 243 |
5 119 |
+ 124 |
5 112 |
+ 131 |
|
5.545 |
54 |
5 407 |
5 062 |
+ 345 |
5 050 |
+ 357 |
|
5.645 |
40 |
5 000 |
5 007 |
-7 |
4 989 |
+ 11 |
|
5.745 |
29 |
4 845 |
4 952 |
- 107 |
4 930 |
- 85 |
|
5.845 |
41 |
5 256 |
4 898 |
+ 358 |
4 872 |
+ 384 |
|
5.945 |
21 |
4 595 |
4 845 |
- 250 |
4 815 |
- 220 |
|
6.045 |
17 |
4 382 |
4 792 |
- 410 |
4 760 |
- 378 |
|
6.145 |
3 |
4 088 |
4 740 |
- 652 |
4 705 |
- 617 |
|
6.245 |
6 |
5 666 |
4 689 |
+ 977 |
4 653 |
+ 1013 |
|
6.345 |
4 |
4 779 |
4 638 |
+ 141 |
4 601 |
+ 178 |
|
6.445 |
2 |
5 495 |
4 588 |
+ 907 |
4 550 |
+ 945 |
|
6.545 |
2 |
4 735 |
4 538 |
+ 197 |
4 501 |
+ 234 |
|
6.645 |
2 |
4 281 |
4 488 |
- 207 |
4 453 |
- 172 |
|
6.745 |
2 |
4 670 |
4 439 |
+ 231 |
4 405 |
+ 265 |
|
6.845 |
1 |
3 417 |
4 390 |
- 973 |
4 359 |
- 942 |
|
Mean error |
323 |
329 |
||||
|
Root mean-square error |
421 |
428 |
*Excluded in fitting curves and computing errors.
19 US]
RELATION BETWEEN FAT CONTENT AND MILK YIELD
603
TABLE 5. — CORRELATION OP THE VARIABLES PERCENTAGE FAT CONTENT AND
YIELD OP MILK
Data from Jersey Register of Mprii, Vols. 1916, 1917, 1918, 1919 All Long-Time Records, Including Reentries
Percentage fat content of milk; class mid-points (add .045)
|
3 8 |
A 9 |
4 0 |
1 1 |
4 2 |
4 8 |
4 4 |
1 ri |
4 6 |
4 7 |
4 R |
1 't |
r> 0 |
5 1 |
fi •> |
5 3 |
5 4 |
5 5 |
5 6 |
~i 1 |
ft 8 |
S 9 |
Continued below |
|
|
35 45 55 65 75 85 95 105 115 125 135 145 155 165 175 185 195 |
|||||||||||||||||||||||
|
1 42 70 112 92 09 45 21 12 10 6 .1 |
2 61 80 153 110 55 32 25 17 8 5 1 1 |
5 «8 92 159 97 48 88 21 11 8 2 2 3 1 |
7 79 97 134 100 56 31 22 13 5 4 3 |
12 09 130 156 90 56 30 24 12 4 4 fll |
14 62 141 109 92 5t 33 15 15 2 8 1 |
20 80 121 108 84 47 30 13 6 5 3 2 |
22 62 119 81 68 43 25 28 5 7 2 1 \ |
20 63 125 80 46 41 28 9 5 2 1 1 |
24 74 94 73 41 33 20 6 .7 2 2 2 |
||||||||||||||
|
1 2 15 20 22 14 10 6 1 1 |
1 18 18 32 20 12 11 11 2 8 2 |
8 19 38 38 29 22 13 6 6 2 8 |
8 37 88 52 33 20 20 13 7 8 |
Hi 40 61 70 44 31 14 4 4 3 1 2 1 |
25 65 107 95 59 40 22 13 11 5 2 |
24 01 102 74 51 43 19 16 9 5 8 |
|||||||||||||||||
|
2 1 2 8 1 1 |
2 2 8 7 5 8 2 |
4 1 7 9 2 7 |
|||||||||||||||||||||
|
1 |
"i 1 |
||||||||||||||||||||||
|
1 |
1 |
||||||||||||||||||||||
|
1 |
|||||||||||||||||||||||
|
1 |
1 1 |
2 |
|||||||||||||||||||||
|
1 |
ft |
1 |
|||||||||||||||||||||
|
1 |
|||||||||||||||||||||||
|
1 |
|||||||||||||||||||||||
|
Total |
1 |
2 |
11 |
.SO |
85 |
92 |
125 |
178 |
233 |
291 |
445 |
407 |
483 |
550 |
555 |
551 |
596 |
541 |
519 |
404 |
421 |
378 |
|
6.0 |
6.1 |
6.2 |
8.3 |
6.4 |
6.5 |
6.6 |
6.7 |
6.8 |
6.9 |
7.0 |
7.1 |
7.2 |
7.8 |
7.4 |
7.5 |
7.6 |
7.7 |
7.8 |
7.9 |
8.0 |
8.1 |
Total |
|
|
35 45 55 65 75 85 95 105 115 125 135 145 155 165 175 185 195 |
1 |
1 251 988 1593 1735 1348 853 542 330 187 100 59 28 14 7 1 1 |
|||||||||||||||||||||
|
18 54 66 66 41 22 17 a 6 a i 2 |
27 42 55 45 27 15 10 3 2 1 |
10 49 37 24 20 15 8 1 |
15 26 30 18 19 4 5 4 |
14 28 27 14 7 5 2 2 2 |
14 14 20 13 a 6 |
11 12 16 4 |
4 5 10 9 7 |
4 4 5 |
3 2 6 B |
"6 1 |
1 2 1 1 |
1 1 |
1 |
1 |
|||||||||
|
1 |
|||||||||||||||||||||||
|
4 |
1 |
||||||||||||||||||||||
|
a |
8 |
||||||||||||||||||||||
|
1 |
1 |
||||||||||||||||||||||
|
2 8 |
2 |
1 1 |
1 1 |
1 |
|||||||||||||||||||
|
1 |
|||||||||||||||||||||||
|
1 |
1 |
1 |
1 |
||||||||||||||||||||
|
1 |
|||||||||||||||||||||||
|
Total |
304 |
228 |
160 |
121 |
102 |
75 |
47 |
33 |
16 |
21 |
9 |
7 |
3 |
0 |
1 |
2 |
0 |
0 |
0 |
0 |
0 |
l |
8038 |
604
BULLETIN No. 245
[June,
TABLE 6. — COMPARISON OP MEAN MILK YIELDS AS OBSERVED, AND AS CALCU- LATED FROM LOGARITHMIC AND CONSTANT ENERGY CURVES
Jersey Register of Merit, Vols. 1916, 1917, 1918, 1919 All Long-Time Records, Including Reentries
(See Table 5)
|
t |
f |
Mo |
M, |
D |
Me |
D |
|
3.845 |
1 |
9 500 |
10 415 |
- 915 |
9 940 |
- 440 |
|
3.945 |
2 |
11 000 |
10 146 |
+ 854 |
9 789 |
+ 1211 |
|
4.045 |
11 |
9 227 |
9 913 |
- 686 |
9 643 |
- 416 |
|
4.145 |
30 |
9 700 |
9 707 |
- 7 |
9 502 |
+ 198 |
|
4.245 |
35 |
10 357 |
9 520 |
+ 837 |
9 364 |
+ 993 |
|
4.345 |
92 |
9 572 |
9 349 |
+ 223 |
9 231 |
+ 341 |
|
4.445 |
125 |
9 384 |
9 190 |
+ 194 |
9 101 |
+ 283 |
|
4.545 |
178 |
9 061 |
9 041 |
+ 20 -. |
8 974 |
+ 87 |
|
4.645 |
233 |
8 954 |
