Holy Cross, Romanos III, with the hole of a nail from the Crucifixion
The miracle displayed in the video below is the traditional mark of authenticity of any splinter of wood which people might claim to be a segment of the true Holy Wood. The video shows a monk from Mount Athos placing the splinter of the Holy Wood in a glass of water. Initially, the splinter naturally floats, but after the monk says the Trisagion prayer, Psalms 50 and 142 , and makes the sign of the Cross three times with this splinter on the water, when he places it in the water again, the splinter sinks to the bottom.
The monk also displays a fragrant relic of St. Haralambos towards the end for veneration.
ORTHODOX CHRISTIAN FAITH AND LIFE 
I don’t understand the significance of it sinking.
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I think that it is a special ‘sign’ because it is a ‘violation’ of the laws of nature. Any normal splinter of wood would float, and indeed it does float in the beginning. But because it is no ordinary splinter of wood, but part of the Precious Cross of our Lord, endowed with super-narural properties, because our Lord was crucified and shed His most precious Blood on it, this is why it does not float, but sinks as a special sign, a miracle. No other splinter of wood on earth can do this, other than the splinters of wood which are part of our Lord’s authentic Holy Cross. Cf. The Travels of Macarius, Patriarch of Antioch, Volumes 1-4 at https://books.google.co.uk/books?id=WWiVkOz9XDoC&pg=PA374&lpg=PA374&dq=why+does+the+Holy+Cross+not+float+but+sink+in+water?&source=bl&ots=h9P3oQ8ytn&sig=ZqQHVAifLKKJtgltY8DjTpdnx1Y&hl=en&sa=X&ved=0ahUKEwid9sGxoe7ZAhWMJ8AKHcXKARsQ6AEIPDAD#v=onepage&q&f=false
Do you understand it any better or should I ask our priest for a better explanation? Our parish is blessed with the possession of a splinter of the Holy and Life-Giving Cross, and I am recalling him doing that same “experiment”, with success, to test the authenticity of the splinter. In our case, this tiny, authentic piece from our Lord’s Cross came down through the generations in the family of a spiritual child of his. A great-great-great-great … grandfather did a pilgrimage to the Holy Land on a donkey, served at the Holy Sepulchre and was given this blessing. But I can ask for more details if you are interested.
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