472 Prof. Booth 07i the Volume of a Segment of a Surface 



nearly the same as the velocity at latitude 60° ; and if we take 

 the means of the forces at two latitudes 10° apart, on each 

 side of -iO" and 50° ; we find the same degree of force over- 

 come on the polar side as on the equatorial, thus 



Lat. Force. Lat. Force. 



Mean of 50° & 60° 0-051 



Mean of 40° & 30° 0-051 

 Mean of 30 & 20 0-042 

 Mean of 20 & 10 0-028 



Mean of 60 & 70 0-042 

 Mean of 70 & 80 0-027 



Thus then between 40° and 30° of latitude, a uniformly 

 accelerating force of 0-051 foot per second, to which the air is 

 subjected in a direction from the pole towards the equator, 

 predominates over the contrary forces ; whilst between lati- 

 tudes 30° and 20°, a force of 0-042 foot per second is unequal 

 to them, and between latitudes 60° and 70° the same degree 

 of force is overcome ; and between 50° and 60° the force equal 

 to that between 40° and 30°, viz. 0*051 foot is again predo- 

 minant, although in the former regions the difference of 

 height is much greater than in the latter ; showing that those 

 causes which tend to counteract the centrifugal force are much 

 modified in different zones, as must evidently be the case by 

 such circumstances, as the relative proportions of easterly and 

 westerly winds ; an easterly wind being, we may suppose, when 

 flowing* towards the equator, in some part of its course an 

 ascending current, and therefore tending to check the upper 

 current by the velocity, acquired by its motion in the con- 

 trary direction ; thus coinciding in its effects with the centri- 

 fugal force, or if there is no ascending movement, at least not 

 opposing it ; — an opinion, which is in accordance with the 

 fact generally mentioned by navigators, that westerly winds 

 prevail in much greater degree between latitudes 30° and 50° 

 than between 50° and ^5°^ where the increase in the height of 

 the barometer towards the equator is the greatest, the greater 

 rate of increase being probably occasioned by the greater pro- 

 portion of easterly winds. 



LXIX. On the Volume of a Segment of a Surface of the Second 

 Order, hounded by parallel Planes. By James Booth, 

 Esq., M.A., M.R.I. A., Pri7icipal of and Professor of Ma- 

 thematics in Bristol College*. 

 TN the Geometry of Legendi-e, Brewster's edition (page216), 

 an expression is given for the volume of a segment of a 

 sphere bounded by parallel planes ; an analogous expression 

 of great simplicity may be found when the investigation is 

 so generalized as to include surfaces of the second order. 

 • Communicated by the Author. 



