TRANSACTIONS OF SEGTION A. 399 
in co-operation with Professor George E. Hale. One of the chief points 
of interest is the effects on the permanent magnetisation of the earth, 
which appear to be associated in some manner with changes in solar 
activity. The magnetic and solar data utilised embrace the period May 
1906 to January 1909. It was found that the absolute magnetic effect, 
connected apparently with an increase in solar activity, is equivalent, in 
general, to a diminution in the earth’s mean intensity of magnetisation, 
amounting between the dates February 1, 1907, and February 1, 1908, to 
about soy part. It was shown that for a successful analysis it is necessary 
to embrace all the magnetic elements and to separate the observed effect 
into its component parts—that due to the change in the external system 
of forces and that to be referred to changes in the system of magnetic 
forces below the earth’s surface. 
2. The Surface Movement of Air in certain Circular Storms. 
By J. I. Crata, M.A., F.R.S.E. 
The paper considered the curve traced by a particle of air which moves in such 
a way that the tangent to its path always makes a constant angle (a) with the 
circumference of a moving circle passing through the particle and described 
about a centre which is moving rectilinearly. The speed of the particle parallel 
to the circumference (V cosa) bears a given ratio (1/A) to the speed of the 
moving circle (U) so that U=AVcosa. This is an idealised case of ordinary 
cyclonic movement in nature. 
References to previous work were given as follows: Theoretical—(1) Dr. 
W.N. Shaw, F.R.S., ‘Q. J. R. Met. 8.,’ vol. xxix. 1903, p. 233, and ‘ Monthly 
Weather Review,’ vol. xxxi. 1903, p. 318; (2) Professor W. H. H. Hudson, 
‘Rep. Brit. Assoc.,’ York Meeting, p. 483; (8) Mr. G. T. Bennett, wide (4) 
below, p. 98. Practical—(4) Dr. W. N. Shaw, F.R.S., and Mr. R. G. K, 
Lempfert, ‘The Life History of Surface Air-Currents ’ (London, 1906). 
he equation of motion relative to the centre is first studied and found to be 
when A<1,4#(1+A sin 6)=a exp. [-2tes tan’ ‘7 ] where A?+y42=1, and 
io 
7 = (tan 39+ A)/u 
When A=1,7(1+ sin 6)=a exp. (2 tana/(1+ tan 46)] 
whett A>1, r(1+Asin 6)=a[(1+ tan 3A tan 46)/(1+ cot 34 tan 30) /*™ 7 14 
Where cosec B = A, 
~ The particular case studied by Mr. Bennett, when there is no incurvatire, is 
eisily derived by putting a=0, The curve is then given by the equation 
r(1+Asin 6)=a and is an hyperbola, a parabola or an ellipse according as 
Ais > = or <1. ; 
Some particular examples exhibiting thé general properties of the curves 
have been computed for values of A from 8 to 1/3, and of a from 0 to 45°, which 
include most of the cases of interest in practice. ! 
A difference may be noted between the trajectories when A>>1, und when 
A>1. In the first case all the trajectories finish in the centre, with the 
exception of the limiting case where there is no incurvature. In the second 
case some trajectories with small incurvatute do not finish in the centre, while 
if the incurvature is increased the fesultitig trajectories do so finish. These 
classes are separated by a parabolic trajectoty. 
The trajectories observed in practice by Dr. Shaw and Mr. Lempfert were then 
compared with those deduced theoretically, and found to be in satisfactory 
agreement with them. : 
This point of view supports Dr. Shaw’s statement that dppYoximatély circular 
storms cannot be satisfactorily explained as revolving vortices of air ¢arried along 
by currents of different velocities, 