8 900 |
+ 54 |
8 851 |
+ 103 |
|
4.745 |
291 |
8 654 |
8 766 |
- 112 |
8 732 |
- 78 |
|
4.845 |
445 |
8 606 |
8 639 |
- 33 |
8 615 |
- 9 |
|
4.945 |
407 |
8 643 |
8 516 |
+ 127 |
8 502 |
+ 141 |
|
5.045 |
483 |
8 497 |
8 399 |
+ 98 |
8 392 |
+ 105 |
|
5.145 |
550 |
8 214 |
8 285 |
- 71 |
8 284 |
- 70 |
|
5.245 |
555 |
8 073 |
8 175 |
- 102 |
8 179 |
- 106 |
|
5.345 |
551 |
7 979 |
8 068 |
- 89 |
8 077 |
- 98 |
|
5.445 |
596 |
7 885 |
7 964 |
- 79 |
7 978 |
- 93 |
|
5.545 |
541 |
7 810 |
7 862 |
- 52 |
7 881 |
- 71 |
|
5.645 |
519 |
7 646 |
7 763 |
- 117 |
7 786 |
- 140 |
|
5.745 |
464 |
7 801 |
7 666 |
+ 135 |
7 693 |
+ 108 |
|
5.845 |
421 |
7 255 |
7 572 |
- 317 |
7 603 |
- 348 |
|
5.945 |
378 |
7 378 |
7 478 |
- 100 |
7 514 |
- 136 |
|
6.045 |
304 |
7 535 |
7 387 |
+ 148 |
7 428 |
+ 107 |
|
6.145 |
228 |
7 078 |
7 297 |
- 219 |
7 343 |
- 265 |
|
6.245 |
160 |
6 907 |
7 209 |
- 302 |
7 261 |
- 354 |
|
6.345 |
121 |
6 929 |
7 122 |
- 193 |
7 180 |
- 251 |
|
6.445 |
102 |
6 746 |
7 036 |
- 290 |
7 102 |
- 356 |
|
6.545 |
75 |
6 807 |
6 951 |
- 144 |
7 025 |
- 218 |
|
6.645 |
47 |
6 308 |
6 869 |
- 561 |
6 949 |
- 641 |
|
6.745 |
33 |
7 075 |
6 786 |
+ 289 |
6 875 |
+ 200 |
|
6.845 |
16 |
6 306 |
6 704 |
- 398 |
6 803 |
- 497 |
|
6.945 |
21 |
7 452 |
6 624 |
+ 828 |
6 732 |
+ 720 |
|
7.045 |
9 |
7 056 |
6 544 |
+ 512 |
6 662 |
+ 394 |
|
7.145 |
7 |
7 500 |
6 466 |
+ 1034 |
6 595 |
+ 905 |
|
7.245 |
3 |
6 166 |
6 387 |
- 221 |
6 528 |
- 362 |
|
7.345 |
1* |
9 250 |
6 310 |
+ 2940 |
6 463 |
+2787 |
|
7.445 |
1 |
3 500 |
6 234 |
-2734 |
6 399 |
-2899 |
|
7.545 |
2 |
5 500 |
6 158 |
- 658 |
6 336 |
- 836 |
|
8.145 |
1 |
4 500** |
||||
|
Mean error |
439 |
457 |
||||
|
Root mean-square error |
770 |
777 |
*Taken from Roberts,6 Table V.
**Excluded in fitting curves and computing errors.
19183]
RELATION BETWEEN FAT CONTENT AND MILK YIELD
605
TABLE 7. — CORRELATION OF THE VARIABLES PERCENTAGE FAT CONTENT AND
YIELD OF MILK
Data from Jersey Register of Merit, Vols. 1911, 1913, 1915, 1916, 1917, 1918, 1919 All Seven-Day Records of Cows Four Years Old and Over
Percentage fat content of milk; class mid-points (add .045)
|
3.G |
3.7 |
3.8 |
3.9 |
4.0 |
4.1 |
4.2 |
4.3 |
4.4 |
4.5 |
4.6 |
4.7 |
4.8 |
4.9 |
5.0 |
5.1 |
8.2 |
5.8 |
5.4 |
5.5 |
6.6 |
5.7 |
Continued below |
|
|
190 210 230 250 270 290 310 330 350 370 390 410 430 450 |
|||||||||||||||||||||||
|
1 1 "2 1 |
8 2 2 8 1 |
1 8 1 2 |
|||||||||||||||||||||
|
3 6 4 4 2 1 1 1 |
8 4 4 4 |
6 4 5 3 3 |
ti 3 2 2 |
||||||||||||||||||||
|
3 14 3 3 1 3 1 2 |
4 10 7 1 "i i i |
8 3 5 1 3 |
6 5 2 4 <3 4 |
||||||||||||||||||||
|
1 7 2 |
3 2 9 4 1 1 |
(i 11 "3 3 3 |
|||||||||||||||||||||
|
5 2 a |
3 |
||||||||||||||||||||||
|
3 ] |
1 4 |
8 |
|||||||||||||||||||||
|
1 |
1 |
8 |
2 |
||||||||||||||||||||
|
1 |
2 |
2 1 |
1 |
3 |
2 |
1 I |
1 1 |
||||||||||||||||
|
1 |
1 1 |
1 |
|||||||||||||||||||||
|
1 |
•1 |
1 |
|||||||||||||||||||||
|
1 |
1 |
1 |
2 |
1 |
|||||||||||||||||||
|
l |
|||||||||||||||||||||||
|
1 |
1 |
1 |
1 |
||||||||||||||||||||
|
Total |
1 |
4 |
1 |
6 |
c. |
5 |
13 |
(i |
15 |
20 |
27 |
30 |
25 |
1(5 |
24 |
22 |
24 |
23 |
17 |
7 |
12 |
9 |
|
5 8 |
5 q |
R 0 |
R 1 |
R ? |
6.3 |
R 4 |
R 5 |
R R |
R 7 |
6 8 |
R <) |
7 0 |
7 1 |
7 V |
7 8 |
7 4 |
7 5 |
7 R |
7 7 |
7 X |
Total |
|
|
190 |
1 |
1 |
2 |
|||||||||||||||||||
|
210 |
8 |
A |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
22 |
|||||||||||
|
230 |
4 |
4 |
8 |
1 |
1 |
1 |
43 |
|||||||||||||||
|
250 |
1 |
fl |
1 |
1 |
41 |
|||||||||||||||||
|
270 |
1 |
1 |
1 |
•1 |
1 |
1 |
1 |
71 |
||||||||||||||
|
290 |
2 |
62 |
||||||||||||||||||||
|
310 |
1 |
35 |
||||||||||||||||||||
|
330 |
2 |
1 |
32 |
|||||||||||||||||||
|
350 |
25 |
|||||||||||||||||||||
|
370 |
1 |
14 |
||||||||||||||||||||
|
390 |
7 |
|||||||||||||||||||||
|
410 |
6 |
|||||||||||||||||||||
|
430 |
1 |
2 |
||||||||||||||||||||
|
450 |
1 |
5 |
||||||||||||||||||||
|
Total |
9 |
14 |
0 |
e |
5 |
2 |
5 |
1 |
0 |
1 |
0 |
2 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
1 |
367 |
606
BULLETIN No. 245
[June,
TABLE 8. — COMPARISON OF MEAN MILK YIELDS AS OBSERVED. AND AS CALCU- LATED FROM LOGARITHMIC AND CONSTANT ENERGY CURVES
Jersey Register of Merit, Vols. 1911, 1913, 1915, 1916, 1917, 1918, 1919 All Seven-Day Records of Cows Four Years and More of Age
