1886.1 Computation of the Harmonic Components, tyc. 367 



granular after a certain mode of treatment is said to be albuminous. 

 It is perfectly possible that such a cell should secrete a substance 

 which is more allied to mucin than to albumin. We do not yet know 

 enough about the chemical characters of the bodies intermediate 

 between proteid and mucin to make any dogmatic statement on this 

 head. 



A fuller account of the points dealt with in this paper will shortly 

 be published in the " Journal of Physiology." 



II. " On the Computation of the Harmonic Components, &c." 

 By Lieut.-General Strachey, R.E., C.S.I., F.R.S. Received 

 April 15, 1886. 



(Abstract.) 



The object of this paper is to propose a method of computing the 

 harmonic components of formulas to represent the daily and yearly 

 variations of atmospheric temperature and pressure, or other recur- 

 ring 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 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. 



Approximate methods of determining the coefficients and of the 

 components for each interval of the series, are also given, from which 

 last a graphical representation of the components may easily be ob- 

 tained. 



The system of computation is applicable to all cases in which the 

 angular intervals between the observations are such as to make the 

 circle a whole series, exactly divisible by 6 and 8, and it has been 

 extended, by aid of an interpolation, to the case of the 73 five-day 

 means of a yearly period, in which the calculation by the ordinary 



VOL. XL. 2 c 



