EKE Repository of Publications

Csuzdi, Csaba

Chang, C-H.

Pavlicek, T.

Szederjesi, Tímea

Esopi, D.

Molecular Phylogeny and Systematics of Native North American Lumbricid  Earthworms (Clitellata: Megadrili)

Balázs, Mihály

Monok, István

Szamosközy István és a Corvina

Varga, András

Baranyai Decsi Jánosnak a török elleni háborúra buzdító beszéde 1598-ból

Franczia, Tamás

- 2 7 -
TAMÁS FRANCZIA 
AN ANALYTICAL METHOD FOR CALCULATING MULTICENTRE 
INTEGRALS BUILT UP FROM GTF-S I. 
Abstract: In this paper we explain the principles of an analytical method 
for calculating multicentre potential integrals built up from Gaussian 
basis functions. The method is based upon the theory of complex variable 
functions and the Fourier series form solutions of the two dimensional 
Laplace-equation. The multicentre integrals built up from Slater-type ba-
sis functions will be treated in the second part of the paper. 
Note before the introduction: As almost each work from C3 3 to c 12 3 in 
the referred literature contains the principles of the main part of the 
introduction in details we refer to books or articles only in a few cases 
in order to avoid the interruption of the text with references in many 
instances. 
Received on the 20-th of January 1986. 
- 28 -
Introduction: Let us consider a pair of two valence electrons a quantum 
mechanical system, which is the chemical bonding pair of a diatomic 
molecule. Let other valence electrons not be in the above-mentioned 
chemical bond. It is possible to construct the Hamilton operator of this 
electron pair if we choose the following work-hypotheses of the suitable 
ones. If the other electrons of the molecule are not valence electrons 
but so called core electrons belonging to either one or the other nucleus 
their effect on either of the valence electrons can be taken into account 
together with the influence of that nucleus they belong to. The effective 
potential of a system consisting of a nucleus and its core electrons can 
be expressed approximately with the aid of many pseudopotentials. i±j 
These pseudopotentials can be derived from the statistical theory of 
atoms or from the wave mechanics. ci3,C23,C33 
In the case of a valence electron mentioned above the effect of a nucleus 
and its core electrons on the valence electron can be given - among 
others - with the following pseudopotential form: 
VCrO=V CiO+V Cr), l r s r * 
Z cx_, a 
V. Cr) -£. - Ű 2 l r r 
2(r 2 +d 2] 2[r 2 +d 2] 
r C D = 2 A tr p exp (-«^r«). 
- 29 -
In these formulas v l rCr) given by BardsleyEd] is a "long range" pseudo-
potential while Mr is a "short range" one. The "r" variable means 
the distances between the nucleus and the points of the three-dimensional 
space. Zc is the effective number of the elementary positive charges in 
the system of the nucleus and its core electrons. The >ad,clq* 
quantities are atomic constants, p and q are integers. 
The first member of v L r is the effective potential of the nucleus and 
its core electrons affecting on the valence electrons of the atom, when 
it is not chemically bound to another one. The second and third members 
of v Cr) are the consequences of the fact that the atoms chemically 
l r 
bound to each other and having different electronegativities polarize the 
atomic cores of each other, in consequence of which the atomic cores take 
effect on the valence electrons not with a pure Coulomb-type 
pseudopotential, but with a modified potential compared to the Coulomb-
type one. If we put the origin of the system of co-ordinates in the 
nucleus of the first atom the Hamilton operator of the system of the two 
valence electrons has the following form in atomic units: 
- 30 -
a C2) a (2) 
2 q 
CI) 
is the position vector of the second 
where = (x1,yJ,z1J, 
?
2
= [x2>y2>z2)> 
that are the position vectors of the corresponding electrons. 
When the two-electron system is in the n-th stationary state its state-
function having the ri> r 2 position-vectors, the S>, , 
spin-co-ordinates and the t time-variable as arguments can be written in 
the following form according to the non-relativistic quantum-mechanical 
theory of the many-body problem: 
r 2 n v r p ' 
, C2) 
where h is the Planck-constant, En is the energy of the system 
satisfying the following equation too: 
- 31 -
S < " [ r i> r 2 > S l' S 2 ] d T 
C33 
where dr is the volume element in the configuration space of the system 
including the spin-co-ordinates of the electrons. The integral in (3) 
must be taken over the complete domain of all the variables. In the 
integration there is always included also a summation on the spin 
coordinates. [ri »r 2> si»s 2 ] is to be expressed with a linear 
combination of innumerable Slater-determinants of the second order built 
up from one-electron functions of yvCr,s:> type: 
21. ^ ( r i ' r 2 ' S l ' S 2 ) = ^ CL*L ( ri' r2' Sl' S 2] ' 
( l a ) 
22. $ = 
Vix(ri' Sl] ViTx[ri>Sl) 
C 4 b ) 
where i denotes the i-th repetitionless second-class combination of an 
innumerable discrete sequence of one-electron s ) functions, and the 
I,II indeces denote the first and the second member of the i-th 
combination of the y(r,s) one-electron functions 
- 3 2 -
As [r1,r2,s 1,s2,tj has to be normalized with the norm 1, 
^r1,r2,si ,s2J must also be normalized with the same norm. 
That is why the determinants are to be built up from normalized 
V(r,s) functions. The most general form of these yCr,s> functions 
is the following: 
yCr, s ) = yy+ C r + ifj_Cr)ß , CS) 
where and ^ Cr) have to satisfy the 
 |y/*Cr)y+Cr) + y/*Cr)v_Cr)J d 3r = 1 C61 
CO 
condition, a and ß are the basic spin-functions forming an orthonormal 
function-system. In the spinor representation given by Pauli 
v ő -
The V +Cr) and y_Cr) functions of (4a) are usually unknown. In order 
to reduce the number of the unknown functions in (4a) the y/Cr,s) ones 
are frequently written in the following forms that are less general and 
flexible than the form of V*?,s>in (5): 
- 3 3 -
<PßMß 
Let each determinant in (4b) be built up from theVCr,s) functions of 
the form given in (7). Thus the sum in (4a) can contain - among others-
such determinants in which "f>aCl':) - *V3Cr:>*Let <t. and <& be such 
J k 
determinants: 
