1877.] 



On Rainfall and the Sun-spot Period. 



249 



In working out the result it will be most convenient to use consistently 

 the C.G.S. system. On this system of measurement the pressure 

 employed was 9| x 981 dynes per square centimetre, and therefore the 

 work expended per second in generating the waves was 196 x 9| x 981 

 ergs. ISTow the mechanical value of a series of progressive waves is the 

 same as the kinetic energy of the whole mass of air concerned, sup- 

 posed to be moving with the maximum velocity of vibration (v) ; so that, 

 if S denotes the area of the wave-front considered, a be the velocity of 

 sound, and p be the density of air, the mechanical value of the waves 

 passing in a unit of time is expressed by -g-S . a . p . v 2 , in which the 

 numerical value of a is about 34100, and that of p about *0013. In the 

 present application S is the area of the surface of a hemisphere whose 

 radius is 82000 centimetres ; and thus, ii the whole energy of the escap- 

 ing air were converted into sound, and there were no dissipation on the 

 way, the value of v at the distance of 82000 centimetres would be given 

 by the equation 



v2= 2xl96x9jx981 



2tt(82000) 2 x 34100 x '0013' 

 whence ^='0014 centimetre per second. 



This result does not require a knowledge of the pitch of the sound. If 

 the period be r, the relation between the maximum excursion x and the 

 maximum velocity v is 



x=—. 



In the present case the note of the whistle was/ iv , with a frequency of 

 about 2730. Hence 



•0014 1A -a Q1 



x—- — — =10 x 8-1, 



2ttx2730 



or the amplitude of the aerial particles was less than a ten-millionth of 

 a centimetre. 



I am inclined to think that on a still night a sound of this pitch, 

 whose amplitude is only a hundred-millionth of a centimetre, would still 

 be audible. 



III. " On the alleged Correspondence of the Rainfall at Madras 

 with the Sun-spot Period, and on the True Criterion of Peri- 

 odicity in a series of Variable Quantities/'' By General 

 Strachey, R.E., C.S.L, F.R.S. Received May 3, 1877. 

 A paper has recently been printed by Dr. Hunter, the Director-General 

 of Statistics to the Government of India, having for its object to show 

 that the records of the rainfall at Madras, for a period extending over 

 sixty-four years, establish a cycle of rainfall at that place which has a 

 marked coincidence with a corresponding cycle of sun-spots — the rainfall 

 and sun-spots attaining a minimum in the eleventh, first, and second 

 years, and a maximum in the fifth year. 



