Chapter II: Part 2

Values of λ and κ for points on the discriminant give curves with two modes coinciding. All points on one side of the discriminant have three real and distinct modes, and all on the other have one real and two imaginary modes. To determine on which side the points giving three real modes lie we examine a point inside the discriminant. When κ = 0 the modal equation becomes

3λt^3 + (1 + 6λ)t = 0.

______________ Hence the roots are t = 0 and t = ±√(-(1 + 6λ)/3λ). The quantity under the radical is positive for values of λ between 0 and-⅙. Therefore, all points within the discriminant curve yield tri-modal curves and all without uni-modal curves.

_Fig. I_

(_The horizontal scale is twice the vertical scale_)]

The infinite values of dy/dx arise from zero values of the quadratic, 1 + 2κt + 3λt^2. The greatest possible number of modes for any one curve is therefore five, three from the cubic and two from the quadratic. Since for infinite values of dy/dx the corresponding ordinates are infinite, it is advisable to study the location of the infinite points of the curve, rather to the neglect of the idea of maximum values at such points.

=Infinite Ordinates.= The infinite points on a curve are given by the values of t satisfying the equation

3λt^2 + 2κt + 1 = 0.

Except under certain limited conditions to be determined later a curve with infinite ordinates can not be of great statistical value.

The parabola, κ^2-3λ = 0, obtained by equating the discriminant of this quadratic to zero separates the points on the (λ, κ) plane which correspond to curves of _no_ infinite points from those corresponding to curves of _two_ infinite points.

Therefore, all pairs of values of λ and κ within the parabola, with the exception of the very narrow region also within the first discriminant curve, give uni-modal curves without infinite ordinates.

=Types of Curves.= Without entering into detailed proofs we will now investigate the general shape of the curves corresponding to values of λ and κ in each of the distinct regions of the plane of λ and κ.

In the region beneath the parabola and to the right from the shaded area of Fig. I the curve is essentially of the shape shown in Fig. II. This type includes the most common skew curves and hence is of great importance in statistics.

As the point (λ, κ) moves from the λ-axis the crest rises until the parabola is reached when the infinite ordinates appear as two coincident lines, shown in Fig. III.

After the parabola is passed, the infinite ordinates separate and the curve apparently separates into three branches as in Fig. IV.

In crossing the κ-axis to the left one asymptote moves off to infinity giving a curve of the type shown in Fig. V.

Then the asymptote reappears giving a curve of the type shown in Fig. VI.

This general shape is preserved as the point moves toward the λ-axis and when the point reaches the discriminant curve the middle branch is flattened at the minimum point.

For points within the discriminant curve two minimum points appear and the central branch now shows a maximum with a minimum point on either side as in Fig. VII.

=The Tri-modal Curves.= The curves corresponding to values of (λ, κ) within the discriminant, because of the requirement that an element of area under the translated curve must always be equivalent to the corresponding element under the base or generating curve, can be of statistical value only under the following conditions.

The area between the two ordinates corresponding to t = ±3 is 0.99998 of the total area under the curve, so that when neither of the minimum points corresponds to points closer than three units to the origin of the base curve the curve may be practically valuable. A moment’s consideration will show that the abscissas of the two minimum points must be practically the same as that of the corresponding infinite ordinates. The roots of the quadratic

3λt^2 + 2κt + 1 = 0

are numerically greater than 3 for all pairs of values of (λ, κ) lying above the line

27λ - 6κ + 1 = 0

As statistically promising within the discriminant of the cubic we then have the shaded area of the (λ, κ) plane.

=The Origin.= The generating curve is the symmetrical normal probability curve with origin at its center. Since x = 0 when t = 0, the origin of the translated curve coincides with that of the base or generating curve. The translated curve may not be symmetrical so that the mean ordinate may not coincide with the modal ordinate. Because of the relation between corresponding areas the ordinate at the origin must continue to divide the area under the curve into equal parts, that is, the origin and median always coincide.

=Determination of the Constants.= Since the exact position of the median can not ordinarily be determined by inspection or direct computation there are in reality four constants to be determined: the distance between the median and the mean, a, κ and λ.