(See Table 7)
|
t |
f |
Mo |
M, |
D |
Me |
D |
|
3.645 |
1 |
350.0 |
362.7 |
-12.7 |
353.2 |
- 3.2 |
|
3.745 |
4 |
360.0 |
354.4 |
+ 5.6 |
347.7 |
+ 12.3 |
|
3.845 |
1 |
330.0 |
347.1 |
-17.1 |
342.3 |
-12.3 |
|
3.945 |
6 |
353.3 |
340.5 |
+ 12.8 |
337.2 |
+ 16.1 |
|
4.045 |
6 |
333.3 |
334 5 |
- 1.2 |
332.1 |
+ 1.2 |
|
4.145 |
5 |
338.0 |
328.9 |
+ 9.1 |
327.2 |
+ 10.8 |
|
4.245 |
13 |
325.4 |
323.6 |
+ 1.8 |
322.5 |
+ 2.9 |
|
4.345 |
6 |
336.7 |
318.7 |
+ 18.0 |
317.9 |
+ 18.8 |
|
4.445 |
15 |
319.3 |
313.9 |
+ 5.4 |
313.4 |
+ 5.9 |
|
4.545 |
20 |
311.0 |
309.4 |
+ 1.6 |
309.1 |
+ 1.9 |
|
4.645 |
27 |
311.5 |
305.1 |
+ 6.4 |
304.8 |
+ 6.7 |
|
4.745 |
30 |
295.3 |
301.0 |
- 5.7 |
300.7 |
- 5.4 |
|
4.845 |
25 |
286.0 |
297.0 |
-11.0 |
296.7 |
-10.7 |
|
4.945 |
16 |
295.0 |
293.1 |
+ 1.9 |
292.8 |
+ 2.2 |
|
5.045 |
24 |
295.8 |
289.3 |
+ 6.5 |
289.0 |
+ 6.8 |
|
5.145 |
22 |
277.3 |
285.7 |
- 8.4 |
285.3 |
- 8.0 |
|
5.245 |
24 |
271.7 |
282.1 |
-10.4 |
281.7 |
-10.0 |
|
5.345 |
23 |
273.5 |
278.6 |
- 5.1 |
278.2 |
- 4.7 |
|
5.445 |
17 |
271.2 |
275.2 |
- 4.0 |
274.8 |
- 3.6 |
|
5.545 |
7 |
284.3 |
271.9 |
+ 12.4 |
271.4 |
+ 12.9 |
|
5.645 |
12 |
261.7 |
268.6 |
- 6.9 |
268.1 |
- 6.4 |
|
5.745 |
9 |
267.8 |
265.4 |
+ 2.4 |
265.0 |
+ 2.8 |
|
5.845 |
9 |
243.3 |
262.2 |
-18.9 |
261.8 |
-18.5 |
|
5.945 |
14 |
255.7 |
259.1 |
- 3.4 |
258.8 |
- 3.1 |
|
6.045 |
6 |
246.7 |
256.1 |
- 9.4 |
255.8 |
- 9.1 |
|
6.145 |
6 |
273.3 |
253.1 |
+20.2 |
252.9 |
+ 20.4 |
|
6.245 |
5 |
270.0 |
250.1 |
+ 19.9 |
250.1 |
+ 19.9 |
|
6.345 |
2 |
260.0 |
247.2 |
+ 12.8 |
247.3 |
+ 12.7 |
|
6.445 |
5 |
230.0 |
244.3 |
-14.3 |
244.6 |
-14.6 |
|
6.545 |
1 |
270.0 |
241.4 |
+ 28.6 |
241.9 |
+ 28.1 |
|
6.745 |
1 |
210.0 |
235.9 |
-25.9 |
236.8 |
-26.8 |
|
6.945 |
2 |
200.0 |
230.3 |
-30.3 |
231.8 |
-31.8 |
|
7.045 |
1 |
230.0 |
. 227.6 |
+ 2.4 |
229.5 |
+ .5 |
|
7.345 |
1 |
210.0 |
219.6 |
- 9.6 |
222.6 |
-12.6 |
|
7.845 |
1 |
210.0 |
206.7 |
+ 3.3 |
212.0 |
- 2.0 |
|
Mean error |
10.4 |
10.4 |
||||
|
Root mean-square error |
13.0 |
13.1 |
RELATION BETWEEN FAT CONTENT AND MILK YIELD
607
TABLE 9. — COMPARISON OF MEAN MILK* YIELDS AS OBSERVED. AND AS CALCU- LATED FROM LOGARITHMIC AND CONSTANT ENERGY CURVES
Guernsey Advanced Register* All Entries and Reentries to and Including Vol. XXIX
|
t |
f |
M0 |
M, |
D |
Me |
D |
|
3.7 |
4 |
10 750 |
10 992 |
- 242 |
10 393 |
+ 357 |
|
3.8 |
4 |
10 749 |
10 718 |
+ 31 |
10 232 |
+ 517 |
|
3.9 |
8 |
10 000 |
10 456 |
- 456 |
10 076 |
- 76 |
|
4.0 |
16 |
10 563 |
10 216 |
+ 346 |
9 925 |
+ 637 |
|
4.1 |
41 |
9 908 |
9 995 |
- 87 |
9 778 |
+ 130 |
|
4.2 |
68 |
9 661 |
9 790 |
- 129 |
9 635 |
+ 26 |
|
4.3 |
111 |
9 484 |
9 599 |
- 115 |
9 497 |
- 13 |
|
4.4 |
122 |
9 782 |
9 421 |
+ 361 |
9 362 |
+ 420 |
|
4.5 |
187 |
9 346 |
9 253 |
+ 93 |
9 232 |
+ 114 |
|
4.6 |
211 |
9 359 |
9 095 |
+ 264 |
9 105 |
+ 254 |
|
4.7 |
246 |
8 912 |
8 945 |
- 33 |
8 981 |
- «9 |
|
4.8 |
275 |
8 949 |
8 804 |
+ 145 |
8 861 |
+ 88 |
|
4.9 |
275 |
8 824 |
8 670 |
+ 154 |
8 744 |
+ 80 |
|
5.0 |
294 |
8 644 |
8 542 |
+ 102 |
8 629 |
+ 15 |
|
5.1 |
305 |
8 436 |
8 420 |
+ 16 |
8 518 |
- 82 |
|
5.2 |
273 |
8 367 |
8 303 |
+ 64 |
8 410 |
- 43 |
|
5.3 |
241 |
8 279 |
8 191 |
+ 88 |
8 304 |
- 25 |
|
5.4 |
216 |
8 166 |
8 083 |
+ 83 |
8 201 |
- 35 |
|
5.5 |
204 |
8 151 |
7 980 |
+ 171 |
8 101 |
+ 50 |
|
5.6 |
135 |
7 909 |
7 881 |
+ 28 |
8 003 |
- 94 |
|
5.7 |
87 |
7 951 |
7 785 |
+ 166 |
7 907 |
+ 44 |
|
5.8 |
76 |
7 552 |
7 693 |
- 141 |
7 813 |
- 261 |
|
5.9 |
52 |
7 750 |
7 604 |
+ 146 |
7 722 |
+ 28 |
|
6.0 |
42 |
7 083 |
7 518 |
- 435 |
7 633 |
- 550 |
|
6.1 |
21 |
7 297 |
7 435 |
- 138 |
7 546 |
- 249 |
|
6.2 |
20 |
6 599 |
7 354 |
- 755 |
7 461 |
- 862 |
|
6.3 |
10 |
6 950 |
7 276 |
- 326 |
7 377 |
- 427 |
|
6.4 |
7 |
7 964 |
7 199 |
+ 765 |
7 296 |
+ 668 |
|
6.5 |
7 |
6 678 |
7 111 |
- 433 |
7 216 |
- 538 |
|
6.6 |
3 |
6 249 |
7 055 |
- 806 |
7 138 |
- 889 |
|
6.7 |
1 |
6 250 |
6 985 |
- 735 |
7 062 |
- 812 |
|
6.8 |
1 |
6 249 |
6 917 |
- 668 |
6 987 |
- 738 |
|
6.9 |
1 |
9 250 |
6 852 |
+ 2398 |
6 914 |
+2336 |
|
Mean error |
331 |
349 |
||||
|
Root mean-square error |
546 |
569 |
*From Roberts,' Table X.