<p. [?2]«C2> <p. [?J/3C2> 
According to (3) and (4a): 
- 34 -
r
00 
~ J 2 c* ** H 2 cL # l  = 
l =1 
OO CD 
• J 2 2 c * C l  H dr = 
1=1 i=i 
OO OO 
- I I c* ct J H 4>l dr = 
 =1 L=i 
C9I> 
H ®i d T integral in that case when i=j, £=k 
from (8a) and (8b). " 
v. [ r J a C D <p. (rJ/3Cl> 
^ [ ? J a C 2 > ¥>j(?J/3C2> 
^ ( r J a C l ) ^(rJflCl* 
dr: 
 -  . 
CD 
- 35 -
"\ffo K ] « C í W 2 > ] * £ [lP k[rJ#) k(? ajaCl W2>]dT -
" J h W 2 ) ] * S [ * k ( F j * k [ F j a C 2 W l * ] d T -
CD 
" J h f2]«C2)/3Cl)]^ H [iPk(Fj*k(r Ja<l>0C2>]dr + 
CD 
CIO) 
ao 
Taking into account the fact that the aCl),ßCl) and aC2),ßC2> 
spin-function pairs are separately orthonormal function-systems we get 
from (10): 
J 5 i kdr = 2 | H (?J*>k ( r J J d ^ d V , C I D 
CD OU CO 
H being a sum of operators the right-hand side of (11) is a sum of 
integrals. Let us consider the following member of this sum satisfying 
the "undermentioned equation: 
a .C2) 
 K i ^ k 'J* ^ j 3— r 2 = 
- 3 6 -
^ J T T -
ad<2> 
C12) 
Let us investigate the first integral-factor in the right-hand side of 
(12). Let and ^k [ ri] be real functions, [ ri] and 
'f>k írij c a n ^ written in the form of the linear combination of 
Gaussian-functions: 
[rJ = 2 c. 
2a 
J-E. exp [- « j J r ^ R j 2 ] CI3a) 
J = 2 
2 a 
•kq 
kcj. exp [- « k q [ r i - R j 2 ] C13b> 
where c . , c. , a. , ct. J P k q j p ' kq are real constants. Putting (13a) and 
(13b) in the first integral-factor of (12) we get: 
h N T T T -
a ,C2) a 
[ M J X I 
^k[ ri] d 3 ri " 
r 2a. 
3 
4 
K P M J ' ] Í 5 « i P exp 
oo P 
a (2) 
a 
"kq 
2a 
JL2. exp [- a k q ( r 1 - E j 2 ] d ! C14) 
- 37 -
This integral is also equal to a sum of integrals. The general member of 
this sum is the following: 
h 4 C. c, P kq 
4a. a. ip k<» exp 
a,C2> a 
[ M j ' - a * 
CIS) 
In this part of the paper we want to give a method for the beginning of 
the calculation of this integral. 
Treatment: First let us express the exponent with the components of the 
R p a R q , r i vectors: 
 T 
It will be sufficient to investigate in details only the members of (15) 
depending on x. because the members depending separately on x., y., 
- 38 -
or z^ have the same structure. 
a. f x -x 1 2 - a , fx - x l 2 = -a. Í X 2 - 2 X x +x2l-a^ f x 2 - 2 x x +x2l 
J P l P 1J M l q J p l P p i t J kq L q q 1 lj 
= - fa. X 2 - 2a. X x + a. x 2 + a, X 2 - 2a, X x, + a, x2l = I. J P P JP P 1 J p l kq q kq q 1 kq lj 
= -ffa. +a 1 x 2—2 fa. X X ]x +a. X2+a, X21 = 
LI. JP kqj i L JP P kq qj i jp p kq qj 
2 fa. X +a, X 1 
r ^ I L J P P kq q J 
= - a +a 
I J P kqj a. +a, 
j p kq 
a X +a XJ 
J P P k q q 
a. +a, j p k q 
= - | a . +a, 
I j p kqj 
a. X +a, X 
J P P k q q 
a +a. j p k q 
a. X +a X^ 
J p P k q q 
a +a. 
J P kq 
a. X +a, X j p p kq q 
a. +a, 
J P KQ 
= - fa. +a I 
I JP k q ) 
a. X +a, X 
J p P k q q 
a. +a, 
J P k q 
fa. X +a X 1 
I J P P kq qj 
a. +a, 
J P kq 
- fa. X 2 + a X21. C17> 
I J P P kq qj 
Now we can see that introducing the 
a. X +a, X 
j p p k q q 
< = X — — C18a) 
a +a, 
J P kq 
a. Y +a Y 
J P P kq q 
n = y - _ — — C18b3 
a +a, 
J P k q 
- 39 -
oc. Z +a, Z 
J p p k q q 
^ - Z - C18c) 
1 a. +a, 
J P kq 
arguments in place of ( X, , the exponential function factor in 
the integrandus is to be written in the 
exp [- [a j p+a k q] (<2+7?2+<2] form. 
The integral in (15) expressed with the arguments gets a 
constant multiplier in front of the sign of the integration: 
exp 
fa. X +a. X ]2+ía. Y +a, Y ] % f a Z +a, Z 1 
I J P P kq q j I JP P k q qJ I JP P kq q j 
a. + a, 
J P kq 
ia. X2+a X 2] - fa. Y2-*-a. Y 2] - ía. Z2+a, Z 2 ] 
L J P P kq q j I JP P k q qj I J P P kq qj 
rising only from the (17) expression of the exponent because from (18) we 
get the 
- 40 -
dx í 
. ( 1 o b 5 dz =dí; C19c) 
C19a), dy^dr? C19bJ, ± 
equations not giving constant multipliers to be written in front of the 
sign of the integration. 
Introducing the 
i 
f l 2 ^ C20a> 
i 
h p 
i 
(20b> 
<20c) 
arguments in place of Kf^^K the form of the exponential factor i 
the integrandus will be simpler: 
exp [-[K *)• 
From (20) we get: 
- 41 -
d< = C21 a) 
_ 1 
dr, = [ a j p + a k J ~ W C21b) 
_ i 
d < = h p + a k J C 2 i c : > 
Taking into account (18) and (21) we can write: 
__ i 
d X i = h p + C , k q ] ^ C 2 2*> 
1 
d y i = ( a i p + a k j ^ C 2 2 b ) 
_ 1 
(21) gives another constant multiplier accompanying to the first one 
mentioned between (17) and (18): 
fa. +« 
I J P k q j 
Now let us transform the "polarizational" part of the integrandus. Its 
original form is: 
- 42 -
a, C2> a,C2) 
. a d 
[ M J «:] [(*.-".) •(*.-'.) -C8,-.) «;]' 
C 2 3 3 
Applying the 
f ct. +a 
I J P kqJ 
a X +a, X 
J P P kq q 
a. +a. 
J P k q 
C24a) 
^ [°jP+akq] 
a Y +a, Y j p p kq q 
a. +a, 
J P k q 
C 24b) 
a. Z +a, Z 
J P P kq q 
OÍ. +a, 
J P kq 
C24c) 
formulas rising from (18) and (20) in (22) we get for the right side of 
(23): 
a, (2) 
a 
X
2 - V c T +a, 
r j p kq 
. a X +a, X 
^ , .1 P P k q q 
T c T +a. ' 
y j p kq J 
« A Ö ) 
T J p k q 
, a Y +a. Y 
, + .1 P P iL2__a 
_/ a . +a , * j p k q 
- 43 -
a, (2) d 
1 , ex. Z +a. Z 2 — £ +—LE_P ct Q + rl2 
- y a. +a • 
L ' J p kq -J a. +a. 1 * J p kq 
Multiplying (25) with exp 2 + r ) 2+K 2 J J w e ^ o r m 
integrandus expressed with the < >< arguments and not containing 
any constant multipliers in front of the sign of the integration. Further 
on we will disregard the constant multipliers because it is possible to 
expound the principles of the beginning of the calculation disregarding 
them. 
The integration in (15) was ri - type and we have 
OD 
transformed it to the jFCp)d3p form, where p = , rj J, d 3p = 
CD 
d< . dr? - d< i TK<2 JVcp) d p integration means simple integrations 
OO 
on the <',17',*;' arguments from -co to + cd in each case. It is 
allowed to begin the integration with that variable we want to, because 
the limits of the three single integrations are constants. So let us 
begin with the integration on j*' .In this case the two other variables 
are to be considered as constants. The form of the integral on <i s the 
- 4 4 -
following: 
tC2) exp [-(V 2 +i;' 2]]ex P 
X2~ 
T j p kq 
, a. X +a, X 
K + l l p p q q 
I v ^ T T ^ k q 
d^ (26) 
+d 
where 
i' 2 
-/a" +a, 1 
T J P kq 
, a. Y +cx, Y 
ry + ,i P P k q q 
___ — I 
T J P kq 
Z2-
y J P kq 
K + 
a. Z +a, Z 
