METHODS OF PERIODIC ANALYSIS. 



89 



sunspot cycle. 



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. TABLE 6.- Discontinuities in the 

 Let us call this part of the sequence A n 

 and its broken continuation near the 

 center B n , and the lower and later part 

 giving the 11.4-year period C n . Thus we 

 get at once three periods, 9.3, 11.4, and 

 something over 13 years. If, now, we 

 bring the average A n into line with the 

 average C n as the periodograph does, we 



get 11.4 years. If we bring the average A n into line with the C n _i, we 

 get close to 10 years. If we bring into line A n and the heavier parts 

 of C n _2, we get 8.4 years or thereabouts. And at 5.6 years we find 

 a period which is just half of C n and at 4.7 the half of A n , and so on. 

 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, D. 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 