In determining the constants it is usual to compute the value of the first four moments. The third and fourth moments are extensions of the idea of the well known formulas for the first and second moments. Denoting the moments about the median by μ, we have

1 ⌠+∞
μ_{1}^´ = ——— │ xy dx
N ⌡-∞

1 ⌠+∞
μ_{2}^´ = ——— │ x^{2}y dx
N ⌡-∞

1 ⌠+∞
μ_{3}^´ = ——— │ x^{3}y dx
N ⌡-∞

1 ⌠+∞
μ_{4}^´ = ——— │ x^{4}y dx
N ⌡-∞

where N is the total area under the curve.

The values of the μ’s are computed from the data[8] and equated to the corresponding integrals which of course involve the four constants. In this way four equations are obtained from which the values of the constants may be determined. Since it is our present object to discuss the solution only of these equations, merely the principal results will be given.

The general form for the moments about the median of the area under the translated curve is

1 ⌠+∞
μ_{n}^´ = ——— │ x^{n}y dx
N ⌡-∞

1 ⌠+∞ a^n(t + κt^2 + λt^3)^n
= —————— │ ———————————————————————— e^{-t^2/2} a(1 + 2κt + 3λt^2) dt
√(2π)N ⌡-∞ a(1 + 2κt + 3λt^2)

1 ⌠+∞
= —————— │ a^n(t + κt^2 + λt^3)^ne^{-t^2/2} dt.
√(2π)N ⌡-∞

On applying the two well known formulas:

⌠+∞
│ x^{2n + 1}e^{-x^2} dx = 0
⌡-∞

⌠+∞ 2n + 1 ⌠+∞
│ x^{2n + 2}e^{-x^2} dx = —————— │ x^{2n}e^{-x^2} dx,
⌡-∞ 2 ⌡-∞

the determination of μ_1´, μ_2´, μ_3´ and μ_4´ is reduced to a matter of algebraic detail. Then on transferring to the arithmetic mean as origin the values of μ_2, μ_3, and μ_4 can be determined in terms of a, κ and λ. It is most convenient however, to make use of the quantities β_1 = μ_3^2/μ_2^3 and β_2 = μ_4/μ_2^2 or rather β = β_1/8 and ϵ = (β_2 - 3)/12 and express the constants in terms of these quantities. It is to be noted that both ϵ and β are zero for a normal distribution, that is, for λ = κ = 0.

Omitting the detailed reduction[9] which is straightforward and direct, we have

(1) μ´ = aκ

(2) μ_2 = a^2(1 + 6x + 15x^2 + 2κ^2)

2κ^2(2κ^2 + Q)^2
(3) β = ——————————————————————
(2κ^2 + R)^3

4κ^4 + 4κ^2S + T
(4) ϵ = ——————————————————————
(2κ^2 + R)^2

where the symbols, S, R, Q and T are defined as follows:

S = 1 + 18λ + 90λ^2,
R = 1 + 6λ + 15λ^2,
Q = 1.5 + 18λ + 135/2λ^2,
T = 2λ + 36λ^2 + 270λ^3 + 810λ^4.

Obviously no algebraic solution can be obtained from equations (3) and (4) for κ and λ in terms of the computed values β and ϵ, and hence a resort to tables is necessary. The values of β and ϵ for values of κ from 0 to 0.0335 and of λ from -0.040 to +0.100 have been computed.[10] The process of determining the constants of the translated normal curve consists first in computing β and ϵ from the given data, and then in entering the table and interpolating for the corresponding values of κ and λ.[11] On substituting these values in (2) the value of a can be found and thence on multiplying a by κ the position of the median of the distribution is obtained.

The sign of κ is determined by the sign of the third moment about the mean μ_3, that is, by the direction of the skewness or asymmetry. For positive skewness the mean must lie to the right of the median and hence μ_1´, the first moment about the mean, must be positive which necessitates a positive sign for κ. Therefore, the sign of κ is the same as that of the skewness.

To fit a curve to the given data, after the constants have been determined it is necessary to find, by solving a cubic equation for each value, the values of t corresponding to the x’s of the respective classes. The cubic is

aλt^3 + aκt^2 + at - x = 0.