608
BULLETIN No. 245
[June,
TABLE 10. — COMPARISON OF MEAN MILK YIELDS AS OBSERVED, AND AS CALCU- LATED FROM LOGARITHMIC AND CONSTANT ENERGY CURVES
Ayrshire Advanced Registry (Ayrshire Breeders' Association Year Book), 1907,
1911, 1913, 1914*
|
t |
f |
M0 |
M, |
D |
Me |
D |
|
3.0 |
1 |
12 000 |
11 581 |
+ 419 |
: 11 012 |
+ 988 |
|
3.1 |
2 |
11 000 |
11 063 |
- 63 |
10 820 |
+ 180 |
|
3.2 |
5 |
10 400 |
10 683 |
- 283 |
10 636 |
- 236 |
|
3.3 |
14 |
10 536 |
10 385 |
+ 151 |
10 457 |
+ 79 |
|
3.4 |
49 |
10 082 |
10 142 |
- 60 |
10 285 |
- 203 |
|
3.5 |
56 |
9 768 |
9 938 |
- 170 |
10 118 |
- 350 |
|
3.6 |
75 |
9 720 |
9 763 |
- 43 |
9 956 |
- 236 |
|
3.7 |
106 |
9 651 |
9 610 |
+ 41 |
9 799 |
- 148 |
|
3.8 |
149 |
9 440 |
9 476 |
- 36 |
9 648 |
- 208 |
|
3.9 |
121 |
9 488 |
9 356 |
+ 132 |
9 501 |
- 13 |
|
4.0 |
132 |
9 360 |
9 249 |
+ 111 |
9 358 |
+ 2 |
|
4.1 |
117 |
9 120 |
9 152 |
- 32 |
9 220 |
- 100 |
|
4.2 |
96 |
8 911 |
9 064 |
- 153 |
9 085 |
- 174 |
|
4.3 |
65 |
9 154 |
8 984 |
+ 170 |
8 955 |
+ 199 |
|
4.4 |
46 |
8 663 |
8 910 |
- 247 |
8 828 |
- 165 |
|
4.5 |
28 |
9 089 |
8 843 |
+ 246 |
8 704 |
+ 385 |
|
4 6 |
10 |
9 500** |
||||
|
4 7 |
10 |
10 500** |
||||
|
4.8 |
6 |
8 833** |
||||
|
4.9 |
2 |
9 000** |
||||
|
JT |
1 |
11 000** |
||||
|
147 |
229 |
|||||
|
Root mean-square error |
181 |
317 |
*From Roberts,* Table XX.
**Excluded in fitting curves and computing errors.
RELATION BETWEEN FAT CONTENT AND MILK YIELD
609
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BULLETIN No. 245
[June,
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RELATION BETWEEN FAT CONTENT AND MILK YIELD
611
TABLE 13. — COMPARISON OP MEAN MILK YIELDS AS OBSERVED, AND AS CALCU- LATED FROM LOGARITHMIC AND CONSTANT ENERGY CURVES
Brown Swiss Register of Production, Jan. 1, 1922 All Long-Time Records, Age-Corrected
(See Table 12)
|
t |
f |
M0 |
M, |
D |
M. |
D |
|
2.945 |
2 |
16 500* |
||||
|
3 345 |
1 |
11 500* |
||||
|
3.445 |
6 |
14 500 |
14 261 |
+ 239 |
13 886 |
+ 614 |
|
3.545 |
17 |
13 559 |
13 835 |
- 276 |
13 663 |
- 104 |
|
3.645 |
19 |
13 184 |
13 465 |
- 281 |
13 446 |
- 262 |
|
3.745 |
32 |
13 781 |
13 143 |
+ 638 |
13 236 |
+ 545 |
|
3.845 |
31 |
12 984 |
12 862 |
+ 122 |
13 033 |
- 49 |
|
3.945 |
43 |
12 593 |
12 616 |
- 23 |
12 835 |
- 242 |
|
4.045 |
49 |
12 398 |
12 402 |
- 4 |
12 643 |
- 245 |
|
4.145 |
35 |
12- 329 |
12 214 |
+ 115 |
12 458 |
- 129 |
|
4.245 |
34 |
11 265 |
12 051 |
- 786 |
12 277 |
-1012 |
|
4.345 |
15 |
13 233 |
11 910 |
+ 1323 |
12 103 |
+ 1130 |
|
4.445 |
9 |
12 611 |
11 787 |
+ 824 |
11 932 |
+ 679 |
|
4.545 |
9 |
11 389 |
11 683 |
- 294 |
11 766 |
- 377 |
|
4.645 |
4 |
9 500 |
11 595 |
-2095 |
11 605 |
-2105 |
|
4 . 84 o |
4 |
10 500 |
11 461 |
- 961 |
11 296 |
- 796 |
|
4.945 |
1 |
13 500 |
11 414 |
+ 2080 |
11 147 |
+ 2353 |
|
Mean error |
671 |
709 |
||||
|
Root mean-square error |
947 |
980 |
*Ezcluded in fitting curves and computing errors.
612
BULLETIN No. 245
[June,
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RELATION BETWEEN FAT CONTENT AND MILK YIELD
613
TABLE 15. — COMPARISON OF MEAN MILK YIELDS AS OBSERVED, AND AS CALCU- LATED FROM LOGARITHMIC AND CONSTANT ENERGY CURVES
Holstein-Friesian Advanced Register, Vols. 24-30 All Long-Time Records, Including Reentries
(See Table 14)
|
t |
f |
M0 |
MI |
D |
Me |
D |
|
2.445 |
2 |
16 500* |
||||
|
2.545 |
5 |
21 360* |
||||
|
2.645 |
21 |
17 214 |
17 667 |
- 453 |
17 212 |
+ 2 |
|
2.745 |
63 |
17 595 |
16 924 |
+ 671 |
16 893 |
+ 702 |
|
2.845 |
112 |
17 000 |
16 365 |
+ 635 |
16 586 |
+ 414 |
|
2.945 |
207 |
15 355 |
15 927 |
- 572 |
16 290 |
- 935 |
|
3.045 |
318 |
15 729 |
15 576 |
+ 153 |
16 005 |
- 276 |
|
3.145 |
511 |
15 273 |
15 289 |
- 16 |
15 730 |
- 457 |
|
3.245 |
650 |
14 800 |
15 053 |
- 253 |
15 463 |
- 663 |
|
3.345 |
753 |
15 028 |
14 857 |
+ 171 |
15 206 |
- 178 |
|
3.445 |
675 |
14 446 |
14 694 |
- 248 |
14 956 |
- 510 |
|
3.545 |
588 |
14 840 |
14 558 |
+ 282 |
14 715 |
+ 125 |
|
3.645 |
485 |
14 091 |
14 446 |
- 355 |
14 482 |
- 391 |
|
3.745 |
326 |
14 009 |
14 353 |
- 344 |
14 256 |
- 247 |
|
3.845 |
222 |
13 973 |
14 278 |
- 305 |
14 037 |
- 64 |
|
3.945 |
120 |
14 475 |
14 217 |
+ 258 |
13 824 |
+ 651 |
|
4.045 |
71 |
14 880 |
14 170 |
+ 710 |
13 618 |
+ 1262 |
|
4.145 |
64 |
13 984 |
14 135 |
- 151 |
13 418 |
+ 566 |
|
4.245 |
34 |
15 617* |
||||
|
4.345 |
20 |
18 050* |
||||
|
4.445 |
11 |
14 318* |
||||
|
4.545 |
6 |
19 000* |
||||
|
4.645 |
1 |
18 500* |
||||
|
4.945 |
1 |
9 100* |
||||
|
Mean error |
348 |
465 |
||||
|
Root mean-square error |
401 |
566 |
*Excluded in fitting curves and computing errors.
