What kind of glue should I use to apply glass "pebbles" to glass ...

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I made a 'gazing ball' from a clear round fishbowl by applying colored glass pebbles, intending to leave it on my screen porch. Super freezing temp's, followed by humidity and rain caused all the pebbles to fall off (a few at a time). I need a weather-proof type of glue. Any suggestions?
q what kind of glue should i use to apply glass pebbles to glass
The complete project.
q what kind of glue should i use to apply glass pebbles to glass
After the winter weather!
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