Any of the various methods of approximating to the solution of a cubic may be used in solving these equations.

The area of each class can now be obtained by computing the corresponding areas under the standard normal curve from a table of the probability integral.

=The Method of Interpolation.= The actual fitting of the curve can now be readily accomplished.[12] The distinctively geometrical operation is the interpolation for the values of λ and κ for a given pair of values of β and ϵ.

Within the limits of the table[13] the curves resulting from the assignment of a constant value to β are practically straight lines, β = 0 is the λ-axis; β = 1 is a line parallel to the λ-axis. Hence we may safely assume that the variation from one column to the next and from one line to the next is linear for values of β. That is, ordinary first difference interpolation methods are applicable.

As regards the system of ϵ curves we have for instance ϵ = .128 at (λ = .050, κ = 0); again, at approximately (.045, .060) and (.40, .085). We are therefore warranted in assuming the applicability of first difference methods to interpolation between the ϵ curves.

As an illustration let us find the values of λ and κ for ϵ = 0.112 and β = 0.044. On inspection of the table it is seen that λ lies between 0.30 and .035 and κ between .090 and .095. When κ = .090, λ = .033 for ϵ = .112. When κ = .095, λ = .031 for ϵ = .112. For β = .042 and κ = .090, λ = .033 and for β = .046 and κ = .095, λ = .031, ϵ = .112 in each case. Hence, to first differences, λ = .032 and κ = .093 for ϵ = .112 and β = .044. For interpolation in parts of the table showing more rapid variations appropriate methods will suggest themselves.

Taken geometrically the table represents two distinct systems of curves, with each curve of one system intersecting all the curves of the other system. Therefore, a pair of values for λ and κ can always be found for values of ϵ and β within the range of the table.

Department of Mathematics, Ohio State University.

TABLE OF ϵ AND β.

(ϵ is the first and β the second number of each pair.)

λ
───┬────────────────────────────────────────────
κ │-040 -035 -030 -025 -020 -015 -010 -005 000
───┴────────────────────────────────────────────
000 -061 -056 -050 -043 -035 -027 -019 -010 000
000 000 000 000 000 000 000 000 000

005 -055 -049 -042 -035 -027 -019 -010 000
000 000 000 000 000 000 000 000

010 -055 -049 -042 -035 -027 -018 -010 000
000 000 000 000 000 000 000 001

015 -049 -042 -035 -027 -018 -009 001
001 001 001 001 001 001 001

020 -048 -041 -034 -026 -017 -008 002
001 002 002 002 002 002 002

025 -047 -040 -033 -025 -016 -007 003
002 002 002 003 003 003 003

030 -046 -039 -032 -024 -015 -006 004
003 003 004 004 004 004 004

035 -045 -038 -031 -023 -014 -005 005
004 005 005 005 005 005 006

040 -037 -030 -022 -013 -004 006
006 006 007 007 007 007

045 -036 -028 -020 -011 -002 008
008 008 008 009 009 009

050 -034 -026 -018 -009 -000 010
009 010 010 011 011 011

055 -032 -024 -016 -007 002 012
011 012 012 013 013 013

060 -022 -014 -005 004 014
014 015 015 016 016

065 -020 -012 -003 006 017
016 017 018 018 019

070 -018 -009 000 009 019
019 020 020 021 022

075 -015 -007 002 012 022
022 023 023 024 025

080 -013 -004 005 015 025
025 026 026 027 028

085 -001 008 018 028
029 030 031 032

090 002 011 021 032
032 033 034 036

095 005 015 025 035
036 037 038 039

100 009 018 028 039
039 041 042 044

(ϵ is the first and β the second number of each pair.)