,1 p p kct q 
y J P kq 
+d d' C27> 
Let us introduce the following notations: 
1 a X +a, X 
F def. - - ; C28a), V def. L£L-£ LSLJl C2Bb) 
7 a , +a ' x a +a 
f J p k q J P k q 
Using these notations the integral in (26) has the following form: 
- 45 -
- g d C 2 ) e x p [ - ( , 2 H > 2 ) ] e x p [ - ^ 2 ] ^ 
. [ K " ^ ' + F x] 2 + d' 2] 2 
Let us introduce the # notation with the following definition: 
& ~ x 2 + Fx » With this notation the integral in (29) can be 
written in the following form: 
3 ctdC2)exp ] H [V
2-K'2] Í] exp 1 K 1 I 
1 [1 • rí'] I2+ I2 
-»oo 
First we have to solve the problem of the calculation of the integral of 
the following-type: 
exp j [ - Í ' 2 ] I 
1  - r? I
2 + d' I 2 
If we solve the problem of the calculation of this integral, then 
multiplying the result with exp 1^7' 2+t; ' 2jj we can continue the 
integration on 17' or in the other case on y . Now let us deal with the 
- 4 6 -
integral in (31). This integral can be calculated approximately with 
the method of the numerical analysis. In this case we ought to apply the 
Hermite-Gauss integration formula approaching the value of the integral 
with a sum. With this technique we could calculate the original • • d 3r 
CD 
integral applying the Hermite-Gauss-forrnula three times. But in this 
article we want to explain the beginning of an analytical method. 
In mathematics one of the methods for calculating definite real integrals 
is based upon the so-called residuum-theorem of the theory of complex 
variable functions. In some cases we can use a simpler form of this 
theorem, the Cauchy-theorem. Let us begin with showing the possibilities 
and the conditions of applying Cauchy's theorem for calculating definite 
real integrals. 
Let z = x+y=T-\ y = x+iy, where x,y are real numbers, x is 
the real part of z while iy is the imaginary one. Consisting of two parts 
z is called a complex number. The complex numbers can be described as the 
vectors of the complex Gauss-Argand number-plane: 
 -
I f Z 2 = X 2 ± i y 2 ' L h e n 
zx ± z 2 = ^ ^ ^ ( y t ^ ) . 
• z2 = = 
= x i x 2 + i x i y 2 + i y i x 2 - y x y 2 = 
= [ xi x 2-yiy 2] - i( xty a + x ayi) 
according to the definitions of the summation and the multiplication of 
complex numbers. 
Let f(z) be a function of z projecting the complex number-plane onto 
itself. As the values of f(z) are complex numbers f(z) consists of a real 
and an imaginary part: 
fCz) = utx,y)+ivCx,y) , 
C32a) 
C32b) 
where u(x,y) and v(x,y) are real functions, 
b 
J fCz)dz means a complex integral of the f(z) function that must be 
a 
taken on the complex number-plane along the G curve between its a and b 
points: 
b b 
J fCz)dz = J ju(x,y)+ivCx,y}IdCx+xy) = 
a a L J 
 a 3  o 3 
b b 
= J [uCx,y)+ivCx>y)Jdx + f [uCx,y)+ivCx,y>JdCiy) = 
- 4 8 -
b b b b 
J* uCx,y)dx+i J vCx,y>dx+i J" uCx,y)dy- J vCx,y)dy= 
CG) CG) 
u o 
= J juCx,y)dx-vCx, y)dyj+i J |uCx, y)dx+vCx, y)dxj , C34) 
where we have used (32a) and (32b). 
It is to be seen that a complex integral of a complex variable function 
can be calculated with the aid of real integrals. 
Let G be a closed curve of the complex number-plane and let f(z) be 
analytical on the set consisting of all points of the closed G curve and 
also in all points of the region of the plane bordered by this curve. In 
this case 
<£ fCz)dz = 0. 
C GD 
C35) 
This is Cauchy's theorem. The analyticy of f(z) on a set means that 
f Cz) l i m h —* O 
fCz+h)-f(z) 
v* + C3Ó) 
exists in each point of the set, where h means complex numbers. The 
operation defined in (36) is called the complex derivation of f(z). 
- 4 9 -
Cauchy and Riemann have proved that f'(z) exists in the z point only in 
1 1 1 . r. •• <?U ÖV 
that case if the cTy> partial derivatives exist in this 
point and satisfy the so-called Cauchy-Riemann equations: 
How can we calculate/ fCx^dxusing Cauchy's theorem? First we have to 
write z in place of x in f(x) then we have to form the fCz)dzintegral 
along a closed G curve containing the ta,b] interval of the x-axis. If 
f(z) is analytical along G and within the region of the plane bordered by 
G we-can write using (35) and the z=x,if y=0 equation: 
§ fCz)dz = J fCz)dz + J fCz)dz + . . . + J fCz)dz + 
_ dy <3u 
Cx C)y ' cjy 
d\i _ Öv rn'y^ 
~ cK C 3 7 ; > 
b 
CL 
b z 
+ J fCx)dx + . . . + J fCzDdz = O 
n 
C38} 
z n-1 
CG 
where G . U G 2 U . . . UAku ... uta,bi u ... ua n - 1 Q. 
(U is the sign of forming the union of sets.) 
If we can calculate the values of the integrals of the sum in the 
- 5 0 -
b 
right-hand side of (36) exceptJ fCx>dxwith simple analytical methods, 
a. 
the (38) equation gives us an analytical formula for the value of 
b 
J fCx)dx. 
a. 
The application of this method and that of the two-dimensional Laplace-
equation for the calculation of the integral in (31) will be treated in 
the second part of this paper. 
- 5 1 -
LITERATURE 
Cl3 p. Gombás: Pseudopotentiale, Springer Verlag, Wien, 1967. 
[23 P. Gombás: Die statistische Theorie des Atoms und ihre Anwendungen, 
Springer Verlag, Wien, 1949. 
C33 H. Hellmann: Einführung in die Quantenchemie, Deuticke, Leipzig 
1937. 
[43 3. N. Bardsley: Case Studies Atomic Physics 1974. 4. 299. 
£31 P. Gombás: Theorie und Lösungsmethoden des Mehrteilchenproblems der 
Wellenmechanik, Birkhäuser Verlag, Basel 1950. 
1 6 3 G. Heber - G. Weber: Grundlagen der modernen Quantenphysik, Teubner 
Verlag, Leipzig 1956. 
C7D G. Marx: Quantum Mechanics, Technical Publishing House Budapest 
1957., 1971. (in Hungarian) 
[83 R. Gáspár: Matrix Elements of Symmetrical Operators with Slater 
Determinants I. Acta Physica et Chimica Debrecina 
Debrecen, Hungaria 1962. 
£93 J. Ladik: Quantum Chemistry, Technical Publishing House Budapest 
1969.,(in Hungarian) 
[103 E. Kapuy - F. Török: The Quantum Theory of Atoms and Molecules 
Publishing House of the Hungarian Academy of Sciences, 
Budapest 1975. (in Hungarian) 
[11] K. Nagy: Quantum Mechanics Publishing House of Text Books 
Budapest 1978. (in Hungarian) 
[123 G. Náray-Szabó: Applied Quantum Chemistry Technical Publishing 
House Budapest 1979. (in Hungarian) 
[ 13 3 A. Ralston: A First Course in Numerical Analysis. Mc. Graw - Hill. 
Book Company 1965. 
L l 4 i J. Duncan: Elements of Complex Analysis John Wiley & Sons. 



