The term cos ( θ ( n ^ ) ) {\displaystyle \cos \,(\theta (\mathbf {\hat {n}} ))} is needed on account of Lambert's law.[15] Mathematically, the quantity F ( x , t ; ν ) {\displaystyle F(\mathbf {x} ,t;\nu )} is not a vector because it is a positive scalar-valued function of the prescribed direction and sense, in this example, of the downward vertical. In this example, when the collected radiation is propagating in the downward sense, the detector is said to be "looking upwards". The measurement can be made directly with an instrument (such as a pyrgeometer) that collects the measured radiation all at once from all the directions of the imaginary hemisphere; in this case, Lambert-cosine-weighted integration of the spectral radiance (or specific intensity) is not performed mathematically after the measurement; the Lambert-cosine-weighted integration has been performed by the physical process of measurement itself.