λ
───┬────────────────────────────────────────
κ │ 005 010 015 020 025 030 035 040 045 050
───┴────────────────────────────────────────
000 010 021 033 045 057 071 084 098 113 128
000 000 000 000 000 000 000 000 000 000

005 010 021 033 045 057 071 084 098 113 128
000 000 000 000 000 000 000 000 000 000

010 011 022 033 045 058 071 085 099 113 128
001 001 001 001 001 001 001 001 001 001

015 011 022 034 046 058 071 085 099 114 129
001 001 001 001 001 001 001 001 001 001

020 012 023 034 046 059 072 086 100 115 130
002 002 002 002 002 002 002 002 002 002

025 013 024 035 047 060 073 087 101 116 131
003 003 003 003 003 003 003 003 003 003

030 014 025 036 049 061 074 088 102 117 132
004 004 004 005 005 005 005 005 005 005

035 015 026 038 050 063 076 089 104 118 133
006 006 006 006 006 006 007 007 007 007

040 017 028 039 052 064 077 091 105 120 135
007 008 008 008 008 008 008 009 009 009

045 019 030 041 053 066 079 093 107 122 137
009 010 010 010 010 011 011 011 011 011

050 021 032 043 055 068 081 095 109 124 139
012 012 012 012 013 013 013 013 014 014

055 023 034 045 057 070 083 097 111 126 141
014 014 015 015 015 016 016 016 016 017

060 025 036 048 060 073 086 100 114 129 144
017 017 017 018 018 019 019 019 019 020

065 028 039 050 062 075 089 102 116 131 146
019 020 020 021 021 022 022 022 023 023

070 030 041 053 065 078 091 105 119 134 149
022 023 024 024 025 026 026 026 026 027

075 033 044 056 068 081 094 108 122 137 152
026 026 027 028 028 029 029 030 030 031

080 036 047 059 071 084 097 111 125 140 155
029 030 031 031 032 033 033 034 034 035

085 039 050 062 075 088 101 115 129 144 159
033 034 034 035 036 037 037 038 039 039

090 043 054 066 079 092 105 119 133 148 163
037 038 039 039 040 041 042 042 043 044

095 046 058 070 083 096 109 123 137 152 167
041 042 043 044 045 046 046 047 048 049

100 050 062 074 087 100 113 127 141 156 171
045 046 047 048 049 050 051 052 053 054

[6] Pearson, Karl:—“Skew Variation in Homogeneous Material;” Phil. Trans. 1895, Vol. CLXXXVI, A, pp. 253 et seq.

“On the Systematic Fitting of Curves to Observations and Measurements,” Biometrika, I, pp. 265 et seq. and Biometrika II, pp. 1 et seq.

Elderton:—“Frequency Curves and Correlation,” pp. 1-105; C. & E. Layton, 1906.

[7] Edgerton, F. Y.:—“On the Representation of Statistics by Means of Analytical Geometry,” Jour. Roy. Stat. Soc., 1914, Feb., Mar., May, June and July.

[8] Elderton, 1. c.

[9] Compare Edgeworth, “A Method of Representing Statistics by Analytical Geometry,” Proceedings Fifth International Congress of Mathematicians, Cambridge, 1912.

[10] Only a part of the original table appears in the accompanying table. The original values were computed to four places of decimals, but three place numbers are sufficient to illustrate the method of approximating to the solution.

[11] Compare “Tables for Statisticians and Biometricians,” Cambridge University Press, 1914.

[12] For the statistical details see Elderton, 1. c.

[13] As may be seen on examining the Table.

A PRELIMINARY LIST OF THE JASSOIDEA OF MISSOURI
WITH NOTES ON SPECIES.

By EDMUND H. GIBSON and ERIC S. COGAN,
U. S. Bureau of Entomology.

The following preliminary list of the Jassoidae of Missouri is mainly the result of collections and notes made by the authors during the summer months of 1915. On account of the lack of records for this state the authors were prompted to undertake such a survey. As far as possible collections were made so as to embrace all conditions in different sections, giving some attention to ecological relations. The list comprises some 98 species.

BYTHOSCOPIDAE.

=Macropsis apicalis= Osb. & Ball. A few specimens swept from
weeds at Charleston, Mo., during the late summer.

=Bythoscopus distinctus= VanDuzee. Found in great numbers
on willows in northern Missouri.

=Pediopsis viridis= Fitch. Not common. Taken from willows
near drainage canals in southeast Missouri. Somewhat
more numerous in northern part of the state.