An analytical method for calculating multicentre integrals built up from GTF-S I.

Szabó, Béla

A német testgyakorlati oktatók  szerepe az  iskolai testnevelés  tanítás  kialakulásában  és fejlődésében a XVIII.  század  végén és a XIX.  század elején

Szilágyi, István

Magyar, román, belga szociális szakos hallgatók összehasonlító érték- és attitűdvizsgálata

Bartos, László

- 3 -
BARTOS LÁSZLÚ
Ü5SZEIIASÜNLÍIÚ FAUNISZTIKAI VIZSGALAIÜK A üUKK-IIEGYGÉG
DÉLI RÉSZÉNEK ORTHOPTERÁIN
Abstract: Author studied the composition o? the Orthoptera - communities 
during a 3 years - period in a steppe - liko habitat in the SW-pat uf the 
Bükk - mountains (National Park, resp.) He has collected 2303 specimens 
of 11 grashopper and 14 locust species with combined methods of 
collection by singling and sweeping. The results are sunimarized in tables 
1-5. On the basis of the résült the Orthoptera-fauna of the giveu arca, 
although relatively rich in species, has decreased in generál since 19ÜÜ. 
It is possible ,that the likely reason is woodfelling and cutting in the 
neighbouring regions.
A mintegy 120 hazai fajt magábanfoglaló Orthoptera rend tagjainak el-
terjedését hiányosan ismerjük, noha irodalmi forrásokból tudott, hogy 
igen alkalmasak különböző, főleg nyílt növénytársulások, rétek, gyepek 
jellemzésére. Az ide tartozó fajok zöme —  táplálkozása révén —  szorosan 
kapcsolódik bizonyos növénytársulásokhoz, és egyben a mi kroki ima tikos 
viszonyokat is jelzi. Ebből következik, hoc/ az egyes növényasszociációk-
nak meghatározott faji összetételű és gyakoriságeloszlású Orthoptera- 
együttesek felelnek meg, mint ezt hazánkban először Nagy Barnabás állapí-
totta meg a Hortobágyon, (1944) majd a Tihanyi-félszigetén (194Ü), vala-
mint hazánk más tájain végzett kutatómunkáéi alapján.
Ezen túlmenően, az Orthopterák vizsgálatának gyakorlati jelentősége 
sem becsülhető alá, mivel az adott ökoszisztéma anyag —  és energiáfor- 
galmában ezek a zömében phytophag táplálkozásé fajok jelentős szerepet 
töltenek be. Ürülékükkel ugyanis a talajba nemcsak jelentős mennyiségű, 
könnyen lebomló szerves anyag kerül, hanem —  főleg cellulózbontó —
4szimbionta mikroorganizmusok tömege is, melyek a talajban a cellulóztar-
talmú anyagok lebontásában nagy jelentőséggel bírnak (Sztcbajev 1957, 
1968).
VIZSGÁLATI MÓDSZER
Az ürthoptera-fauna megismerésének első lépése az előforduló fajok 
megállapítása. Ezért egyeléssel és fűhálózással nagyobb mennyiségű anya-
got igyekeztem begyűjteni. Az egyes mintavételi helyeken, a terepviszo-
nyoknak megfelelően, meghatározott nagyságú területről (kb. 300 m ), 
ugyancsak meghatározott idő alatt (kb. 1/2 —  1 óra) minden fajból, válo-
gatás nélkül, lehetőleg a maximális példányszámot gyűjtöttem be. Az emlí-
tett két gyűjtési módszer kiegészíti egymást: a több szöcskefaj által is 
kedvelt bokros, cserjék helyeken eredményesebb az egyeléssel való gyűj-
tés, míg a nyílt, füves területeken a fűhálózás igen hatékony.
VIZSGÁLATI EREDMÉNYEK
Az Orthopterák vizsgálatát a Bükk-hegység déli részén, a Bükki Nemze-
ti Park területén elhelyezkedő Odorvár közvetlen szomszédságában lévő Tö-
rökréten végeztem. A mintavételek 1900-tó. kezdve, évi 3--4 alkalommal a 
júliustól —  szeptemberig terjedő időszaka estek, mivel az említett ftó- 
napokban az Orthopterák —  zömmel —  teljesen kifejlett példányait sike-
rült begyűjteni, ami lehetővé tette pontos meghatározásukat.
Az említett mintavételi területet, amely a Déli-öükk legmagasabb 
pontját képező Odor-hegy (661 m) délkeleti oldalgerince mentén fekszik a 
Felsőtárkány —  Völgyfőház —  Odorvár felé vezető erdészeti út mindkét 
szélén, az alábbi térképvázlat ábrái szemléltetik.
- 5 -
b ü k k i n emzet i par k
V  1 1 Miskolc
r _
v 2 Eger
^ 3 Felnémet^
4 5zarvaskőf
5 Felsótárkány
6 Bukkzsérc
7 Cserépfalu
8 Cserépváralja 
i Szigorúan védett
terület
Í Mintavételi 
te rü le t
mintavételi helyek
~ 6 -
A vizsgált terület akapkűzete pala, vegetációjára a felvételek i(15- 
pontjában az elsztyeppesedett irtásrét—  kaszáló —  átmenet veit jellem-
ző, az alábbi domináns növényfajokkal: Ari heiialcrum elal.iu:;, CampauuTa 
persicifolia, Echium russicum, Festuca rupicola, Filipendula hexapetala, 
Fragaria vesca, Galium verum, Hel ianthemum óva tűm, tlypnclioeri r; macii la La, 
Phleum plileoides, Plantago média, Rumex acetosa, frifolium alpesire, l'ri- 
folium montanum, Thesium linophyllon, Valeriána off icinali.s, Verbascum 
plioeniceum, Vcronica teucrium, Viscaria vulgáris.
A terület növényzete az intenzív fakitermelési munkák miatt, Ívűi-
től kezdve erősen degradálódott.
