Whittet-Higgins Adapter Assemblies consisting of tapered split sleeves with a locknut and lockwasher are used to locate and secure ball and roller bearings with tapered bores to shafting for use especially within pillow blocks and some other power transmission assemblies. Whittet-Higgins Adapter Assemblies function by sliding shafting into the pillow block containing the sleeve, lockwasher, and locknut, or if otherwise used, the sleeve along over a shaft, followed by the tapered bearing, the lock washer, and finally the lock nut. As the locknut is tightened onto the threaded portion of the adapter, it drives the tapered bore of the bearing up the taper of the sleeve. This action causes the sleeve to compress and exert clamping forces around the shaft. Once fully pre-loaded, the entire assembly is securely fastened to the shaft. This style of adapter sleeve is not symmetric around the shaft’s axis and therefore cannot be used in applications requiring dynamic balancing.