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Application Registration[
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Without including the path Windows does not know where to find "second.exe". Also I recommend using "/" or "\\" as your path separator instead of "//" you could also prepend @ to the start of your path string like so: @"C:\Honey\second.exe".
Anyway in order for your app to be found without passing the path you will need to register it by either adding it to the system PATH environment variable or the App Paths registry key as show in the link.
Edit: If you copy the second EXE to the same path as the app you are creating the process from you would then be able to use Process.Start(Application.StartupPath + "\\Second.exe");