Az egyes mintavételi periódusok alatt az adott területen 11 szöcske, 
valamint 14 sáskafaj, összesen 2.3G3 példányát gyűjtöttem be.
A gyűjtött anyag faji összetételét, cgvidszámát, dominanciáját, vala-
mint életforma és faunaelem jellegét az alábbi táblázatok foglalják 
össze:
F a j o k  Fgycdszám
(Tettigonoidea)
Leptophyes albovittata 202 
Bicolorana bicolor 131 
Ephippigera ephippiger 39 
Platycleis grisea 25 
Pholidoptera fallax 22 
Pholidoptera cinerea 11 
Isophya pyrenaea 9 
Phaneroptera falcata 9 
Pachytrachis gracilis 4 
Rhacocleis germanica 1 
Saga pedo 1
Dominancia Életforma Inuiiwolem
0,004 Ch. Eu.
0,05s Th. Szil)
0,01 f', Th. iioi.
0,010 ' 111. Eu.
0,009 Th. Pont
0,0Cí Th. Eu.
0,00^ Ch. Eu.
0,002 Th. Hol.
0,001 Th. Pnn t.
0,0004 Th. Punt
0,0004 Th. Pont
- 7 -
F a j o k Egyedszám Dominancia Életforma Faunaelem
(Acridoidea)
Glyptobothrus apricarius 480
Stenobothrus lineatus 475
Euthysthira brachyptöra 460
Chortippus longicornis 221
Stenobothrus crassipes 206
Pseudopodisma.fieberi 37
Glyptobothrus brunneus 27
Tetrix bipunctata 9
Oedipoda coerulescens 7
Calliptamus italicus 5
Tetrix tenuicornis 4
Gomphocerippus rufus 3
Chortippus dorsatus 3
Chortippus montanus 2
Jelmagyarázat: Ch.:
Th. :
Geo.:
Ch.-geo.:
Eu.:
Szib.:
Hol. :
Pont.:
Euszib.-pol.:
0,201 Ch. S z i b .
0,199 Ch. S z i b .
0,193 Ch. Szib.
0,092 Ch. Szib.
0,086 Ch. Pont.
0,015 Ch. Eu.
0 ,0U8 Ch. E u s zi b.-
pol.
0,003 Ch. E us zi b.-
p o l .
0,002 Geo. H o l .
0,002 Ch.-geo. Hol.
0,001 Ch. Euszib.-
pol .
0,001 Ch. S z i b .
0,001 Ch. S z i b .
o,o:oo Ch. Szib.
Chortobiont
Thar nobiont -
Geo!, iont
Cho^to-geobiont
Európai
Szibériai
Holomediterrán
Pontomediterrán
Eur'.szibériai - policentrikus
- 8 -
A DOMINANCIA VISZONYOK ELEMZÉSE
Mindhárom évben . (1980; 1981; 1982j lényegében azonos időpontban és
azonos módon végeztem a mintavételeket. Ennek alapján a fajösszetétel és 
a dominancia változásait követtem nyomon. A gyűjtőhelyek alapfaunáját 
azok a fajok adták, amelyek valamennyi miniavételi helyen mindhárom évbon 
viszonylagosan egyenletes gyakorisággal fordulnak elő. Ezek voltak: Ste- 
nobothrus lineatus, Euthyshira brachyptera, Chortippus longicornis, 
Glyptobothrus apricarius, Bicolorana bicolor. A Stenobothrus lineatus az 
összes mintavételben jelen volt, de minden évben tömegesen csak a 3. sz. 
gyűjtőhelyen fordult elő. A felvett minták zömében ingadozó vagy alacso-
nyabb gyakorisággal fordultak elő az alábbi fajok: Stenobothrus crassi- 
pes, Platycleis grisea, Phaneroptera falcata, Pholidoptera cinerea, Pseu- 
dopodisma fieberi, Tetrix bipunctata.
Olyan faj nem volt, amely kizárólagosan jellemző lett volna mindhárom 
évben valamennyi mintavételi helyre.
A vizsgálati periódusban csökkent gyakoriságot mutatott az Ephippiye- 
ra ephippiger, Glyptobothrus brunneus, Pholidoptera fallax, Isophya pyre- 
naea, Leptophyes albovittata, növekedett viszont a Stenobothrus crassipcs 
dominanciája mindhárom gyűjtőhelyen az 1982. évben.
Erősen változtatta helyét a Tetrix bipinctata és a Pholidoptera fal-
lax .
Csak igen kis egyedszámnal fordultak elő az állatföldrajzi szempont-
ból szinező elemekként jelenlévő Pachytrachis gracilis, Rhacocleis genna- 
nica és a Saga pedo, melyek valamennyien rsökevényes szárnyú, holyhezkö- 
tött, ragadozó szöcskék.
Alkalmilag előforduló fajok a Calliptjmus italicus, Oedipoda coeru- 
lescens, Gomphocerippus rufus, Chorthippus rnontanus, Chorthippus dorsa- 
tus, melyek hosszúszárnyú, jól repülő sáskák.
- 9
A FAJ- ÉS ÉLETFORMA OIVERZITÁS ELEMZÉSE
Mindhárom gyűjtési év összesített dominancia-adataiból kiszámítottam 
a fajdiverzitást a Shannon-Weaver képlet segítségével, mely a minta sok-
féleségét két komponens; a fajgazdagság és fajgyakorisági eloszlás alap-
ján adja meg:
- « ■ I P i x In pi
ahol: - H = diverzitás
pi = relatív gyakoriság (egyedőrtékszám/öss 
egyedértékszám)
In pi = relatív gyakoriság természetes alapú 
logori tmus:*
I - összegzési utasítás
Az éves fajdiverzitási értékek a begyűjtött példányszám összmennyisé- 
gével fordítottan arányosak, miként ezt az alábbi táblázat is mulatja:
Év 1900, 1901, 1902,
Összmennyiség 
Fajdiverzitás
442 074 1067
2,32 2,10 1,95
Ez a jelenség annak a következménye, hogy a nagyobb üsszpéldányszám 
csupán néhány faj nagyobb tömegű előfordulására vezethető vissza, amint 
ez az alábbi táblázatból is kitűnik:
- 10 -
F a j o k 1980. 1981. 1982. Ossz. példányszám
Glyptobothrus apricarius 61 153 266 400
Stenobothrus lineatus 92 172 211 475
Euthysthira brachyptera 72 252 129 460
Chortippus longicornis 47 103 71 221
Stenobothrus crassipes 28 14 164 206
Leptophyes albovittata 20 82 90 192
