1 3:2 Count Paul de Saint-Robert on a Barometrical Formula 



other construction, as being not based on demonstration, and 

 not by him demonstrable, although Euclid may not have known 

 it to be, in its result, imperfect. The interest of the speculation 

 stretches indeed back to a still earlier age, and may be con- 

 nected in imagination with what we read of the " wisdom of the 

 Egyptians." But I trust that I shall be found to have abstained, 

 as I was bound to do, from any expression which could imply 

 an acquaintance of my own with the archaeology of Egypt, and 

 that I may at least be pardoned, if not thanked, for having thus 

 submitted, to those who may be disposed to study the subject, a 

 purely mathematical* discussion, although connected with a ques- 

 tion of other than mathematical interest. 



TV. R. H. 



Observatory of Trinity College, Dublin. 

 December 22, 1863. 



XXV. Barometrical Formula resulting from the Observations 

 made by Mr. James Glaisher in Eight Balloon- As cents in 1862. 

 By Count Paul de Saint-Robert-]-. 



THE knowledge of the law of decrease of temperature with 

 the altitude is most important, since the determination of 

 heights by the barometer, as well as that of atmospheric refrac- 

 tion, depends upon it. 



Tn the present state of meteorological physics, we know only 

 the general causes which tend to lower the temperature of the 

 air as we recede from the earth's surface we are ignorant of the 

 precise amount of their respective actions. 



It is certain that the mean temperature of the air in contact 

 with the earth's surface must be equal to that of this surface, 

 and that that of the superior limit of the atmosphere cannot sur- 

 pass the temperature at which that fluid loses all its elasticity. 



The first condition results from the continual contact of the 

 inferior layer of the atmosphere with the earth's surface. 



The second is a condition necessary to the equilibrium of the 

 fluid mass : in fact, if the air at the upper limit of the atmo- 

 sphere were still expansible, the limiting stratum would dissi- 

 pate itself into space; after which the immediately inferior 



* Xote added during printing. — Some friends of the writer may be glad 

 to know that these long arithmetical calculations hare been to him rather 

 a relaxation than a distraction from his more habitual studies, and that there 

 are already in type6/2 octavo pages of the "Elements of Quaternions/ a work 

 which fas he hopes j is rapidly approaching to the stage at which it mav be 

 announced for publication. 



Observatorv. January 19, 1864. 



t Communicated by the Author. 