614
BULLETIN No. 245
[June,
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19SS3]
RELATION BETWEEN FAT CONTENT AND MILK YIELD
615
TABLE 17. — COMPARISON OP MEAN MILK YIELDS AS OBSERVED, AND AS CALCU- LATED FROM LOGARITHMIC AND CONSTANT ENERGY CURVES
Holstein-Friesian Advanced Register, Vols. 18-24 • All Long-Time Records, Including Reentries
(See Table 16)
|
t |
f |
M0 |
M, |
D |
Me |
D |
|
2.545 |
1 |
13 500* |
||||
|
2.645 |
4 |
15 000 |
16 286 |
-1286 |
16 505 |
-1505 |
|
2.745 |
4 |
16 250 |
15 856 |
+ 394 |
16 199 |
+ 51 |
|
2.845 |
5 |
17 100 |
15 542 |
+ 1558 |
15 905 |
+ 1195 |
|
2.945 |
24 |
15 167 |
15 286 |
- 119 |
15 621 |
- 454 |
|
3.045 |
67 |
15 321 |
15 063 |
+ 258 |
15 347 |
- 26 |
|
3.145 |
95 |
15 290 |
14 863 |
+ 427 |
15 084 |
+ 206 |
|
3.245 |
113 |
14 385 |
14 679 |
- 294 |
14 828 |
- 443 |
|
3.345 |
148 |
14 264 |
14 507 |
- 243 |
14 581 |
- 317 |
|
3.445 |
132 |
14 182 |
14 344 |
- 162 |
14 342 |
- 160 |
|
3.545 |
133 |
13 816 |
14 188 |
- 372 |
14 111 |
- 295 |
|
3.645 |
89 |
13 938 |
14 039 |
- 101 |
13 887 |
+ 51 |
|
3.745 |
72 |
12 583 |
13 895 |
-1312 |
13 671 |
-1088 |
|
3.845 |
44 |
13 704 |
13 755 |
- 51 |
13 460 |
+ 244 |
|
3.945 |
36 |
13 890 |
13 618 |
+ 272 |
13 256 |
+ 634 |
|
4.045 |
12 |
14 750 |
13 485 |
+ 1265 |
13 059 |
+ 1691 |
|
4.145 |
12 |
13 083 |
13 355 |
- 272 |
12 867 |
+ 216 |
|
4.245 |
6 |
15 000* |
||||
|
4 345 |
2 |
13 000* |
||||
|
4.445 |
4 |
14 750* |
||||
|
Mean error |
524 |
536 |
||||
|
Root mean-square error |
720 |
746 V |
*Excluded in fitting curves and computing errors.
616
BULLETIN No. 245
[June,
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1923}
RELATION BETWEEN FAT CONTENT AND MILK YIELD
o
EH
T3
9
3
3 5 5
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618
BULLETIN No. 245
[June,
TABLE 20. — COMPARISON OF MEAN MILK YIELDS AS OBSERVED, AND AS CALCU- LATED FROM LOGARITHMIC AND CONSTANT ENERGY CURVES
Holstein-Friesian A. R. O. Seven-Day Records First 277 Original Entries, Age-Corrected
(See Table 19)
|
f |
M0 |
M, |
D |
M. |
D |
|
|
2.145 |
1 |
625.0* |
||||
|
2.345 |
1 |
525.0 |
534.4 |
- 9.4 |
526.5 |
- 1.5 |
|
2.445 |
1 |
475.0 |
521.3 |
-46.3 |
516.2 |
-41.2 |
|
2.545 |
2 |
600.0 |
509.4 |
+90.6 |
506.2 |
+93.8 |
|
2.645 |
6 |
491.7 |
498.5 |
- 6.8 |
496.7 |
- 5.0 |
|
2.745 |
12 |
487.5 |
488.4 |
- 0.9 |
487.5 |
0.0 |
|
2.845 |
22 |
477.3 |
478.9 |
- 1.6 |
478.6 |
- 1.3 |
|
2.945 |
24 |
487.5 |
470.1 |
-1-17.4 |
470.1 |
+ 17.4 |
|
3.045 |
30 |
460.0 |
461.8 |
- 1.8 |
461.9 |
- 1.9 |
|
3.145 |
32 |
450.0 |
454.1 |
- 4.1 |
453.9 |
- 3.9 |
|
3.245 |
28 |
442 9 |
446.9 |
- 4.0 |
446.2 |
- 3.3 |
|
3.345 |
22 |
436.4 |
440.0 |
- 3.6 |
438.8 |
- 2.4 |
|
3.445 |
22 |
434 1 |
433.5 |
-1- 0.6 |
431.6 |
+ 2.5 |
|
3.545 |
20 |
415.0 |
427.4 |
-12.4 |
424.6 |
- 96 |
|
3.645 |
14 |
421.4 |
421.6 |
- 0.2 |
417.9 |
+ 3.5 |
|
3.745 |
8 |
412.5 |
416.1 |
- 3.6 |
411.4 |
+ 1-1 |
|
3.845 |
7 |
396.4 |
410.8 |
-14.4 |
405.1 |
- 8.7 |
|
3.945 |
8 |
412.5 |
405.8 |
+ 6.7 |
3»8.9 |
+ 13.6 |
|
4.045 |
6 |
391.7 |
401.1 |
- 9.4 |
393.0 |
- 1.3 |
|
4.145 |
2 |
425.0 |
396.5 |
+28.5 |
387.2 |
+37.8 |
|
4.245 |
4 |
425.0 |
392.2 |
+32.8 |
381.6 |
+43.4 |
|
4.345 |
2 |
350.0 |
388.1 |
-38.1 |
376.2 |
-26.2 |
|
4.445 |
2 |
400.0 |
384.1 |
+ 15.9 |
370.9 |
+29.1 |
|
4.845 |
1 |
425.0* |
||||
|
Mean error |
15 9 |
15 8 |
||||
|
Root mean-«quare error |
26.1 |
27.0 |
•Excluded in fitting curves and computing errors.
19S3]
RELATION BETWEEN FAT CONTEXT AND MILK YIELD
619
Is
--
| 5 5 = i * 3 3 5 5 5
i-
*• _
-H -H
— M N —
C C M ^ f.