Ugyanezen képlet segítségével —  összegezve az azonos életformájú és 
faunaelem jellegű fajok gyakorisági adatait —  kiszámítottam az életfor-
ma- és faunaelem —  diverzitás értékeit is, melyeket az egyes életformák 
és faunaelemek relatív gyakorisági értékeinek feltüntetévésével, az aláb-
bi táblázatban foglaltam össze:
ÉLETFORMA-DIVERZITÁS
Év
Életforma
1980, 1901, 1902.
Chortobiont 0,7534 0,9004 0,9034
Chorto-geobiont 0,0113 - -
Geobiont 0,0150 - -
Thamnobiont 0,1244 0,0915 0,0965
Életforma-div./év ' 0,5805 0,3059 0,3173
- 11
FAUNAELEM-DIVE RZIT ÁS
Év
Életforma
1900, 1981. 1902.
Holomediterrán 0,6564 0,0331 0,0246 .
Szibériai 0,2081 0,8237 0,7057
Euroszibériai-
policentrikus 0,04797 0,0080 0,0246
Európai 0,0316 0,1167 0,1190
Pontomediterrán 0,0633 0,0183 0,1658
Faunaelem-div./év 0,9379 0,6347 0,0461
AZ EREDMÉNYEK KIÉRTÉKELÉSE
A vizsgálat időtartama alatt begyűjtött egyed- és fajszám alapján (11 
szöcske- és 14 sáskafaj 2383 példánya), megalapítható, hogy az adott te-
rületen aránylag fajgazdag Orthoptera-közösscg fordul elő.
Az Orthoptera-egyuttes 4 féle életformával és 5 féle faunaelemmel 
jellemezhető.
A vizsgálati területen fokozatos degradáció figyelhető meg, ami 
összefügg azzal, hogy az itt végzett rendszeres fakitermelés károsító ha-
tása kiterjed az erdőirtások közelében lévő rétekre is. Ezt igazolja, 
hogy két életforma-típus (chorto-geobiont és geobiont) a vizsgálat kezdő 
évéhez viszonyítva teljesen eltűnt, az életforma-diverzitás erősen 
visszaesett. A faunaelem-diverzitás 1900-ről 1901-re jelentősen csökkent. 
1982-re viszont kisebb mértékben újra emelkedett. Az általános fajdiver- 
zitás és az életformánként! fajdiverzitás i': csökkenő tendenciájú a vizs-
gálati időszakban.
- 12 -
A fent említett vizsgálati eredmények alapján levonható végkövetkez-
tetés ismételten alátámasztja azt a tényt, tiogy az eddigieknél nagyobb 
hangsúlyt kell fordítani az emberi környezetátalakító tevékenység', vala-
mint a környezet- 0s természetvédelem nem könnyű feladatainak összehango-
lására még akkor is, ha a népgazdasági érdekeknek (jelen esetben pl, fa-
kitermelésnek) elsődleges helyet biztosítunk. Ennek elmulasztása esetében 
fennáll annak veszélye, hogy a természtes ökoszisztémák biológiai egyen-
súlya felborul, aminek végül is maga az ember látja kárát.
IRODALOM
Adamovic, Z. R. (1971): Orhoptera of the dry, grassy habitats of the 
Djerdap gorge and its surrounding country, NE Serbia, Acta Ént. 
Dug. 7. 1. p. 11— 18. Zagreb.
Boldogh, I. (1970): Összehasonlító vizsgálatok hazai szárazgyepek, i11. 
karsztbokorerdő-gyep mozaik komplexek egyenesszárnyú (Orhoptera) 
együtteseinek zoocönológiai viszonyairól. Szakdolgozat. KL1E 
Állattani Tanszék, Debrecen.
Móczár, L. (1969): Állathatározó I. kötet. Tankönyvkiadó, Budapest.
Nagy, B. (1943): Adatok a Tiszántúl Orthoptera-faunájának ismertetésé-
hez. Föl. Ént. Hung. VIII. 1— 4. p. 33— 44. Bpl.
(1944): A Hortobágy sáska- és szöcukevilágo I. Acta Scient. 
Math. Nat. p. 3— 57. Kolozsvár. .
(1947) : A Hortobágy sáska- és szöcnkevilága II. Közi. a debre-
ceni Tudományegyetem Állattani Int.-bői, Debrecen.
(1948) : 0n the Orthoptera fauna of the Tihany peninsula (Laké 
Balaton, western Hungary). Archiv. Bioi. Hung. II. 18. p. 59— 64.
(1953): Bátorliget egyenesszárnyú-faunája Orthoptera—
- 13 -
Galtatoria. In Székessy, V.
(1953): Bátorliget élővilága p. 10/— 193. üp.
(1958) : Ökológiai és faunisztikai adatok a Kárpát-medence sás-
káinak ismeretéhez. Föl. Ént, Hung. XI. 9. p. 218--230.
(1959) : Das Sicheingraben von Acrotylus longipes und A. 
insubricus (Qrthoptera, Acrididae.) Acta Zool. Acad. Scient. Ilung.
V. 3— 4. p. 369— 387.
Rácz, I. (1973): Összehasonlító vizsgálatok északkelet-magyarországi
homok-, lösz- és szikespusztai gyepek Ürthopteráin. Szakodolgozat. 
KLTE Állattani Tanszék, Debrecen.
CTeőaeB M. B . , (1957): OcoóennocTM 3KO/ior»n naceicoMbix b padone KoirraKTe
CTenetl h nycTHHb, iianpMMep, iiph mo k puj ih v  Cenepo-3aMa;uioro Ilpmcaciimi
I .  06c. Bmo ji. 18 ,2  : 137— 152.
(1968): ílpocTpaHCTBeHHaa cTpyKTypa nace^emia wra Cmó hph b
CBB3H c ocoóemiocTBMM CTpyKTypu hx noMneimoro noitponu. HoitJirut
CMÓMpciíMx noaBOBe^oB k X Mex/i.y Hapo^n. Konrp. riOMBOBe^ oB: 93— 107.
HOBOCMŐlipCK
Stebaev, I. V., Naplekova, N. N. and Volkovincer, V. V. (1960): Epigáisc 
Zoo-Mikrobionten - Komplexe mit Orthopteren und Tenebrioniden im 
Südostlichen Altaj-Gebirge und ihre Beziohungen zu bodenbi Idei idén 
Prozessen. Pédobiologia 8: 345— 306.
Varga Z., (1960): Összehasonlító vizsgálatok, hazai száraz gyepek Orthnp- 
tera-társulásairól. Kézirat,