=Idiocerus nervatus= VanDuzee. The only species taken from
willows about Chillicothe.

=Idiocerus verticis= Say. Listed by VanDuzee as occurring in
the state.

=Idiocerus crataegi= VanDuzee. Swept from grasses at
Chillicothe.

=Idiocerus snowi= Gill & Baker. Recorded from Lutesville and
Charleston. Feeding on millet and grasses. Nymphs numerous
during August.

=Agallia sanguinolenta= Prov. Most plentiful in southern part
of state. A decided pest of clover and alfalfa. Other food
plants include wheat and several weeds. Adults abroad in fields
all seasons of the year. Abundant in northern Arkansas.

=Agallia constricta= VanDuzee. One of the earliest jassids to
appear in the spring. Most numerous on grains. Attacks wheat,
rye, oats, alfalfa and grass. Abundant in southern counties.

=Agallia uhleri= VanDuzee. Not very numerous. Occurring
principally near swamps along the Mississippi River. Also
collected from clover fields.

=Agallia novella= Say. Rather uncommon. Taken only in
southern half of state. Adults collected from alfalfa and
from weeds growing in marshes and bogs.

=Agallia 4-punctata= Prov. Clover and alfalfa are among its
food plants. Most abundant in southern counties.

=Agallia gillettei= O. & B. Quite rare. A few adults taken
at Charleston.

TETTIGONIDELLIAE.

=Oncometopia undata= Fabr. Occurs throughout the state, but
not abundant. Swept from grass, weeds and a number of shrubs.

=Oncometopia costalis= Fabr. Occasional specimens taken
throughout southern part of state. Also recorded in the
collection of the Experiment Station at Columbia.

=Homalodisca coagulata= Say. Occasional specimens taken from
cotton and cowpeas. Not abundant.

=Aulacizes irrorata= Fabr. Recorded from the collection of the
Experiment Station at Columbia.

=Kolla bifida= Say. Swept from weeds in marshy lands and from
willows and several shrubs. Recorded only in Mississippi County.

=Kolla geometrica= Sign. Not common. Recorded from Springfield
on grass.

=Kolla tripunctata= Fitch. Mentioned in VanDuzee’s Catalogue
of Described Jassoidea of N. A. as occurring in Missouri.

=Tettigoniella gothica= Sign. Only one specimen taken. From
grass at Lutesville, August 13.

=Tettigoniella occatoria= Say. Common in eastern part of state.
Feeds on clover and weeds.

=Tettigoniella hartii= Wood. Quite numerous throughout the
state during the late summer. Captured only from meadows and
grass lands.

=Tettigoniella hieroglyphica= Say. Rather common in all parts
of the state. Known to feed on clover and several weeds.

=Tettigoniella hieroglyphica= Say. var. hieroglyphica Say. One
adult captured from grass at Rolla, September 21,
by Mr. Geo. W. Barber.

=Tettigoniella hieroglyphica= Say. var. uhleri Ball. Rather
common in eastern half of state. Taken from clover and weeds.

=Tettigoniella hieroglyphica= Say. var. confluens Uhler. Taken
with the above variety.

=Diedrocephala coccinea= Forst. Very generally distributed.
Common but not in great numbers. Injurious to many
ornamental plants in the Missouri Botanical Gardens at
St. Louis. Nymphal cast shins observed on leaves of
Magnolia and American Holly. Adults taken from several
kinds of trees near swamps along the Mississippi River.

=Diedrocephala versuta= Say. Very abundant in central and
southern Missouri. Adults first observed in June. All
stages abroad in fields from July to November. Injurious
to cowpeas in Southeast Missouri. Food plants include
alfalfa, clover, sunflower, grasses, and many weeds. Common
on several ornamental plants and shrubs in the Missouri
Botanical Gardens at St. Louis during September.

=Draeculacephala reticulata= Sign. Rather common at Charleston
and Sikeston during July and August and September, on corn,
alfalfa and grasses. Taken at Chillicothe, Sept. 6, Stanberry,
Sept. 7. The last two records extend the distribution of this
jassid to north of the Missouri River, a fact which is interesting
in view of the distribution recorded by Prof. Osborn in
Bull. 108. Bur. of Ent.

