4.66 TRANSACTIONS OF SECTION A. 
being impressed in the usual way, it will contain the brighter stars of all the 
regions to which exposure was made: and with a little care the stars of each 
region can be given sensibly the same réseau co-ordinates as on the separate plate S, 
already measured for the Catalogue. The superposition of several regions will 
give no trouble in measuring if the co-ordinates are called out from the existing 
measures (e y., the measures already printed) by an assistant; and new-measures 
made on the composite plate C will give, with very little work, the differences 
C—S, of scale value and orientation (I say nothing here of errors of centre, which 
are to be for the present neglected, though I am not without hopes of determining 
them also by photographing a fixed mark with each region) between the separate 
plate S, and the composite plate C. Now the constants of the separate plates, 
S,, S., 8,, &c., have all been determined, though the determinations are rough, 
owing to the roughness of the meridian places and the small number of stars on 
each plate. Owing to this roughness, when we add the measured differences 
(C—S,) for any of the plate constants to the provisionally found §,, we shall get 
values 0, =(C--8,)+8,, C.=(C-—8,) +8,, and so on, which are also rough, but the 
mean value ©, of C,, C,, &c., will be a much better determination than any of its 
separate members ; and we can now deduce from the well-determined C, and the 
measured differences (C—§,), (C—S,), &c., much better values of the constant in 
question for the individual plates. That for the first plate, for instance, will be 
C,-(C-§,). 
‘ A correction to the orientation is required for precession between the epoch 
1900°0 (for which the constants of S, were calculated) and the epoch at which C 
is taken; but this is a simple matter. 
The method is being tried at Oxford—two composite plates of thirteen regions, 
each having been obtained and measured, and one of them reduced—and the 
results are satisfactory so far. But the work is not yet complete. If successful, 
the method will be of value in reducing the amount of new meridian observation 
required. 
6. On the Determination of Periodicity from a Broken Series of Maxima. 
By Professor H. H. Turner, 7.2.8. 
By his work with the periodogram Professor Schuster has emphasised the fact 
that we must try all possible periods in a systematic manner if we would properly 
analyse a set of observations, Even when we seem to have already found the 
mean period (as, for instance, the eleven-year period in the case of sun-spots) sys- 
tematic trial of other periods may give us unsuspected information. The labour is 
great, but there is no evading it. 
The periodogram method is applicable only when the series of observations is 
regular and complete over a certain lapse of time. The sun-spot record is not ab- 
solutely complete, but it can be made so for practical purposes. This is not so in 
other cases, as, for instance, for the light curve of a variable like U Geminorum, 
which differs from the sun-spot record in two principal features. 
(1) Observations near minimum are generally absent altogether and cannot 
be supplied ; so that the record is essentially a record of maxima only. 
(2) Even these are often lost from cloudy weather or other circumstances, so 
that the record is a broken one. 
In these circumstances it is necessary to substitute for the regular Fourier 
analysis some other process by which a number characterising each tentative 
period can be obtained. The suggestion of this note is that, having obtained the 
epochs of maxima E,, E,, E,...E,,, and having written down a series of theo- 
retical epochs Ep,Eo + 2n,Ey + 4n,E)+6n, &c., where 2n is a period to be tried, 
we should then form the differences of the observed epochs from the nearest theo- 
retical epochs. Calling these differences 1,, 7,, 7"; . . « "my, we form— 
(a) the algebraic mean = (+0, +++ +7m) 
(4) the sums of the squares 7,°+7,.°+ +++ +7’. 
