(Click image to enlarge. Photo from http://www.yellowjersey.org/photosfromthepast/swizzlejb.jpg as of 2012/08.)

In the late 1890's, rear hubs were made with one rear sprocket, which was about in line with the right bearing. As more sprockets were added, the bearing moved away from the dropout and towards the center, so loads got more overhung. The axle size was typically not increased, so by the 1970's, axle failures with freewheels were common even for light riders. The rear axle may have been the second most fragile part on many bicycles, with only tubes failing more often.

Frequent failures ultimately gave rise to the cassette freehub being reintroduced in the early 1980s. Oddly, at least as early as the 1970's, some freewheel hub makers used larger axles and had almost no failures; yet most hub makers continued to use thin axles for the next decade, until cassette freehubs mostly replaced multi-speed freewheels.[*]

  

(From http://en.wikipedia.org/wiki/File:Labeled_Bicycle_Hub_Comparison-en.svg as of 2012/08.)

The most common rear axle failure point is at the inboard edge of the right rear cone, where loads are the highest. Worse, the axle is threaded, increasing stresses. Instead of larger axles, another solution is a shouldered axle with the right cone snugged against the shoulder (or a spacer carrying loads from the cone to the shoulder). Shouldered axles were used widely in inexpensive hubs and also in some rear hubs — probably from the 1950's — they likewise were not used widely.

Pair of BSA hub axles. New old stock. front and rear. never installed. Threads are perfect. Some light corrusion on the center of the axle, does not affect performace. (hub in photograph not for sale, only there to show what type of hub uses this axle). $25.00 http://www.bikeville.com/hubparts.html as of 2012/08.

[*] As a further ironic note, by the 1990s, once cassette hubs of the design above were common, another design re-emerged in which the bearings are even more overhung than with a conventional freewheel hub. Axle failures were initially common, but (unlike most freewheel hubs in the 1970s and 1980s, which stuck with skinny axles), these designs switched to using a larger axles, leading to much-reduced failure rates. An example design is shown below. The orange-color bearings support the hub shell and blue-color bearing support the sprockets; both run on the same axle. (Above image from BikeRumor as of 2014/08.)

See also FAIL-196.html.