=Draeculacephala angulifera= Walker. Quite common on grass at
Charleston.

=Draeculacephala mollipes= Say. Abundant throughout the state.
All stages present from April to November. Of great economic
importance. A decided pest to young grains and grasses. Known to
feed on an innumerable list of plants and shrubs, field crops,
and ornamentals. Adults migrate in large numbers. About the most
common jassid in Missouri.

=Draeculacephala noveboracensis= Fitch. Taken on grass at
Charleston.

=Helochara communis= Fitch. Swept from wheat on many warm,
sunny days during the winter. In July collected from alfalfa.
Recorded only from Mississippi County.

=Gypona 8-lineata= Say. Occurs throughout the state. Has
special liking for shady and damp places. Appears to be
essentially a grass feeder.

=Gypona flavilineata= Fitch. Swept from grass lands at
Chillicothe.

=Gypona cana= Burm. Taken with G. flavilineata.

=Gypona pectoralis= Spangb. Taken with G. flavilineata.

JASSIDAE.

=Xestocephalus pulicarius= VanDuzee. One specimen of this form
taken at an electric light at Charleston, July 28.

=Xestocephalus tesselatus= VanDuzee. Collected from elm
leaves at Charleston. Quite rare.

=Hecalus lineatus= Uhler. Not common. Nymphs more numerous than
adults during August. Swept from rank growing grasses near the
Mississippi River at Hannibal.

=Parabolocratus viridis= Uhler. Recorded from Springfield,
Columbia, Chillicothe, and Charleston. Observed feeding on grass,
sweet clover and sorghum.

=Platymetopius acutus= Say. Only one adult collected. Swept from
weeds near a bog at Charleston, July 28.

=Platymetopius frontalis= VanDuzee. Very common throughout the
state. Attacks clover, alfalfa, and grasses. Also taken from woody
shrubs.

=Deltocephalus nigrifrons= Forbes. Generally distributed in all
sections of the state. Very abundant during October. Known to feed
upon clover, alfalfa, wheat, many grasses including blue grass,
and several weeds. Attracted to lights at night.

=Deltocephalus weedi= VanDuzee. Quite common on weeds along
roadsides and shady places. Collected at Lutesville and
Charleston during the late summer.

=Deltocephalus flavicosta= Stal. Quite abundant during middle
and late summer, principally in southern part of state. Swept
from native grasses and weeds. Occasional specimens taken from
wheat.

=Deltocephalus sayi= Fitch. Recorded from grass lands in North
western parts of state in September. Quite common in blue grass.

=Deltocephalus inimicus= Say. Common in all parts of the state.
All stages taken from May to November. Food plants include wheat,
oats, alfalfa, clover, cowpeas, timothy, blue grass, other native
grasses, and weeds.

=Deltocephalus albidus= Osb. & Ball. Recorded from the
collection of the Experiment Station at Columbia.

=Deltocephalus obtectus= Osb. & Ball. Quite scarce. Recorded
only from Mississippi County. Near swamps.

=Deltocephalus misellus= Ball. Captured but one adult, in a corn
field near Mississippi River at West Quincy.

=Deltocephalus productus= Walker. Rather scarce. Swept from
clover and weeds at Stanberry.

=Deltocephalus debilis= Uhler. Quite common on grasses in rye
and wheat stubble fields about Hannibal and West Quincy.

=Athysanus exitiosus= Uhler. Occurs throughout the state. With
the exception of Draeculacephala mollipes it is the most common
jassid of northwestern Missouri. Adults present at all seasons of
the year. Food plants include wheat, oats, corn, alfalfa, grasses,
and weeds.

=Athysanus bicolor= VanDuzee. Numerous in southern part of
state, especially in low or bottom lands. Feeds upon many weeds,
grasses and alfalfa.

=Athysanus obtutus= VanDuzee. Not common. A few adults taken
from sweeping wheat fields in the early spring. Recorded only
from Mississippi County.

