Since the 1970s oceanic velocity gradients have been extracted from the differential motions of drifters in clusters. These algorithms rely either on a linear flow model based on a Taylor expansion of the drifter positions or velocities or on a generalized Stokes theorem integration around the convex hull of the cluster. An essential assumption is that the mean velocity and the velocity gradient components (the kinematic properties, or simply KPs) are constant over the area defined by the cluster. In recent years, as the density of drifter observations has increased dramatically, these methodologies have experienced a renaissance, including applications to deriving KPs from sea ice (Lukovich et al., Cryosphere, 2017). This approach requires a minimum of 3 drifters. In a critique of various aspects of the paradigm, Kirwan (JGR, 1988) proposed an alternative method for estimating KPs, whereby the flow equations are solved analytically. In this approach, the critical assumption is that the KPs are approximately constant over the time between 3 consecutive position observations. The advantages of this approach are that the expansion region is localized to a single position instead of a cluster area, and the KPs can be obtained from just one drifter. The disadvantage is that the solutions involve transcendental functions, in which nonlinear combinations of the KPs are parameters in the function arguments. Consequently, Kirwan stated that this approach would be difficult to implement. We show here that Kirwan was wrong, again. We obtain KP estimates following the basic assumption of that approach by application of linear algebra to individual trajectory data. Using data from recent CARTHE experiments we compare KP values obtained from the new paradigm with those from drifter triplets using the traditional approach. The analysis offers new insight into both the spatial regions and time periods over which Lagrangian estimates of the KPs are approximately constant.