The significant limits within which crustal movement can be determined by geodetic survey methods depend on the quality of the observations, the stability of the markers in the network, and the structure of the network. The paper presents a study of vertical movement in the Lac St. Jean area of Québec. The data used covers the periods 1919–1938 and 1962–1966. With reference to a line of levels from Ste. Anne de la Pérade to La Malbaie along the north shore of the St. Lawrence River, the results show annual uplift as high as 10 mm at Seneterre and subsidence amounting to 4 mm at Stoneham, north of Quebec City. Confidence intervals, at the 95% level, for rates of movement are given as indicators of the quality of the results.

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The concepts of least squares adjustments and the relationships between various types of adjustment are presented in terms of generalized matrix algebra. By developments based on the variance law for independent observations and the linear relationship between independent and correlated observations, variance-covariance matrices and the corresponding weight matrices are developed. The use of generalized matrix algebra permits the derivation of weight matrices from singular, variance-covariance matrices by inversion of the latter matrices. A singular transformation matrix for the elimination of superfluous parameters from observation equations prior to adjustment is presented.