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You are an expert at summarizing long articles. Proceed to summarize the following text: 
BACKGROUND OF THE INVENTION 
     The present invention concerns a hinge for a roof window with a sash pivoting around an axis located between the upper and the lower member of a window. 
     A roof window with a pivot function is at both sides equipped with pivot hinges, comprising two hinge parts, one hinge part secured to the side member of a window frame, and the other hinge part secured to the side member of a sash. Each hinge part has a base plate for securement by fastening screws through screw holes. 
     One side of each base plate has additional means for securing the plate to a window frame or a sash and the other side of the base plate has members mating one another, which connect both plates, enabling their separation, and enable pivoting of the base plates relative to each other. The members constitute: an arched, one-sided open guide with a friction spring located on the base plate secured to a window frame, and a pivoting hook with an arch-bent arm, a guide pin and a bumper for limiting hook pivoting located on the base plate secured to a sash, at the same time the arm-bent hook arm and the guide pin mate the arched guide and the friction spring. 
     Pivot hinges in roof windows are secured between the upper and the lower window member, usually in a place that ensures the balance of a sash in the open position of a window. The balance is achieved when the centre of gravity of a window sash is in its rotation axis or in such a distance from the rotation axis that the hinge friction spring is able to keep an unbalanced sash in any rotational position. Therefore the rotation axis of a roof window sash is usually located at a little distance from the half of the window height. A bigger shift of the sash rotation axis or any additional equipment on any of its parts, the lower or the upper, disturbs the balance and causes that a window is unable to hold its sash in each ajar position and a user operating the window has to use more strength to overcome the unbalanced weight of the sash. 
     A roof pivot window is known from applications WO2005/019574, which is equipped with a known pivot hinge, of the rotation axis located in the upper half of a window, sash, in addition it is equipped with at least one auxiliary device independent from the hinge, presented as a cylinder, which carries the lower, heavier part of a window sash. The device is at one end secured to a window frame and at the other end it is secured to a window sash, in addition the securement allows to separate the device from the window frame. 
     The auxiliary device constitutes an additional fixture of a roof window and it requires performing of additional activities during assembly of a window and during installation of a window in a roof, it deteriorates aesthetics of the window in an ajar position of the sash, moreover if the need arises to remove a sash from a window frame the cylinder must be disconnected from the window frame beforehand. 
     SUMMARY OF THE INVENTION 
     The object of the present invention is a pivot hinge with a balancing system for roof windows with a sash pivoting around the axis located between the upper and lower member of a window, which ensures the state of equilibrium of a window sash when its centre of gravity is located beyond the sash rotating axis and the friction spring of the hinge is unable to hold the sash pivoted in each its position. At the same the time the window fittings, its assembly and installation in a roof as well as its appearance remain unchanged. Also the method of separating both hinge parts—taking a sash out of a window frame—remains unchanged. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       A hinge for roof windows, according to the present invention, is presented in embodiment examples on a drawing where  FIG. 1  and  FIG. 2  present a view of a hinge with a balancing system in the open and closed positions of a sash —in the first embodiment;  FIG. 3  shows the surface of the hinge base plate B mating the plate A—suitable for all embodiments described and presented in the drawings;  FIG. 4  shows the hinge base plate A viewed from the side mating the plate B, in the first embodiment;  FIG. 5  shows the hinge base plate A viewed from the side of the mating surfaces in the second and the third embodiment;  FIG. 6  and  FIG. 7  present a view of a hinge with a balancing system in the open and closed positions of a sash—in the second embodiment;  FIG. 8  and  FIG. 9  present a view of a hinge with a balancing system in the open and closed positions of the sash—in the third embodiment. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Example I 
     A hinge for a roof window with a pivot sash comprises a hinge part A, secured to the side member of a window frame and a hinge part B secured to the side member of a sash frame. Both hinge parts have base plates  1 A and  1 B with screw holes  2  for fastening screws with additional fastening members  3  on one surface. At the other surface the base plate  1 A has an arch-bent guide  4  inside of which a friction spring  5  is secured and a through elongated hole  6  is made in the plate  1 A between arched members of the guide  4 . The base plate  1 B has a pivoting hook  7  with an arch-bent arm, a guide pin  8  and a bumper  9  limiting the range of the hook  7  pivoting. The arch bent arm of the hook  7  and the guide pin  8  mate the guide  4  and the friction spring  5 . 
     The base plates  1 A and  1 B at one end have fasteners  10 A and  10 B for securing external cover members, at the same time after securing the plate  1 A to the side member of a window frame, the fastener  10 A is located above the sash rotation axis, whereas after securing the plate  1 B to the side member of a sash, the fastener  10 A is located below the sash rotation axis. 
     At the side with the fastening member  3  the base plate  1 A has a holder  11  for a spring  12 , whose other end is engaged on a slide  13  located in a hole  6 . 
     The slide  13  protrudes at both sides of the base plate  1 A and mates the guide pin  8 , secured to the base plate  1 B, and moving along the guide  4 . 
     When a window sash is taken out of a window frame or it is pivoted to the maximum, the slide  13  is drawn by the spring  12  towards the holder  11 . During mounting a window sash in a window frame and during closing a window sash the guide pin  8  is guided into the guide  4  and exerts pressure on the slide  13 , moving it away from the holder  11  to the other end of the hole  6  when the window sash is closed. The spring  12  is than extended but the sash stays in the position set by a user thanks to the friction spring  5 , which stops the self-movement of the arm of the hook  7  and the guide pin  8  inside the guide  4 . 
     Turning a window handle fully protects against the uncontrolled movement of the window sash and blocks the window against opening. After realising the lock with a window handle the spring  12  balances the weight of the window sash and a user only needs to use little power enforcing sash pivoting to turn the window sash. 
