VOL. XXX.J PHILOSOPHICAL TRANSACTIONS. 285 



too short, or what is precipitated falls sometimes too fast and sometimes too 

 slow ; for then the little bodies are always, as to sense, in equilibrio with the 

 fluid that contains them." 



" M. Ramazzini, the famous professor at Padua, to whom M. Leibnitz had 

 proposed his experiment, has made it with success, after some fruitless trials. 

 M. Reaumur, to whom the academy had recommended it, has also made it with 

 success : this is a new view in natural philosophy, which, though it depends on 

 a well known principle, is very subtle and far-fetched ; and gives us just reason 

 to fear that in subjects that seem to be exhausted, several things may yet 

 escape us." 



Remarks on M. Leibnitz s New Principle. — Let ab, fig. 1, pi. 8, be the bot- 

 tom of a vessel full of any fluid, whose top is either wider than the bottom as 

 GH, narrower as ep, or equal to it as cd. The pressure of the fluid on the base 

 AB will be equal to the weight of cb, or of a cylinder or prism of the same 

 fluid, made up of the area of the base multiplied into the perpendicular height 

 above it. 



If the fluid be equally dense every way, as water, or of a density uni- 

 formly diminished upwards, this proposition (called by Mr. Boyle the hy- 

 drostatical parodox) will hold good. This is demonstrated by all hydrostatical 

 writers. 



Let EP, fig. 2, represent part of the surface of the earth, and geph a column 

 of the atmosphere, whose height is ge the whole height of the air. Let us 

 suppose the vapours rising out of the earth to form themselves into two clouds 

 A and B, and to settle in that place where the air is of the same specific gravity 

 with themselves. It is evident that they will cause the air to rise so much 

 higher as their bulk amounts to, and will therefore make the surface which was 

 at GH to rise up to ik, so that the bottom ef, which was pressed by a column 

 of air, as geph, is now pressed by a higher column as iepk. Now if the 

 clouds A,B, by any cause whatever, change their place, so as to comedown- 

 wards, for instance to c,d, the height of the pillar iepk will remain the same as 

 it was, and therefore the bottom ep will be pressed as before ; by the foregoing 

 proposition. 



CoroL 1. — If the clouds a,b descend, and in their descent keep the same bulk 

 as they had before, the surface ik will remain the same, and therefore ep will 

 be pressed as before. 



Corol. 1. — Whether a body be specifically lighter or heavier than a fluid ; as 

 long as it is detained in it, it will add to the fluid as much weight as the weight 

 of an equal bulk of that fluid : therefore a body does not lose all that weight 



