METHODS OF PERIODIC ANALYSIS. 89 
By means of this diagram one can discover at a glance the origin 
of many of the periods which Michelson thought were illusory and in 
which opinion he was largely right. We can plainly see a 9.3-year 
period in the early part of the curve. Tassie 6—Discontinuities in the 
Let us call this part of the sequence A, sunspot cycle, 
and its broken continuation near the 
center B,, and the lower and later part 
giving the 11.4-year period C,,. Thus we ives 
get at once three periods, 9.3, 11.4, and Between 1788 and 1806. 1798 
something over 13 years. If, now, we etween 1830. an : 
bring the average A, into line with the <a ge ga) wt a 
average C,, as the periodograph does, we 
get 11.4 years. If we bring the average A, into line with the C,41, we 
get close to 10 years. If we bring into line A, and the heavier parts 
of C,_2, we get 8.4 years or thereabouts. And at 5.6 years we find 
a period which is just half of C,, and at 4.7 the half of A,, and so dn. 
It is like a checker-board of trees in an orchard; they line up in many 
directions with attractive intensity. But plate 9, c, helps remove some 
of the complexity of the sunspot problem. It shows us that while these 
various periods are apparent, they are improbable and needless com- 
plications. The diagram supplies a basis for profitable judgment in 
the matter. Hence to avoid just such awkward cases as the sunspot 
curve, a differential pattern is considered to be a necessary accom- 
paniment of the periodogram in doubtful cases. 
Production of differential pattern.—The work described above, con- 
sisting particularly in the production of a periodogram from the differ- 
ential pattern, was done at Harvard College Observatory in 1913. The 
next fundamental improvement in the apparatus was in 1914, and con- 
sisted in a method of producing the differential pattern without all the 
labor of cutting out the curves. It was simply the combination of a 
certain kind of focal image called a ‘“‘sweep,” and an analyzing plate. 
A single white or transparent curve on a black background is all that 
is now needed as a source of light. An image of this is formed by a 
positive cylindrical lens with vertical axis. In the focal plane image so 
produced each crest of the curve is represented by a vertical line or 
stripe and the whole collection of vertical lines looks as if it has been 
swept with a brush unevenly filled with paint and producing heavy 
and faint parallel lines. Each of these lines represents in its brightness 
the ordinate of the corresponding crest. The sweep of the sunspot 
numbers is shown in plate 9,p. Any straight line whatever in any 
direction across this sweep truly represents the original curve, not as a 
rising and falling line but in varying light-intensity. A plate with 
equally spaced parallel opaque lines, called the analyzer or analyzing 
plate, is placed in the plane of this sweep. These lines may be seen in 
Periodogram. Turner. 
