The object of this paper is to propose a method of computing the harmonic components of formulæ to represent the daily and yearly variations of atmospheric temperature and pressure, or other recurring phenomena, which is less laborious than the ordinary method, though practically not involving sensibly larger probable errors. According to the usual method the most probable values of the harmonic coefficients are found by solving the equations of condition supplied from the hourly or other periodical observations, by the method of least squares. The number of these equations is, however, much larger than the number of unknown quantities, when these are limited, as is usual, to the coefficients of the first four orders, and the numerical values of the coefficients of those quantities which depend on a series of sines of multiple arcs, afford peculiar facilities for the eliminating process, so that values of the harmonic coefficients may be obtained by applying certain multipliers to combinations of the original observations obtained by a series of additions and subtractions, the results giving probable errors virtually the same as those got by the method of least squares. These multipliers for the two first orders of coefficients are so nearly equal to 2/30, and for the third order so nearly 0·07, that the values may readily be found without tables, though such tables have been calculated to facilitate computations.
Microwave temperature and pressure measurements with the Odin satellite: I. Observational method
