There are a few clues, but the murderer is still at large.
The first clue is about Mrs Lestrange. Lawrence wheedles a maid into telling him what she overheard when the colonel and Mrs Lestrange talked the night before the murder. I have the hunch that Mrs Lestrange is Colonel Protheroe’s first wife, and the reason she has come to Saint Mary Mead is to see her daughter Lettice. Yet, it seems the colonel was not forthcoming. Could this be a plausible motive? Could Mrs Lestrange have killed the colonel because he opposed to her seeing her daughter? A mother can go to great lengths for a child. Yet, that doesn’t match what we know from her. After all, she left her daughter behind to flee with another man.
The other clue, which I think hasn’t been registered yet, is the information the pharmacist gave Mr Clement about the train from London being delayed the day of the murder. Somehow this might be linked to his wife going to London. Did she really go to London or did she lie? And what is the jewel he has just found in the study where the colonel was murdered? Did it belong to his wife? We know that the room has been sealed off until now, but why didn’t the police see this piece of jewellery?