622 
LIEUT.-GBNERAL R. STRACHEY ON HARMONIC ANALYSIS OF 
be termed casual irregularities in the position of the phase of maximum, in dealing 
with some of which it becomes uncertain whether the maximum has been thrown 
forward or backward. 
In dealing with the series of Greenwich temperature values, a doubt of this sort 
arises in relation to the abrupt changes in the value of between January and 
February, and again between October and November, which might be attributed 
either to retrogression of the phase of maximum, or to progTCSsion. The uncertainty, 
however, in such a case hardly affects the mean monthly values, which are fanly 
consistent; but a doubt is introduced in determining an annual mean, the numerical 
value of which will depend on the conclusion adopted as to the way in which the 
changes take place. This hesitation is unavoidable in the absence of a series of values 
calculated for short periods while the change is going on. 
Much greater uncertainty prevails in dealing with the barometric values than with 
the thermometric, the irregularities in the former being far more numerous and per¬ 
plexing. 
It may be noticed with reference to the quantities p, q, that their absolute amounts 
represent tlie extent of the amplitudes of the components, while their signs only 
indicate the phase, or epoch of maximum, in relation to the successive quadrants in 
each recurring series of components. A succession of signs in the order + Id + fZ 
— "k fZ ’ — P’ — ? > "k — 9.^ corresponds to an epoch of maximum gradually 
Ijecoming later, and vice versd. The mutual destruction of a series of positive and 
negative values of p, q will, therefore, merely signify that there is no true time of 
maximum, or that all positions are equally probable or uncertain. 
When, as is not seldom the case, there are considerable variations in the values of p, 
an assumption may become necessary, in computing the mean of these values, as to the 
direction in which the departure of the separate values from the mean should be 
reckoned, whether onward or backward. 
For instance, in the Greenwich tables for temperature, the value of p-o in the month 
of Ma}^ for the year 1885 would by the computation appear as 85° 1'. Inasmuch, 
however, as will be seen from the separate values, the mean value is evidently much 
nearer to the commencement of the first quadrant, to which /x^ appertains, than to 
its termination, it has been assumed that the value instead of being 85° 1' should be 
represented by — 4° 59'; that is to say, that the departure of the maximum from the 
mean has taken place by occurring earlier and not later. All the entries of g in the 
Tables marked with the minus sign indicate that an assumption of this description 
has been made. 