5
-
§ $!$
o — rt —
I
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r- X
620
BULLETIN No. 245
[June,
TABLE 22. — EQUATIONS TO FITTED CURVES EXPRESSING RELATION BETWEEN PERCENTAGE FAT CONTENT AND YIELD OF MILK
(Y = yield of milk, in pounds; t = percentage fat content of milk)
|
REFERENCE TO — |
Y : |
Logarithmic = a + bx + c logio |
(x + o) |
Constant energy a |
Constant fat a |
||||
|
Fig. No. |
Table No. |
Records |
|||||||
|
2.66+t |
t |
||||||||
|
a |
b |
c |
a |
0 |
a** |
a |
|||
|
1 8 9 10 2 3 4 5 6 7 |
2 15 17 20 4 6 8 9 10 13 |
Holstein C.T.A. |
10 732.0 22 026.3 16 645.7 1 017.5 6 952.4 12 117.5 430.9 18 869.2 13 039.9 31 457.9 |
- 38.95 + 165.50 - 88.50 + 1.87 - 36.80 - 49.10 - 1.71 + 12.70 + 28.00 +249.10 |
- 2 718.2 - 8 317.2 - 1 539.9 - 442.3 - 907.9 - 2 530.2 - 89.9 - 7 482.2 - 3 736.8 -17 084.4 |
5.5 2.5 .5 11.5 1.5 3.5 4.5 9.5 1.5 9.5 |
24.45 25.45 25.45 <22.45 36.45 37.45 35.45 36.00 29.00 33.45 |
43 548 91 309 87 559 2 635 41 432 64 659 2 227 66 100 62 325 84 776 |
24 909 50 532 48 457 1 460 27 087 43 142 1 457 43 177 36 091 51 317 |
|
Holstein-Friesian A.R. (Vols. 24-30) |
|||||||||
|
Holstein-Friesian A.R. (Vols. 18-24) |
|||||||||
|
Holstein-Friesian A.R.O. (7-day), age-corrected. . . . Jersey C.T.A. (yearly) |
|||||||||
|
Jersey R.M. |
|||||||||
|
Jersey R.M. (7-day)* |
|||||||||
|
Guernsey A.R. |
|||||||||
|
Ayrshire A.R. (yearly) |
|||||||||
|
Brown Swiss R.P. (yearly), age- corrected |
*The records of cows under four years of age were excluded in making up this correlation table because the entrance requirement (12 pounds of fat, re- gardless of age) is relatively high for young cows, and it was thought this might tend unduly to exclude cows of lower fat percentage under the age of four years.
**This constant should afford an equitable physiological basis of comparison for the production of the groups and breeds. The data have not been treated with this object in mind, however, and there are three things which are not al- ways comparable, viz.: length of record, age, and period when the records were made. Judging by the cow testing association records, the values of a indicate that the Jersey is 95 percent (41432/43548) as high a producer as the Holstein. By the advanced registry records, she is only 71 percent (64659/91309) as high. Looked at in another way, the Jersey advanced registry records are more repre- sentative of what the breed does under commercial conditions than is the case with the Holstein. Comparing all the breeds, the rank in descending order of pro- duction is: Holstein, Brown Swiss, Guernsey, Jersey, and Ayrshire. This sug- gests that size, rather than efficiency of the mammary apparatus, may be the cause of that rank.
1923]
RELATION BETWEEN FAT CONTENT AND MILK YIELD
621
TABLE 23. — ERRORS OF FITTED CURVES (The mean error is given first; the root mean-square error, second)
|
REFERENCE TO — |
TYPE OF CURVE |
|||
|
Table No. |
Records |
Logarithmic |
Constant energy |
Constant fat |
|
2 |
Holstein OT.A |
248 397 |
249 391 |
555 775 |
|
15 |
Holstein-Friesian A.R. (V. 24-30) |
348 401 |
465 566 |
1001 1203 |
|
17 |
Holstein-Friesian A.R. (V. 18-24) |
524 720 |
536 746 |
981 1355 |
|
20 |
Holstein-Friesian A.R. O. (7-day) |
15.9 26.1 |
15.8 27.0 |
37.4 49.6 |
|
4 |
Jersey C. T. A |
323 421 |
329 428 |
426 551 |
|
6 |
Jersey R.M. (yearly) |
439 770 |
457 777 |
498 867 |
|
8 |
Jersey R.M. (7-day) |
10.4 13.0 |
10.4 13.1 |
16.1 21.3 |
|
9 |
Guernsey A.R |
331 546 |
349 569 |
386 673 |
|
10 |
Ayrshire A.R |
147 181 |
229 317 |
437 521 |
|
13 |
Brown Swiss R.P |
671 947 |
709 980 |
772 1101 |
AUTHOR INDEX
623
AUTHOR INDEX
Anderson, H. W. Dendrophoma Leaf Blight of Straw- berry 125-136
Andrews, J. B., Handschin, W. F., and Rauchenstein, E. The Horse and the Tractor. .169-224
Carmichael, W. J., and Bice, John B. Variations in Far- row : With Special Reference to the Birth Weight of Pigs 65-96
Davidson, F. A., and Gaines, W. L. Relation between Per- centage Fat Content and Yield of Milk : Correction of Milk Yield for Fat Con- tent 575-622
Dungan, G. H., Tisdale, W. H., and Leighty, C. E. Flag Smut of Wheat, with Special Reference to Varietal Resist- ance 507-538
Edmonds, J. L., and Kammlade, W. G. Feeding Pure-Bred Draft Fillies 329-360
Edmonds, J. L., and Kammlade, W. G. Feeding Farm Work Horses and Mules 409-428
Flint, W. P., and Hackleman, J. C. Corn Varieties for Chinch- Bug Infested Areas 539-550
Gaines, W. L., and Davidson, F. A. Relation between Per- centage Fat Content and Yield of Milk : Correction of Milk Yield for Fat Con- tent 575-622
Hackleman, J. C., and Flint, W. P. Corn Varieties for Chinch- Bug Infested Areas 539-550
Hall, H. F., Ross, H. A., and Rhode, C. S. The Feed Cost of Milk and Fat Production as Related to Yields 551-574
Handschin, W. F., Andrews, J. B., and Rauchenstein, E. The Horse and the Tractor. . .169-224
PAGE
Harding, H. A. Effect of Tem- perature of Pasteurization on the Creaming Ability of Milk 393-408
Harding, H. A., and Prucha, M. J. An Epidemic of Ropy Milk 109-124
Harding, H. A., and Prucha, M. J. Elimination of Germs from Dairy Utensils. I. By Rinsing. II. By Drying in Sun and Air 137-168
Harding, H. A., and Ptucha, M. J. Germ Content of Milk. III. As Influenced by Visi- ble Dirt 361-392
Hopkins, Cyril G. How Greece
Can Produce More Food. 429-470
Kammlade, W. G., and Edmonds, J. L. Feeding Pure-Bred Draft Fillies 329-360
Kammlade, W. G., and Edmonds, J. L. Feeding Farm Work Horses and Mules 409-428
Leighty, C. E., Tisdale, W. H., and Dungan, G. H. Flag Smut of Wheat, with Special Reference to Varietal Resist- ance 507-538
Mitchell, H. H. A Graphical Presentation of the Financial Phases of Feeding Experi- ments 269-328
Pearson, F. A. The Seasonal
Cost of Milk Production.. .1-18
Pearson, F. A., and Ross, H. A. Comparative Expense of Me- chanical and Hand Milk- ing ... 491-506
Prucha, M. J., and Harding, H. A. An Epidemic of Ropy Milk 109-124
Prucha, M. J., and Harding, H. A. Elimination of Germs from Dairy Utensils. I. By Rinsing. II. By Drying in Sun and Air . ..137-168
02-1
AUTHOR INDEX
PAGE
Prucha, M. J., and Harding, H. A. Germ Content of Milk. III. As Influenced by Visible Dirt 361-392
Rhode, C. S., Ross, H. A., and Hall, H. F. The Feed Cost of Milk and Fat Production as Related to Yields 551-574
Rice, John B., and Carmichael, W. J. Variations in Farrow: With Special Reference to the Birth Weight of Pigs. .65-96
Richmond, Thomas E., and Whit- ing, Albert L. Sweet Clover for Nitrate Production. .253-268
Ross, H. A. The Production and Utilization of Manure on Dairy Farms 471-490
Ross, H. A., and Pearson, F. A. Comparative Expense of Me- chanical and Hand Milk- ing 491-506