=Athysanus plutonius= Uhler. Rather rare. Occasional specimens
swept from wheat in Scott and Mississippi Counties.

=Athysanus curtisi= Fitch. Only one adult captured sweeping
weeds at Hannibal.

=Eutettix clarivida= VanDuzee. Recorded from Lutesville and
Charleston, from millet and grasses. Nymphs numerous during
August.

=Eutettix osborni= Ball. Collected by Geo. W. Barber at Poplar
Bluff, from White Aster, used in ornamental plantings.

=Eutettix seminuda= Say. Rather numerous but not abundant.
Occurring in all parts of the state. Collected principally from
weeds and woody shrubs near swamps. Also from grape vines.

=Eutettix strobi= Fitch. Only one adult captured. Feeding on a
leaf of a willow tree growing in a swamp.

=Phlepsius apertus= VanDuzee. Very common throughout the state,
especially in the southeast section. Occurs in great numbers on
alfalfa and clover upon which crops they must be considered a
pest. Also recorded from grasses and weeds. Most abundant during
July and August.

=Phlepsius irroratus= Say. Very common and generally distributed
throughout the state. Of economic importance, attacking alfalfa,
clover, cowpeas, corn, wheat, oats, grape, many grasses, and
weeds.

=Phlepsius cinereus= VanDuzee. Recorded only from Mississippi
County. Most numerous in early summer. Often taken at lights.

=Phlepsius pallidus= VanDuzee. Collected at lights during summer
months. Generally distributed but not abundant.

=Phlepsius superbus= Uhler. Not abundant. Occasional specimens
captured in Mississippi County.

=Scaphoideus sanctus= Say. Occasional specimens taken in
southern part of state.

=Scaphoideus productus= Osborn. One adult collected at Rodney,
August 25.

=Scaphoideus scalaris= VanDuzee. Quite common. Recorded from
Springfield and Hannibal. Taken only from weeds.

=Scaphoideus jucundus= Uhler. Occurs on rank weeds and willows.
Only record is from Stanberry.

=Scaphoideus immistus= Say. Swept from woody shrubs and rank
grasses about Charleston.

=Scaphoideus immistus= Say. var. minor Osborn. One adult taken
at Charleston.

=Thamnotettix clitellarius= Say. An occasional adult taken in
sweepings from grasses and weeds in southeast Missouri. Also taken
from grape at Columbia.

=Chlorotettix viridius= VanDuzee. A few adults taken during the
summer from grasses and weeds growing in low and swampy lands.
Recorded from Pattonsburg and Charleston.

=Chlorotettix unicolor= Fitch. Rather common in central and
northern parts of state. Collected from willows growing in
lowlands.

=Chlorotettix tergatus= Fitch. One adult collected at
Charleston, September 2.

=Chlorotettix necopina= VanDuzee. Only record is from Charleston
where adults were swept from weeds growing in marshy places.

=Chlorotettix galbanata= VanDuzee. Quite rare. Occasional
specimens taken from weeds growing along roadsides in Mississippi
County.

=Jassus olitorius= Say. Not common. A few adults taken in
southeast Missouri. Observed them feeding upon alfalfa.

=Balclutha punctatus= Thunbg. Only record of occurrence is from
Pattonsburg.

=Gnathodus impictus= VanDuzee. Not numerous. Observed feeding on
grasses and several weeds at Charleston during May.

=Cicadula 6-notata= Fall. Occurs in all sections of the state,
most abundant in northeast. Known to feed upon wheat, oats, and
grasses. Especially numerous during October.

=Empoasca mali= LeB. One of the most common and probably the
most injurious leafhopper. Feeds on a great variety of plants,
shrubs and trees. A pest of field crops, nursery stock, and
orchards. Especially abundant during the summer of 1915 on alfalfa
and clover. In early spring adults have been observed feeding on
wheat, rye and native grasses. Exhibits great adaptability to
changes of climate and host plants.

=Empoasca smaragdula= Fall. Listed by Gillette as occurring in
the state.

=Empoasca radiata= Gillette. Swept from willows growing in the
Missouri Botanical Gardens at St. Louis.

