An inertial navigation around the surface of the earth is usually mechanized as the north slaved local level (NSLL). A distinctive feature of this mechanization is as follows: Provided is a platform which is always made level and north slaved by gyros and accelerometers on it, and from the outputs of the accelerometers time derivatives of the east-west and the north-south components of ground velocity are extracted, then these derivatives are time integrated twice to obtain the changes of latitude and longitude. In this case, the referred level is the geographic horizontal plane which is perpendicular to the gravity vector g. On the other hand, there exists another "horizontal" plane called the free surface of liquid. This plane has a characteristic of being perpendicular to the specific force vector α. The aforementioned two planes are coincident with each other only when a//g. If a platform always perpendicular to the vector α is provided by some means, and also provided an accelerometer whose sensitive axis is perpendicular to the plane of this platform, the accelerometer measures the total specific force a^p_Z the magnitude of which equals |α| Then, using some appropriate one or two spacial references, if the east-west and the north-south components of α, a^n_X and a^n_Y, are extracted from the output a^p_Z there results a new method of inertial navigation. This mechanization is apt to be named as the free surface, abbreviated as the FS, mechanization. This report describes the theotical bases of this mechanization.
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