Ross, H. A., Hall, H. F., and Rhode, C. S. The Feed Cost of Milk and Fat Production as Related to Yields. .. .551-574
PAGE
Schoonover, Warren R., and Whit- ing, Albert L. Nitrate Pro- duction in Field Soils in Illinois 19-64
Stewart, Robert. Sulfur in Rela- tion to Soil Fertility 97-108
Tisdale, W. H., Dungan, G. H., and Leighty, C. E. Flag Smut of Wheat, with Special Reference to Varietal Resist- ance 507-538
Whiting, Albert L., and Schoon- over, Warren R. Nitrate Pro- duction in Field Soils in Illinois 19-64
Whiting, Albert L., and Rich- mond, Thomas E. Sweet Clover for Nitrate Produc- tion 253-268
Division of Applied Chemistry of the University of Illinois; the Illinois Geological Sur- vey; and the Agricultural Experiment Station . . ..225-252
INDEX
fF-fAf625
INDEX
(The headings in capitals are subjects of entire bulletins)
PAGE
Acidity of soil in Greece 439-44
and plant diseases 457
Alhambra experiment field, chinch- bug damage 548-49
Alsike clover, effect of potassium
on production 249
Alunite, potassium supplied by
-. . . . .244, 245, 247, 249, 250, 252 Ammonia in soil samples, de- termination of 22
Ascochyta Fragariae 135
Ayrshire records, relation be- tween fat percentage and
milk yield 589-90
Bacteria, see Germs
Barley, effect of potassium on
production 249
Bedding for draft fillies 333
Beets, effect of potassium on pro- duction 249
Bone meal, amount applied in
nitrate experiments 29
Brown Swiss records, relation be- tween fat percentage and
milk yield 590
Buckwheat
Effect of kainit and shale on
production 251
Effect of potassium on pro- duction 247, 250, 252
Effect of shales on growth. .233-34 Effect of various fertilizers on
growth 246
Butter fat, see Fat Calculations for determining cost of gains in feeding experi- ments 269-328
Cement-making, 111. shales for... 230 Chicago, milk filtration tests at. 370 ' ' Chilisaltpeter, ' ' see Sodium
nitrate
Chinch-bugs, corn varieties resist- ant to 539-50
Clover
Effect of potassium on produc- tion 247, 249
Influence on nitrate produc- tion 59
Pot-culture experiments with
potassium 245
see also Melilotus ; Sweet clover
PAGE
Corn
Effect of kainit and shale on
production 251
Effect of potassium on produc- tion 247
Effect of shale on production. 228 Experiment to determine nitro- gen production in soil grow- ing 30
Nitrate needs 45-46
Development of chincn-bug re- sistant varieties 546-48
Sweet clover as fertilizer for. . 267 Corn fodder, effect of potassium
on production 250
CORN VARIETIES FOR CHINCH-BUG INFESTED
AREAS 539-50
Cost-accounting, study of milk- production 1-18
Cows, see Dairy Cows Cream
Distinction between layer and
line 397
Effect of temperature of pas- teurization on 393-408
Cropping, influence on nitrate
production 54-55, 60
Dairy cows
Feed costs 551-73
Manure production 477
Milk from clean 371-73
Milk from dirty
373-74, 384-87, 391
Dairy farms, production and
utilization of manure on. .471-90 Dairy utensils
Treatment of milk cans during epidemic of ropy milk. . .118-19
Washing 140-41
DAIRY UTENSILS, ELIMINA- TION OF GERMS FROM 137-68 by drying in sun and air... 157-68 by rinsing with hot water . . 142-56 Dairying, see Milk production DENDROPHOMA LEAF BLIGHT OF STRAW-
BERRY 125-36
Dendrophoma. obscurans 135
DRAFT FILLIES, FEEDING
PURE-BRED . ..329-60
626-
VOLUME 16
PAGE Drainage, loss of sulfur from
soil by 104-06
Experiment fields, see names of
fields
Fairfield experiment field, chinch- bug damage 549
Farm organization, studies in 111. 173 Fat content of milk, relation to
yield of milk 575-622
Fat production
Feed consumed as related to. 555-63
Relative feed cost 563
see also Feed cost of milk and
fat production Feed
Quantity as related to butter fat
production 555-63
Quantity for milk produc- tion 8, 9, 10, 12, 15
Variation in cost for milk pro- duction 5, 8, 12
significance 11
FEED COST OF MILK AND FAT PRODUCTION AS RELATED TO YIELDS . 551-74
Bibliography 573
Conclusions 572
Records used 553-54
Feeding, Forced, for milk produc- tion 570-71
Feeding Experiments, a Graphi- cal Presentation of the
Financial Phases of 269-328
Feeding experiments
Factors in determining cost . . . 273 Farm work horses and mules. 409-28
Pure-bred draft fillies 329-60
FEEDING FARM WORK
HORSES AND MULES. 409-28 Fillies, see Draft fillies FINANCIAL PHASES OF FEEDING EXPERI- MENTS, A GRAPHICAL PRESENTATION . . ..269-328 FLAG SMUT OF WHEAT, WITH SPECIAL REFER- ENCE TO VARIETAL RE- SISTANCE 507-38
Bibliography 538
Control of 519
conclusions 537
crop rotation 521-22
date of seeding 522-23
seed treatment 519-21
Dissemination 516, 519
Fungus 515-16
Losses due to 513-14
Occurrence 512-13
Symptoms 514-15
Flax, effect of potassium on pro- duction . . 249
PAGE
Food, How Greece can produce
more 429-70
Garget Ill
Geneva Exp. Sta., experiment to show loss of sulfur in drain- age water 105
Germs
Elimination from dairy uten- sils ". 137-68
Germ content of milk 363
Method of counting 141
Ropy milk 114-15
Gestation period for pigs. 68-69, 71, 77 Graphical methods for interpre- tation of feeding experi- ments 270-328
Greece
Fertility of soils 440-49
HOW GREECE CAN PRO- DUCE MORE FOOD 429-70
Limestone in 449-51
Guernsey records showing rela- tion between fat content and
milk yield' 589
Gypsum as fertilizer 99
Hancock co., 111., Rainfall varia- tion in 176
Hart and Peterson determine sul- fur content of plants 100
Holstein Friesian records show- ing relation between fat con- tent and milk yield 591-93
Holstein records showing relation between fat content and milk
yield 584
HORSE AND THE TRACTOR,
THE 169-224
Horses
Analysis of farm horse-power
requirements 202-09
Cost of horse-labor 178-86, 221
reducing . . 187-201
Farm operations for. . .203, 205-206
Feed, cost of 419
Feeding experiments . 329-60, 409-27 Fillies used in feeding experi- ments 339-47
Manure production 477
Used in horse-labor studies. ... 176
Iron, essential plant food 99
Jersey records showing relation between fat content and milk
yield 585-86, 588-89
Kainit, potassium supplied by
244, 245, 247, 249, 250, 251, 252 Labor
Amount and cost of caring for
cows milked mechanically . . . 502 Amount and cost for milking 497-98, 499, 502
INDEX
PAGE
Cost for hauling manure. . . .487—89 Quantity for milk production
8, 9, 10, 12, 15
Variation in cost for milk pro- duction 8, 12
significance 11
see also Horses, cost of labor
Land-plaster 99
Leucite, potassium supplied by
244, 245, 247, 249, 250, 252
Limestone
Amount applied in nitrate ex- periments 29
Analysis by farmers 452
Effect on nitrate production
24, 27, 53-54
In Greek soils 439-444
In soils 447-48
Sources in Greece 449-451, 453
Lupine for soil improvement 457
Lysimeter experiment, Cornell. 104-06 MANURE, THE PRODUCTION AND UTILIZATION ON ILLINOIS DAIRY FARMS
