1818.] of the Profle of Mount Jura. SiT 



the time when it ceased to be visible, it appeared under the 

 form of a very obtuse pyramid upon the top of an apparent hill, 

 produced by the effect of refraction upon the plain, the refracted 

 points of which, in consequence of their distance, exhibiting to 

 me an inclined plane imitating upon the horizon the projection 

 of a hill. The poplar, whose enormous pyramid rose to the 

 height of 28 metres, appeared to me then reduced to a spherical 

 mass of three or four metres in height ; and if we recollect that 

 the contour of the line to which I referred these appearances was 

 itself elevated by refraction in proportion to its distance, we 

 shall have an idea of the differences of terrestrial refraction at 

 different times of the day. I give here four figures representing 

 in the opening of the objective of my telescope the profile of the 

 trench and the different aspects of the signal and poplar in its 

 neighbourhood at the four principal epochs. (Plate LXXXVI.) 



I conceive, from a great deal of experience, that the refractions 

 in the same season are nearly horary. Hence it would be of 

 great importance for geodesy to determine the horary values of 

 the coefficient. We might then hope to obtain good vertical 

 measurements by means of zenith distances. Till this great and 

 useful undertaking be accomplished, I can recommend to geo- 

 graphers a method which has succeeded with myself, and 

 which I regret that I did not think of sooner. It is founded on 

 the coincidence of hours. To determine the difference in the 

 height of two points, I observe them reciprocally at the same hours, 

 though on different days. This expedient is not rigorously exact; 

 but 1 am persuaded that it has the advantage of eliminating, in 

 the same season, the principal error. It may be employed by a 

 single observer, as is often necessaiy in practice. By adopting 

 this method, so simple and so easy, which neither requires more 

 means nor more calculations, and which spares the time that 

 would be uselessly wasted on taking repeated zenith distances, 

 I believe with confidence that we should be able to reduce the 

 limits of disagreement to small fractions of a metre. I intend to 

 employ this method in the new geodesical operations with which 

 I am going to be charged ; and I expect from it the most com- 

 plete success. 



It has been proposed to determine the circumstantial coeffi- 

 cient by observing the zenith distance of a point whose height 

 is already known ; but this supposes the refraction to remain 

 constant during the intervals of the observations ; and, likewise, 

 that the trajectories of the rays coming from all the points of the 

 horizon are similar curves, modified in proportion to the dis- 

 tances ; but all these suppositions are gratuitous, and contrary 

 both to theory and experiment. The method which I propose 

 has not the same inconvenience. The luminous ray passing 

 through tin; same space undergoes very probably the same modi- 

 fications, especially if the barometrical pressures aud the temper- 



