﻿436 Mr. J. K. Laughton on Barometric Differences 



We know that if a vessel containing fluid be made to rotate 

 uniformly round a vertical axis with an angular velocity a>, the 

 surface or the strata of equal pressure of the fluid assume, as a 

 position of equilibrium, the form of a paraboloid of revolution, 



the latus rectum of which is ~ , and that, by the ordinary equa- 

 tion to the parabola, if d denote the depression of the lowest 

 point or vertex, below any other point whose distance from the 

 axis of rotation is r, 



, t» 2 r 2 



or if v be the linear velocity of the point (r, J), 



It is evidently impossible to expect a simple formula such as this 

 to apply with correctness to the motion of the air in cyclones ; 

 for since the air rotates independently and grinds on all sides, 

 whether against the surface of the earth or non-rotating air, the 

 friction must effect very great changes; the linear velocity, in- 

 stead of increasing as the point recedes from the centre, dimi- 

 nishes ; and the velocity at the surface, which we can observe, 

 is very much less than it is at some considerable height, though 

 we have very scanty means of ascertaining what the difference 

 may be. The balloon which landed near Christiania on the 

 25th of last November, travelled from Paris at the rate of from 

 40 to 45 miles an hour, whilst the wind below had a velocity of 

 not more than 20. The differences noted by Mr. Glaisher in his 

 several ascents are still greater : counting only the distance ac- 

 tually made good by the balloon, the mean of nine experiments 

 gave 25 miles an hour as the velocity above, whilst the anemo- 

 meter showed 7 miles an hour as the velocity below*. We can- 

 not say how far this may be considered as representing the ratio 

 between the upper and lower velocities in cyclones or other furious 

 storms : we have simply no evidence ; and when the surface ve- 

 locity is 120 miles an hour, the mind almost refuses to conceive 

 a storm of such tremendous power as would be implied by a ve- 

 locity of even 240 miles an hour. Still, if we take the extreme 

 velocity of the wind observed near the centre as fairly represent- 

 ing the surface velocity of the whirl free from lateral friction, 

 and twice that extreme as representing the upper velocity free 

 from horizontal friction, we find that the depressions so calcu- 

 lated by this simple formula have a very remarkable coincidence 

 with those which have been observed. 



* Travels in the Air, p. 91. 