471-90
Manure
Amount recovered from farm
animals 475-78
Crops utilizing 480-82
Green compared with stable
49, 59, 60
Labor cost of hauling 487-89
Methods of utilizing 482-85
Possible rates of applying. .478-80
Seasonal application 485-86
Sweet clover as green 255-56
see also Organic matter Melilotus in Greece
Field trials 462-64
Grain grown after 459-62
Nitrogen in 456-57
see also Sweet clover
Melilotus alba 255
Melilotus indica 257
Milk
Dirt in 364-369, 374-75
Quality 139
Seasonal variation in price. . .16-17 MILK, EFFECT OF TEMPER- ATURE OF PASTEURIZA- TION ON THE CREAMING
ABILITY OF 393-408
MILK, AN EPIDEMIC OF
ROPY 109-24
MILK, GERM CONTENT OF, AS INFLUENCED BY
VISIBLE DIRT 361-92
Bibliography 390
From cleaned cows 380-82
From dirty cows 384-87
Plan of experiment 371
PAGE Relation to problem of clean
milk 389
Results of experiment 382-83
Summary and conclusions 388
When ordinary pail was used 378-80 When small-topped pail was
used 375-78
Milk cans, see Dairy utensils Milk production
Feed consumed as related to ... 563
digestible nutrients 564
Forced feeding for 570-71
Nutrients required for 100
pounds 569
Records of Holstein cows 564
MILK PRODUCTION, THE
SEASONAL COST OF 1-18
Conclusions 18
Cow cost by months 12-14
Herd cost by months 4—7
MILK YIELD, RELATION BE- T W E E N PERCENTAGE FAT CONTENT AND.. 575-622
Bibliography 598
Coefficient of correlation 584
Conclusions 598
Correction for fat percentage. 594
Hypothesis . . 579-80
Source of data 578-79
Summary 597-98
Milkers, mechanical, conclusions
as to use 493
MILKING, COMPARATIVE EXPENSE OF MECHANI- CAL AND HAND 491-506
Bibliography 506
Minonk experiment field, experi- ment with sweet clover for
nitrate production 261-62
Mules, feeding experiments. . .409-27
Mycosphaerella Fragariae
127, 133, 135
Newton experiment field, experi- ment with sweet clover for
nitrate production 264
NITRATE PRODUCTION, IN FIELD SOILS IN ILLI- NOIS 19-64
Conclusions 60-61
Factors of production 21, 22
Methods of determination . . . 62-63
Relative rates 60-61
Time of maximum 60
Nitrate production, sweet clover
for 253-68
Nitrogen
Amount needed for crops. . .455-56
Cost 455
In soils of America and of
Greece 445-46
Reduction of loss by leaching 61
628
VOLUME 16
PAGE
Source 456-57
Utilization by crops 61
see also Nitrate Oats
Nitrate needs 46-47
Nitrate production in soil grow- ing 43
Pot-culture experiments with
potassium 245
Oblong experiment field, experi- ment with sweet clover for
nitrate production 264-65
Ohio Exp. Sta., experiment to test
effect of sulfur on crops. .102-03
Oil in potash shales 229
Organic matter, value in nitrate
production 35
Osborne method of determining
sulfur content of plants.... 100 Pasteurization
As protection against ropy
milk 121-22
EFFECT OP TEMPERA- TURE ON CREAMING ABILITY OF MILK... 393-408 Establishment of temperatures
for 396
Pasture, nutrients obtained from 567 Pa. Exp. Sta., experiment to test
effect of sulfur on crops. ... 102
Phoma obscurans 133, 134
Phosphates, see Phosphorus ; Rock
phosphate Phosphorus
In soils 446
Sources of 454-55
Value in nitrate production 36
Phyllosticta fragaricola 132, 133
Pigs, birth weight of 65-96
see also Swine
PIGS, VARIATIONS IN FAR- ROW: WITH SPECIAL REFERENCE TO THE
BIRTH WEIGHT OF 65-96
Plants, sulfur requirements of.. 100 Plowing, see Tillage Potash, extraction from shales.. 235 POTASH SHALES OF ILLI- NOIS 225-52
Constitution 231-35
Geology, distribution and occur- rence in Union co 237-43
Potassium
In soils 447, 458-59
Pot-culture experiments with on
peaty soils 245
Shale as source of 244-52
Potassium sulphate as fertilizer 103 Rainfall, sulfur content of 106-08
PAGE
Rape
Effect of potassium on produc- tion 250
Effect of shale on produc- tion 248, 249
Residues, value for nitrate pro- duction in soil 45
Rock phosphate 59, 60
Amount applied in nitrate ex- periments 29
Influence on nitrate production 50
Septoria aciculosa , . 135
Shales
Analysis of Illinois 236
As source of potassium 244-52
Character in Union co 238-39
Potash 229-36
Smut, Flag, of wheat 507-38
Sodium nitrate
Cost 23
Equivalent in nitrogen 28
Soil
Acidity 439, 444
and plant diseases 457
Analysis 439, 445
Dead 458
Difference in 437-38
Improvement, proof of 457-58
Limestone in 447-48
Moisture content in nitrate production experiments .... 31, 33, 37, 39, 42, 44, 56, 57, 58
method of determination 62
Nitrogen in 445—46
Of Greece 438-39, 440-44
fertility 448^9
Phosphorus in 446
Potassium in 447
Sulfur content 100-01
Sulfur in relation to fertility 97-108
Testing by farmers 448
Treatment for production of
nitrate 24, 60
Soybeans, influence on nitrate
production 59
Sows, see Pigs
STRAWBERRY, D E N D R O- PHOMA LEAF BLIGHT
OF 125-36
Control 135-36
Fungi 135
History of disease 132-34
Infection experiments 131-32
Isolation and cultural charac- ters 129
Morphology and life history 129-31
Symptoms 127-29
Taxonomy 134-35
INDEX
629
FAQS
Sulfate of calcium for soil im- provement 99
Sulfur
Content of Kentucky soils 106
Content of rainfall 106-08
Effect on crop production. .101-04
Loss in drainage water 104-06
Requirement of plants 100
SULFUR IN RELATION TO
SOIL FERTILITY 97-108
Sweet clover
As a green manure 255-257
Effect of potassium on produc- tion 250
Effect of shale on production 248 Nitrogen content and
weights 266-67
Value for nitrate production . . 45 SWEET CLOVER FOR NI- TRATE PRODUCTION.. 253-68 see also Melilotus
Swine, feeding experiments. . .283-84, 289, 291-92, 293, 295, 298, 301 see also Pigs Temperature, effect on nitrate
production 25-27
Tillage as factor in nitrate pro- duction 21, 24-25
Toledo experiment field, experi- ' ment with sweet clover for
nitrate production 263
Tractors
Advantages . . 222
Displacement of horses by.. 221-22
PAGE
Farm operations for
202, 203, 206, 208
The horse and the tractor . 169-224
Soil preparation by 224
Survey of use 210-20
Tricalcium phosphate for soils. . 24 Tuberculosis germs killed by
pasteurization of milk 396
Urbana, University North Farm Experiments to determine ni- trate production 29-44
Corn crop 45-46
Oat crop 46-47
Wheat crop 46
Experiments with sweet clover
for nitrate production . . . 259-261 Urbana, University South Farm, Experiments to determine ni- trate production 47, 59
Urbana experiment field, Corn
variety trials 549-50
Urocystis occulta 515
tritici 511, 515, 527
Wheat
Effect of fertility on . .. 437
Flag smut of 507-38
Necessity for Greece to raise. . 464 Nitrate production in soil
growing 40
Nitrogen needs 46
Pot-culture experiments with
potassium 245
Varietal resistance to flag
smut 523-37
Yield in Greece . , . .434-35
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