268 PHILOSOPHICAL TRANSACTIONS. [anNO 1728. 



much more considerable in valleys than at the top of nioimtains, and still greater 

 in proportion at the bottom of wells, mines, &:c. 



But this matter was pursued still further by the members of the Royal Aca- 

 demy of Sciences at Paris, particularly, when by order of Louis the 14th, they 

 drew that extensive meridian line across the whole kingdom of France. M. 

 Mariotte, a celebrated member of that Academy, was one of the first who laid 

 down certain rules for the construction of such tables, as might serve to deter- 

 mine both the elevation of places above the level of the sea, from given altitudes 

 of mercury, and the heights of the air answering to every line of mercury in 

 the barometer, from 28", or inches, where the mercury was supposed to stand 

 at a medium near the sea. The principles he went upon, and the method he 

 followed, are treated at large, in his second Essay de la Nature de I'Air. 



Some time after, in 1 686, the ingenious Dr. Edmund Halley went about 

 another calculation, which he derived partly from principles agreeing with those 

 of M. Mariotte, partly from the specific weight of air and mercury, which 

 were found by experiments to be as J to 10,800; air being to water as 1 to 800, 

 and water to mercury as 1 to 13^, or very near it. If so, as the column of 

 mercury in the barometer is counterpoised by a column of air of equal weight, 

 a cylinder of air of 10,800 inches, or gOO feet, will be equal to 1 inch of mer- 

 cury, and go feet to -^ of an inch, or 75 to -pV part of it. The height of the 

 air, as it answers to 1 inch of mercury, being thus determined, and the expan- 

 sions of the air being reciprocally as the heights of mercury, Dr. Halley, by 

 the help of the hyperbola and its asymptotes, calculated two tables, one show- 

 ing the altitude to given heights of mercury, the other the heights of mercury 

 at given altitudes. These tables, the first that ever were calculated, together 

 with the Doctor's whole method of proceeding, and an ingenious attempt of 

 his to discover the true reason of the rise and fall of mercury on change of 

 weather, were printed in the Philos. Trans. N° 181 ; and the tables themselves 

 were very lately reprinted, with some observations upon them, by Dr. Desagu- 

 liers, ib. N° 386. 



In the year 1703, when the meridian line, first begun by M. Picard in l66g, 

 afterwards continued in l683, was further pursued, several observations of this 

 kind were made, and the heights of several considerable mountains, particularly 

 in the southern parts of France, determined, as well by trigonometrical as 

 barometrical observations. Monsieur Cassini, the younger, took that oppor- 

 tunity to compare these observations with the rules laid down by M. Mariotte, 

 (Mem. de I'Acad. 1705) in order to which, and in conformity to the said rules, 

 he calculated two tables, one showing the height of the atmosphere, as it 

 answers to every line of mercury in the barometer, the other determining the 