=Dicraneura abnormis= Walsh. Not common. Few specimens collected
from blue grass and around lights at night at Chillicothe, during
September.

=Typhlocyba illinoiensis= Gillette. Noted feeding on rose leaves
in the Missouri Botanical Gardens at St. Louis.

=Typhlocyba obliqua= Say. Very abundant on many weeds at
Springfield during August.

=Typhlocyba trifasciata= Say. Listed by Gillette as occurring in
the state.

=Typhlocyba tricincta= Fitch. Abundant on several ornamental
bushes in Missouri Botanical Gardens at St. Louis. Adults
exceedingly quick of movement. Also collected at Pattonsburg and
Columbia.

=Typhlocyba comes= Say. Abundant throughout the state. A severe
pest of grapes, especially in southeast Missouri. Feeds on a
number of weeds. Attracted to lights at night in considerable
numbers.

=Typhlocyba comes= Say. var. vitis Harris. Occurring on
ornamental shrubs, including rose, in the Missouri Botanical
Gardens at St. Louis.

=Typhlocyba comes= Say. var. scutelleris Gillette. Very common
on Sycamore in all stages, and frequently causing severe
infestations. Nymphs and adults feed on under side of leaves
resulting in small whitish brown spots. Occurs in all parts of
Missouri.

=Typhlocyba comes= Say. var. basilaris Say. One adult captured
by Geo. W. Barber at Poplar Bluff, September 4, from white aster.

=Typhlocyba comes= Say. var. ziczac Walsh. Collected from rose
bushes in the Missouri Botanical Gardens at St. Louis.

=Typhlocyba vulnerata= Fitch. Rather numerous on several
ornamental shrubs growing in the Missouri Botanical Gardens.
Feeds on under side of leaves.

NEWS AND NOTES.

The Twenty-fifth Annual Meeting of the Ohio Academy of Science was held at the Ohio State University, at Columbus, on November 26th and 27th. A special program was given in commemoration of the Quarter Centennial Anniversary.

* * * * *

The American Association for the Advancement of Science will hold its Annual Meeting on the Ohio State University Campus, at Columbus, December 27th, 1915 to January 1st, 1916. A large attendance is expected and arrangements have been completed to make the meeting one of unusual interest.

* * * * *

At the November meeting of the Biological Club, the following officers were elected for the ensuing year: President, Dr. F. H. Krecker of the Department of Zoology and Entomology; Vice President, Miss Clara G. Mark, of the Department of Geology; Secretary and Treasurer, Mr. Rollo C. Baker, of the Department of Anatomy.

* * * * *

The following officers were named by the Ohio State University Scientific Society for the year: President, F. C. Blake, Department of Physics; Vice President, Jas. R. Withrow, Department of Chemistry; Secretary, R. J. Seymour, Department of Physiology; Treasurer, C. J. West, Department of Mathematics. These officers constitute an executive committee which will arrange programs for the regular meetings of the society, the first of which will occur during January.

* * * * *

An interesting event occurring during the recent meeting of the Ohio Academy of Science was the short talk given by Dr. T. C. Mendenhall to the New York and San Francisco alumni of the Ohio State University by means of the trans-continental telephone. Dr. Mendenhall, while a member of the University faculty, established the first telephone to be used in central Ohio, a line from his University office to his residence, and he expressed himself as greatly pleased at the opportunity accorded him to speak to his former students over a line extending across the continent.

* * * * *

The Ohio Academy of Science at its November meeting voted to change the date of its annual session to a time corresponding to the Easter recess. The exact time of the meeting is to be determined by the executive committee, the Academy voting to have the next meeting occur in the spring of 1916.

* * * * *

Established last Spring, the latest honorary society, Phi Sigma, a student organization open only to students having completed an amount of biological work equivalent to a minor, has awakened interest in the universities of other states. Inquiries concerning the possibility of establishing other chapters at distant institutions have been received by the parent chapter at Ohio State University and it is probable that such chapters will be formed during the present year. Phi Sigma hopes to publish a biological quarterly in the near future.

Dates of Publication:
November Number, Nov. 22, 1915.
December Number, Dec. 20, 1915.

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