26 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



that is to say, in southern latitudes the pressure F will be against 

 the left hand and will be zero at the equator itself. 



In order to determine the pressure mF exerted upon the right 

 bank by the whole section MX of the river, let A be the area of 

 this section and p the density of the water, then 



mF = Avp 2 10 a. sin / 



This mF relates of course to the pressure exerted by the mass 

 of water that flows through the section MX in a unit time or by 

 the mass Avp. 



In the preceding paragraphs we have assumed a constant or 

 steady and uniform velocity. It seems unnecessary to say that this 

 condition is rarely fulfilled in practical cases, or that the demon- 

 strated result does not hold good in such cases. But since there 

 is a distinction to be made between a theorem that is not yet demon- 

 strated and one that is clearly shown to be erroneous it will be of 

 interest to see from the following modifications of Braschmann's 

 analysis as summarized in the Comptes Rendus, Paris 1861, how 

 in the case of non-uniform motions along paths restricted to the 

 earth's surface, the direction of the horizontal pressure depends 

 on the variations of the respective components of its velocity. 



[The original memoir in the Paris Comptes Rendus contains 

 numerous typographical errors that are corrected by Erman in his 

 Archiv Wiss. Kunde Russland.] 



Let X, Y, Z, be the projections (or rectangular components) of 

 the accelerating force and P x , P P z the projections of the pres- 

 sure exerted on a unit surface, at a point whose coordinates relative 

 to a fixed system of rectangular axes are x A \\ z x ; we have then 



(1) 



If both the axes and the origin of coordinates are all assumed to be 

 in motion then we have to substitute herein the values of the accel- 

 eration at the point \\ y t z v Let .v, y, z be the coordinates of this 