     Example II 
     A hinge for a roof window with a pivot sash comprises a hinge part A, secured to the side member of a window frame and a hinge part B secured to the side member of a sash frame. Both hinge parts have base plates  1 A and  1 B with screw holes  2  for fastening screws with additional fastening members  3  on one surface. At the other surface the base plate  1 A has an arch-bent guide  4  inside of which a friction spring  5  is secured and a through, elongated recess  6  is made in the plate  1 A between arched members of the guide  4 . The base plate  1 B has a pivoting hook  7  with an arch-bent arm, a guide pin  8 , which protrudes beyond the base plate  1 A through the recess  6 , and a bumper  9  limiting the range of hook  7  pivoting. The arched arm of the hook  7  and the guide pin  8  mate the guide  4  and the friction spring  5 . 
     The base plates  1 A and  1 B at one end have fasteners  10 A and  10 B for securing external cover members, at the same time after securing the plate  1 A to the side member of a window frame, the fastener  10 A is located above the sash rotation axis, whereas after securing the plate  1 B to the side member of a sash, the fastener  10 A is located below the sash rotation axis. 
     At the side with the fastening member  3  the base plate  1 A has two holders  11  and  14  located near the bottom edge of the base plate  1 A, where a rod  15  is held with a spiral spring  12  and a slide  13 . The spring  12  rests with one end against the holder  11  and with the other one it rests against the slide  13 . The slide  13  is secured to the pivoting catch  16  mating the guide pin  8 . The catch  16  is fitted with a protrusion  17 , which limits its pivoting movement at one side. 
     When a window sash is taken out of a window frame or when it is open and turned to the maximum, the slide  13  is located near the holder  14 , and the catch  16  rests with the protrusion  17  against the slide  13  in a position ready to mate the guide pin  8 . 
     During mounting of a window sash in a window frame and during closing a window the guide pin  8  together with the arched arm of the hook  7  is guided into the guide  4  and the recess  6  and slides into the catch  16 . During the further movement of the window sash the guide pin  8  slides inside the guide  4  and pulls the catch  16  together with the slide  13  towards the holder  11  and makes the spring  12  compressed. The spring  12  by means of the catch  16  balances the window sash, which stays in any position set by a user thanks to the friction spring  5 , stopping the movement of the pin  8  and the hook  7 . 
     Turning a window handle fully protects against uncontrolled pivoting of a window sash and blocks a window against opening. After realising the lock with a window handle the spring  12  balances the weight of the window sash in any position and the window sash stays in a position set by a user thanks to the friction spring  5  while a user only needs to use little power enforcing sash pivoting to turn the window sash. 
     Example III 
     A hinge for a roof window with a pivot sash comprises a hinge part A, secured to the side member of a window frame and a hinge part B secured to the side member of a sash frame. Both hinge parts have base plates  1 A and  1 B with screw holes  2  for fastening screws with additional fastening members  3  on one surface. At the other surface the base plate  1 A has an arch-bent guide  4  inside of which a friction spring  5  is mounted and a through, elongated recess  6  is made in the plate  1 A between arched members of the guide  4 . The base plate  1 B has a pivoting hook  7  with an arch-bent arm, a guide pin  8 , which protrudes beyond the base plate  1 A through the recess  6 , and a bumper  9  limiting the range of hook  7  pivoting. The arched arm of the hook  7  and the guide pin  8  mate the guide  4  and the friction spring  5 . 
     The base plates  1 A and  1 B at one end have fasteners  10 A and  10 B for securing external cover members, at the same time after securing the plate  1 A to the side member of a window frame, the fastener  10 A is located above the sash rotation axis, whereas after securing the plate  1 B to the side member of a sash, the fastener  10 A is located below the rotation sash axis. 
     At the side with the fastening member  3  the base plate  1 A has a guide  18  mounted along the bottom edge of the base plate  1 A, restricted at one end by the holder  11 . The slide  13  in the form of a rod  13 ′ moves along the guide  18 . The rod  13 ′ is secured with one end to a seat  13 ″ while its other end slides through a hole in the holder  11 . A spiral spring  12  is slid over the rod  13 ′, one side of the spring  12  is engaged at the free end of the rod  13 ′ and its other side rests against the holder  11 . The seat  13 ″ is connected to a pivoting catch  16  mating the guide pin  8 . Pivoting of the catch  16  is limited at one side by a cut-out in the seat  13 ″. 
     When a window sash is taken out of a window frame or when it is open and turned to the maximum, the seat  13  is located near the holder  11 , and the catch  16  assumes the position ready to mate the guide pin  8 . 
     During mounting of a window sash in a window frame or during closing a window the guide pin  8  inserted into the guide  4  and the recess  6  slides into the catch  16 . During a further movement of the window sash the guide pin  8  slides inside the guide  4  and moves the catch  16  together with the slide  13  away from the holder  11  and enforces compression of the spring  12 . 
     Turning of a window handle fully protects against the uncontrolled pivoting of a window sash and blocks the window against opening. After realising the lock with a window handle the spring  12  by means of the catch  16  balances the window sash, which stays in any position set by a user thanks to the friction spring  5  stopping the movement of the pin  8  and the arm of the hook  7  while a user only needs to use little power enforcing sash pivoting to turn the window sash.

Summary:
A pivot hinge for roof windows with a sash pivoting around the axis located between the upper and the lower member of a window, has a balancing system, which ensures the state of equilibrium of a window sash when its centre of gravity is located outside the sash rotating axis and the friction spring of the hinge is unable to hold the sash pivoted in each its position. At the same time the window fittings, its assembly, installation in a roof and its appearance remain unchanged. Also the method of separating of both hinge parts (taking a sash out of a window frame) remains unchanged.