Height series of H { \alpha } spectra in solar limb spicules obtained with the 53 cm coronagraph of the Abastumani Astrophysical Observatory are analyzed .
Each height series covered 8 different heights beginning at 3800 km above the photosphere .
The spatial difference between neighboring heights was 1 ^ { \prime \prime } , consequently \sim 3800 - 8700 km distance above the photosphere has been covered .
The total time duration of each height series was 7 s. We found that nearly 20 \% of measured height series show a periodic spatial distribution of Doppler velocities .
We suggest that this spatial periodicity in Doppler velocity is caused by propagating kink waves in spicules .
The wave length is found to be \sim 3500 km .
However the wave length tends to be \sim 1000 km at the photosphere due to the height variation of the kink speed .
This probably indicates to a granular origin for the waves .
The period of waves is estimated to be in the range of 35-70 s. These waves may carry photospheric energy into the corona , therefore can be of importance in coronal heating .