Let's say you want a build of Chrome 44 for debugging purposes. Google does not offer old builds as they do not have up-to-date security fixes.
However, you can get a build of Chromium 44.x which should mostly match the stable release.
- Look in https://googlechromereleases.blogspot.com/search/label/Stable%20updates for the last time '44.' was mentioned.
- Loop up that version history ('44.0.2403.157') in the Position Lookup
- In this case it returns a base position of '330231'. This is the commit of where the 44 release was branched, back in May 2015.*
- Open the continuous builds archive
- Click through on your platform (Linux/Mac/Win)
- Paste '330231' into the filter field at the top and wait for all the results to XHR in.
- Eventually I get a perfect hit: https://commondatastorage.googleapis.com/chromium-browser-snapshots/index.html?prefix=Mac/330231/
- Sometimes you may have to decrement the commit number until you find one.
- Download and run!
* As this build was made at 44 branch point, it does not have any commits merged in while in beta.
Typically that's OK, but if you need a true build of '44.0.2403.x' then you'll need to build Chromium from the 2403 branch. Some PortableApps/PortableChromium sites offer binaries like this, due to security concerns, the Chrome team does not recommend running them.