Összehasonlító faunisztikai vizsgálatok a Bükk-hegység déli részének orthopteráin

Budai, László

Egyszerű hőöszzegmérés

Vojtkó, András

A Bükk hegység déli riolitvonulatának florisztikai és cönológiai jellemzése

Szatmári, Zoltán

Horváth, Eszter

Fritz, Péter

Ácta Ácademiae Ágriensis, Seetio Sport, 2015. Nova series tóm, XLII. pp. 77-83.
s z a t m á r i z o l t á n , Ho r v á t h e s z t e r , f r i t z  Pé t e r
Eszterházy Károly Főiskola, Sporttudományi Intézet, Eger
a b o u t t h e h i s t o r y o f a n i m a l t h e r a py
a z á l l a t t e r á pia t ö r t é n e t e
Abstract
The animal therapy as a therapy method is really old. People in the antiquity 
used the healing power of animals. Éven Hippocrates, the well known doctor used 
horses to strengthen the trunk muscles. In the middle Ages the knowledge of the 
antiquity lost, the people used animals as tools. Nowadays they started to discover 
these methods again, especially in Germany, in the UK and in the USA. In these 
countries there were created many organisations in the past 50 years. They train 
animals (dogs, horses, dolphins and so one) to help more and more children and 
adults with different kinds of psychological, intellectual problems or locomotor 
disorder. Unfortunately in Hungary this process is not as known as in abroad. 
There are only a few organisations who deal with this ancient technique.
Primarily we do my research about this topic in the library and on the inter-
net. Unfortunately there is not any information about animal therapy in Hungári-
án, but we can find many data in Germán and English.
Doing our research we learn that there are many people, who inquire about 
this method, but unfortunately in our country it won’t be as generál as in abroad. 
The reason of it is mainly the serious and expensive medical examinations of the 
animals. That’s why this tendency cannot spread in Hungary.
Keywords: animal therapy, healing, organisations, learning
Development of the topic
Nowadays we use animals not only as pets but also in the medicine as a 
healing method. Naturally all kind of animal can be a therapy animal, but I’ll 
intensively deal with the dog and the horse therapy. However still these two have 
a really big literature, I would like to emphasize some part which I think are im- 
portant or interesting.
Éven in the prehistory we can speak about connection between people and 
animals. However this relationship is confined only the hunt in this early age. La-
78 Szatmári Zoltán, Horváth Eszter, Fritz Péter
tér people domesticated somé of the animals. The wolves were among the earliest 
from them. They help us in hunting and they also became loyal partners. Then we 
realized the healing power of them.
1
The animal therapy as a therapy method is really old. People used it even in 
the antiquity. Almost all culture in the world has one or more “saint” animals. The 
Egyptians figured nearly all of their gods from animals (Anubis, Bastet, Thot). 
Some of them were used for healing, for example the dogs. They tought the dog’s 
salvia have a healing power. So people really respect the animals in Egypt, ex- 
pecially the cats which was so mumficated like the Pharaoh. The murder of a cat 
was a deadly sin. In Greek the horses were used for cure. Even Hippokrates the 
well known doctor used horses to strengthen the trunk muscles.1 2 Horses were also 
very popular around the Hungárián adventurers, who went even to the afterlife 
with their animals.3
1 h ttp :/ /w w w .ta n k o n y v ta r .h u /h u /ta r ta lo m /tk t/k u ty a ta r -k u ty a ta r /c h 0 5 .h tm c l
2 h ttp ://w w w .p sy c h o lo g y a fr ic a .c o m /2 0 1 2 /0 5 /th e -b e g in n in g -o f-a n im a l-a ss is te d - th e ra p y -a a t/
h ttp :/ /w w w .p a c id o k i.h u /h u /lo v te r_ h u .h tm l# c _ 0 0 1
3
Ábout the history o f animal therapy 79
4 5
In the middle Ages the knowledge of the antiquity lost, people used animals 
more as tools than therapy method. The reason for that were the serious rules of 
the Church. The religion controlled all area of their life, and so the connection 
between people and animals was not as strong like in the antiquity. But even in 
this dark age we can find objects of using this therapy method. Saint Roch (Szent 
Rókus) the Franciscan monk with a dog’s help, which licked his wounds, recove- 
red from the plague. Later he became the patron saint of people who recovered 
from the black death.4 56 *
r------------- ]i
o  c  c  o
i 7
4 h ttp ://b a rk p o s t-a s se ts .s3 .a m a z o n a w s.c o m /w p -c o n te n t/u p lo a d s /2 0 1 3 /0 5 /g re e c e -d o g .jp g
5 h ttp ://w y sin g e r.h o m e s te a d .c o m /e g y p t_ d o g .jp g
6 h ttp ://je le sn a p o k .o s z k .h u /p ro d /u n n e p /s z e n t_ ro k u s
h t t p : / / l .  b p .b lo g s p o t .c o m /- H O p 6 a A B 3 X O c /T 9 - V M 5 s H K - I /A A A A A A A A B - A /y M w H
F G M D n s/sl6O O /2 5 8+ S an+ R occo .jp g
7
80 Szatmári Zoltán, Horváth Eszter, Fritz Péter
After this dark period our society started to discover the knowledge of the 
antiquity again.
At the end of the 1600 John Locke tried to arehive the social- and emphatic 
development of the children with the help of animals.8
In 1750 the doctor of Mária Terézia recommended the queen the horse riding 
as a therapy method for strengthening her weak trunk muscles. However this kind 
of therapy also proved to be very useful in the treatment of emotional disorders.9 
Éven one of the greatest literateur, Goethe firmly believed in the positive effect 
of the horse riding.
The first time when we find written objects about the use o f animal therapy was 
in the 18 century. In a mental hospital in York Retreat in England William Tuke
practiced this method on mental ill patients.
We know Sigmund Freud as the father o f the psychoanalysis, but only a few 
people know that he was also the first who had resort to the help o f a dog in tre- 
ating people. His dog the Chow Chow Jofi was a real therapy dog which always 
presented during the psychological therapy. According to Freud the dogs are the 
best methods to cure people, who have psychosomatic problem. They don’t have 
any stereotype toward the patient, however their emphatic ability is very well 
developed, their presence mean a calming effect for the patient.10 1
In 1919 also in America people started to discover the beneficial effect of 
the animals. The St. Elizabeth Hospital in Washington institute began to apply 
animals in mental healing programs.
