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
°
^
%
—
•*^
•**-.
^
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*
*
at
tea
200
19*
/«<
179
l-l
SJN
*">
o o
teta
0830
fW
MOM*
1.R.V
9 Mt.
»u *
1£
-so
o
tffC
CMUH
U*t
Y"
**»
<**s
•to/
set
o
o
\
o
0
^
\
o
^]
•s
o
\~
XM
118
IU
lit
IDA
^wo"
O^N
<«
w
0
0 0
**
• •
o
*x
M
0
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.
ns»
G'««
i-
&"<
\IM
its
/to
o
0 0
OBS£t
M7MM
«M£.
fie.
-
^S
IOC C
CHU
If*
S»4
sat
•no
74«
\
^
0
>,
0
o
o
°
*S
^
>s°
X,
N°
o
0
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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CO
I
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, u, us u, us u, us us us us us us *
ss
1
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8}UlOd-plUI
JO
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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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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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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RELATION BETWEEN FAT CONTENT AND MILK YIELD
o
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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
> -
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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