VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 133 



height of the mountains above the sea's level, which cannot always be deter- 

 mined geometrically, or would at least be too tedious to perform : therefore, in 

 the meridian of Paris, which crossed very high mountains, M. Cassini was of 

 opinion, that he ought to fix their height by a shorter method, which is that of 

 the height of the simple barometer, observed on the top of each mountain, 

 and compnred with that observed at the same time in another place, whose 

 elevation above the sea's level was known. But as that method supposes the 

 knowledge of the proportion which the different fallings of the mercury keep 

 with the different heights to which the barometer is carried ; and as natural 

 philosophers are not as yet entirely agreed on this head, for want of observa- 

 tions of sufficient accuracy ; thence it happened, that Dr. Desaguliers, making 

 it appear that M. Cassini has not employed the most exact proportion, found 

 reasons for correcting, or at least for doubting, of some of M. Cassini's calcu- 

 lations. Thus it must be by the assistance of new experiments, better circum- 

 stanced than those hitherto made, and pursuant to a theory entirely agreeing 

 with these experiments, that this method may be employed with certainty, for 

 determining the height of mountains by the barometer, and reducing the 

 angles observed from the tops of these high places, to what they would be, if 

 they had been observed on a plane at the level of the sea. Now these new ob- 

 servations can be made on our way in tracing the meridian ; and for that pur- 

 pose M. De Lisle began to construct compound barometers, which being very 

 nice, will serve to observe with accuracy, the quantity of the mercury's fall, at 

 the different elevations to which they shall be carried, to fix with greater 

 certainty the proportion of that fall. 



There is still another method of determining the elevation above the level of 

 the sea of all the points, in which the triangles terminate, that are made for 

 the measurement of the earth. This may be done by beginning these opera- 

 tions near the sea, and actually measuring how many toises and feet the places 

 of the first stations are elevated above the level of the sea. For if the angles of 

 the apparent elevations of the second stations, seen from the first, be after- 

 wards observed, it will be an easy matter, from the known distances, to deduce 

 the true elevations of the latter above the former, and consequently above the 

 sea's level, making proper allowances in the calculations for the difference of 

 the apparent level from the true one. In this method, nothing is to be appre- 

 hended but the variation of refractions ; but for this a remedy may be found, 

 for the most part, by returning again, that is, by reciprocally observing the first 

 stations seen from the second : for if it be found, that as much as the second 

 station appears elevated above the first, so much the first is depressed below the 