Animal therapy was used even during the II. Word War. Smoky, the little 
Yorkshire Terrier is a great example for that. Smoky was a dog of Corporal Wil-
liam Wayne who got hurt in the battle, so while he convalesced, one of his fri- 
ends brought his dog to the hospital to feel himself better. It was a brilliant idea,
8 h ttp ://w w w .p sy c h o lo g y a fr ic a .c o m /2 0 1 2 /0 5 /th e -b e g in n in g -o f-a n im a l-a ss is te d - th e ra p y -a a t/
9 h ttp :/ /w w w .p a c id o k i.h u /h u /lo v te r_ h u .h tm l
10 h ttp ://s ch n au ze rfo to .d e /2 0 1 0 /0 3 /c h o w -ch o w -jo fi-u n d -s ig m u n d -freu d -b e ru e h m te -h u n d e /
11 h ttp ://k u ty a -p o rta l.h u /w p -co n ten t/u p lo ad s/2 0 1 4 /0 1 /Jo f i-% C 3 % A 9 s-S ig m u n d -F reu d .jp g
Ábout the history o f animal therapy 81
because the presenee of Smoky had a very good effect on the other patients. The 
doctor of the hospital noticed this, and he let the dog to visit his keeper regularly, 
as a living antidepressant for him, and for the other soldiers, who often had phy- 
sically or mentally injury.
Although Smoky was not for the war trained dog, he served in the II. Word 
War. He saved his keeper’s life many times, when he forecasted the bombs. But 
his greatest feat was when he showed under a tűnnél a 70 m long cord. A bunch 
of people’s life was saved with this action. Smoky is a national hero now, he has 
many monuments all over America.12 134
13 14
Animal therapy was use even in the Germán military during the II. Word 
War. Ernst Göring, son of the Luftwaffe chef Hermann Göring used therapeutic 
horseback riding to rehabilitate the wounded pilots.15
1968 passes for a milestone in the history of Animal Assisted Therapy, 
namely in this year the idea was born by Prof. Boris Levinson, about using animal 
therapy in Clinical psychology. The psychologist of the American Yeshiva Uni- 
versity, Dr. Levinson deal with mentally handicapped children, and children with 
behaviour disorders. One day he treated a young boy with behaviour disorders. 
Levinson tried to speak to him for months, but it was hopeless, the young boy 
refused to answer. Once he was forced to bring his dog in his surgery. However 
when the boy saw the dog he started to ask questions about it, and slowly he asked 
not only about the dog but he spoke with the doctor. Then Levinson regularly used 
his dog during the treatments. He started to study the relationship between people
12 h t tp s : / /b o o k s .g o o g le .h u /b o o k s ? id = 2 P ru q y a D w 6 w C & p g = P R 1 6 & lp g = P R 1 6 & d q = a n im a l+
a ss is te d + th e ra p y + sm o k y & s o u rc e = b l& o ts= b T tw d K 2 A d d & sig = 0 a a x B sR o O D G jL _ O H D JE o -  
x fg Y v A & h l= d e & s a = X & e i= e _ g a U -D q N o f p y w P a 4 Y C A D g & v e d = O C G U Q 6 A E w B A # v =  
o n ep ag e& q = a n im al% 2 O a ss is ted %  2 O th erap y % 2 O sm o ky & f= false
13 h ttp :/ /u p lo a d .w ik im e d ia .o rg /w ik ip e d ia /e n /b /b 7 /S m o k y _ (d o g )_ in _ h e lm e t.jp g
14 h ttp :/ /w w w .n jp e tc o m m u n ity .c o m /w p -c o n te n t/g a U e ry /n jp e t/sm o k e y /s m o k y -w a r-d o g -y o rk ie -  
y o rk s h ire - te m e r .jp g
15 G e o ffre y  C ocks: P sy c h o th e rap y  in  th e  T h ird  R eich: T h e  G ö rin g  In s ti tu te  IS B N  1-56OOO-9O4-7, 
p. 312.
82 Szatmári Zoltán, Horváth Eszter, Fritz Péter
and animals, he even gave leeture on it, and collected information about other, 
similar cases. ünfortunately his speech was unsuccessful, that time the society 
was not enough open for that kind of discovery.16
The using of AAT spreaded in America and England first, bút later alsó 
became very popular in Germany, Switzerland and in the Netherlands. In 1969 
the RDA was created in England, and in the same year the NAHRA in the USA. 
In 1979 the SCAS was created (Society fór Companion Animál Studies) in the 
UK. Soon much more organizations formed in the world, for example the CSTo G
(Centre fór Service and Therapy Dog’s Germany) in Germany and in 1997 the 
MLTSZ and in 2006 the MATESZE (Magyar Terápia és Segítőkutyás Egyesület) 
in Hungary. In 2004 the ESAAT was born (European Society for Animál Assis- 
ted Therapy).
Nowadays series of surveys demonstrate the effectiveness of the AAT. It can 
be help both to the children, adults and old people. It gives assistance to overcome 
depression and help to build contacts. In Hungary and the neighbouring countries 
the dog and the horse therapy plays a huge role. We can use both of them for mo- 
tion development. With the horses we can improve the trunk muscles.
Sources
http://w w w .psychologyafrica.com /2012/05/the-beginning-of-anim al-assis-
ted-therapy-aat/
http://www.pacidoki.hu/hu/lovter_hu.html#c_001
http://jelesnapok.oszk.hu/prod/unnep/szent_rokus
http://w w w .psychologyafrica.com /2012/05/the-beginning-of-anim al-assis-
ted-therapy-aat/
http://www.pacidoki.hu/hu/lovter_hu.html
http://books.google.hu/books?id=2PruqyaDw6wC&pg=PA25&dq=william+-
tuke+anim al+assisted+therapy+bethlem +hospital& hl=de& sa=X& ei=I-
vQaU406Men_ygOJrIKIBg&ved=0CCwQ6AEwAA#v=onepage&q=wil-
liam % 20tuke% 20anim al%20assisted% 20therapy% 20bethlem% 20hospi-
tal&f=false
http://schnauzerfoto.de/2010/03/chow-chow-jofi-und-sigmund-freud-beruehmte-
hunde/
http://books.google.hu/books?id=2PruqyaDw6wC&pg=PR16&lpg=PR16&dq=a-
nimal+assisted+therapy+smoky&source=bl&ots=bTtwdK2Add&sig=0a-
axBsRoODGjL_OHDJEo-xfgYvA&hl=de&sa=X&ei=e_gaU-DqNofpy-
16 http://www.matud.iif.hu/2011/06/06.htm
Ábout the history o f animal therapy 83
wPa4YCADg&ved=OCGUQ6AEwBA#v=onepage&q=animal%2Oassis-
ted%20therapy%20smoky&f=false
Geoffrey Cocks: Psychotherapy in the Third Reich: The Göring Institute ISBN 
1-56000-904-7, p. 312.
http://www.matud.iif.hu/2011/06/06.htm
Pictures
http://www.tankonyvtar.hu/hu/tartalom/tkt/kutyatar-kutyatar/ch05.htmcl
http://barkpost-assets.s3.amazonaws.com/wp-content/uploads/2O13/O5/gree-
ce-dog.jpg
http://wysinger.homestead.com/egypt_dog.jpg
http://l.bp.blogspot.com/-HOp6aAB3XOc/T9-VM 5sHK-I/AAAAAAAAB-A/
yMwH_FGMDns/sl6OO/258+San+Rocco.jpg
http://kutya-portal.hu/wp-content/uploads/2O14/O1/Jofi-%C3%A9s-Sigmund-
Freud.jpg
http://upload.wikimedia.org/wikipedia/en/b/b7/Smoky_(dog)_in_helmet.jpg
http ://w w w .n jpetcom m unity .com /w p-con ten t/gallery /n jpet/sm okey/sm o- 
ky-war-dog-yorkie -yorkshire -terrier.j pg


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Molecular Phylogeny and Systematics of Native North American Lumbricid Earthworms (Clitellata: Megadrili)