The low-temperature magnetizations of liquid-quenched Au-Ni alloys containing 42 to 55 at% Ni have been measured in an uniform magnetic field (2 to 70kOe) using a motor-driven vibrating sample magnetometer. The spontaneous magnetic moments at 1.5 K were obtained. And the Curie temperatures were determined from Arrott-Noa-kes plots. The measured magnetic moments are first compared with the average moments calculated from Perrier nearestneighbor model. Furthermore, we not only consider the Ni nearest neighbors but also the Ni second-nearest neighbors. The simple model of an environment-dependent moment is presented. It is assumed that one Ni atom has a moment μNi=0.606 μs if surrounded by at least 11 Ni atoms as nearest and second-nearest neighbors (the numbers of the nearest and the second-nearest neighbor are 18 for fee structure), and no moment if not. The calculated values from this model fit the measured values well. The existence of spin clusters and their interactions are discussed. The averagevalues of the internal field μBH/kB, which present the ferromagnetic interaction betweenspin clusters, are estimated.