PHILOSOPHICAL SOCIETY OP WASHINGTON. 107 



This relation expresses a general law applicable in all latitudes 

 to any individual cyclone, or to the resultant of any number of 

 cyclones combining- and interfering with one another. The value 

 of i depends mostly upon friction, and can only be determined by- 

 observation. Its value, however, is generally so small, except on 

 certain parts of the land and near the surface, that it may be 

 neglected without much error, since sec i for a small angle does 

 not differ much from unity. The average value obtained by Mr. 

 Ley for inland stations* is nearly 30°, although Professor Loomis 

 {Silliman/s Journal, July, 1874) obtained an average value of 

 about 45° for the stations of the United States Signal Service. 



The mathematical demonstration of this law or relation is too 

 complex to be given here, and must consequently be reserved for 

 future occasions, in which a complete and thorough investigation 

 of this interesting sul)ject will be attempted. For the present it 

 may be regarded as an empirical law, merely to be compared with 

 and tested by observation. 



We shall give here only a few comparisons of this law with 

 observation. First with regard to the two great polar hemis- 

 pherical cyclones having the terrestrial poles for their centres and 

 the equatorial calm belt for their external limits, and depending 

 upon the mean constant difference of temperature between the 

 equatorial and polar regions. In this case the barometric gradi- 

 ents and velocities are the means obtained from a great many ob- 

 servations, in which the effects of the seasons and of all oixlinary 

 cyclones are eliminated. The value of it in this case is the mean 

 constant east or west angular velocity of the wind, and r is the 

 distance from the earth's axis. The whole value of u, however, 

 in this case is so small in comparison with 2 n sin Z that it may 

 be entirely neglected. 



Observation shows that about the parallel of 35° in the northern 

 hemisphere, and a little nearer the equator in the southern hem- 

 isphere, the barometric pressure is a maximum, and that conse- 

 quently G vanishes. Putting G = 0, the preceding relation can 

 only be satisfied l)y v = 0, that is, by a calm belt at these lati- 

 tudes as actually observed. At the equator also we have (7=0, 

 but here the law is also satisfied by the vanishing of (2 n sin I -f- u) 

 at the equator, and v becomes in this case indeterminate by the 

 preceding relation. 



The mean barometric gradient in the British Islands, as de- 

 clined from the isobars determined by Mr. Glaisher, is about 0.02 

 of an inch. With this value of G the relation is satisfied with 

 t; = 6 miles, supposing the mean direction of the wind to be from 

 the west or nearly so, that is, that the value of i is small. This 

 result is a little less than the value obtained for these islands by 



* Journal of the Scottish Meteorological Society for the first quarter of 

 1873, p. 66. 



