458 kepoht— 1S84. 



It happens occasionally that any one single sunspcfc period does not 

 give a clear periodical variation of some meteorological quantity ; this 

 does not prove that no connection exists, bnt only that, if it does, it is 

 hidden under some larger irregularity. To show a connection we should 

 have to take a longer series of observations into account, and see whether 

 the average at sunspot maxima shows a different value from the average 

 of sunspot minima. It is in investigations such as these that we must 

 be specially careful not to be misled by accidental coincidences. Fourier 

 has taught us that any variable quantity, however ii'regular, can be re- 

 presented by a series of harmonic variations, and there need be no 

 physical reality at all attached to such a periodicity. Let us suppose, for 

 instance, that we want to see whether some quantity shows a periodicity 

 of ten years. The simplest way to pi'oceed would be to break up our 

 series of observations into parts of ten years' duration ; each part would 

 contain ten terms if yearly means are employed, aud we could now 

 take the average of corresponding years ; that is to say, the average 

 between the years 1, II, 21, and so on; then the average between the 

 years 2, 12, 22, and so on. We should then get ten values, and if these 

 values were to show a regular increase or decrease, we might conclude 

 that a ten years periodicity really existed. Bnt that is by no means 

 necessarily the case. Any quantity, however irregular, will, according to 

 Fourier, be decomposed into periods. A marked increase and decrease 

 would only prove that the quantity when so decomposed has the ampli- 

 tudes of all submultiples of ten years smaller than the amplitude 

 of the ten years period. But the amplitudes of periods less than ten 

 years have often, in the investigations to which I am referring, been 

 already reduced or destroyed by the peculiar way of taking means. So 

 that nothing at all is really proved. It is even difficult to see, consider- 

 ing that we have such a small number of sunspot periods at our disposal, 

 how any satisfactory plan of reduction can be devised. It will be better, 

 therefore, at present to attach only very secondary value to coincidences 

 which do not make themselves perceptible in each period. Shouldit ever 

 be proved that there is really a change in the sun's radiating power in 

 different years according to the number of sunspots, the case would be 

 altogether changed. We might theu take it for granted that all met- 

 eorological phenomena present the same period, and the process of 

 averaging between different periods would justly help us to fix the 

 amplitude and the phase of the oscillation. 



I therefore in what follows, for the reasons just given, pass very quickly 

 over, or altogether omit those coincidences which seem to be subject 

 to the above criticism. 



Iutensi.fi/ of Wind. 



The most important investigation under this head is no doubt Mel- 

 drum's comparison of the number of gales in the Indian Ocean in different 

 years. The following table speaks for itself. The greater number of 

 cyclones during times of many sunspots appears very clearly. 



