Definition of "unceasing"

The unceasing fatigue of my daily walks to and from Clapham, with my various trudgings from one Doctor Humbug to another Doctor Whimsical, combined with the before-mentioned causes to affect my health.

1841, William Johnstoun N. Neale, The naval surgeon, page 136

To handle the unceasing traffic increase, immense sums of money are being expended in dealing with bottlenecks.

1962 December, “Beyond the Channel: Switzerland: Federal Railways' progress”, in Modern Railways, page 416