C 375 ] 



L. On a7i easy method of measurivg the distance and height of 



an elevated point, accessible or inaccessible, Jixed 07- moveable, 



by means of a single instrument, and by taking the observation 



from only one station. By M. Elie Wartmann, Professor 



of Physics in the Academy of Geneva * . 



/^EODESICAL and astronomical operations very fre- 

 ^-^ quently require the knowledge of the distance of a remote 

 object. If the object be fixed, the ordinary processes of trigo- 

 nometry readily lead to the desired result. It is only neces- 

 sary to determine a base, and to measure, from each of its ex- 

 tremities, the angle between the other extremity and the object; 

 we thus obtain the value of two angles and of the adjacent 

 side, from which the triangle is easily resolved. 



But for the case in which the distant object is in motion, — 

 a case of great importance, and which occurs in several stra- 

 tegical and cosmological problems, the operation is by no 

 means so simple. It would be necessary first to measure a 

 straight line, more or less extended, and to station at its ex- 

 tremities two observers, who at the same instant should direct 

 the telescopes of their tlieodolites to the same point of the 

 object. When the point is simultaneously visible from the two 

 stations, and the chronometers compared, and when above all 

 the object preserves exactly itsforn), or only changes it imper- 

 ceptibly, it is conceivable that this method may succeed; and 

 the result will be more exact as the readings are repeated at 

 shorter intervals, in order to lessen the probable errors by 

 means. But when these different circumstances do not exist, 

 when there is only a single observer, or the object varies in 

 appearance, or is not visible at the same time from both ex- 

 tremities of the base, then the execution of the process becomes 

 impossible. 



Such are the objections which may be made to the method 

 proposed by M, Pouilletf for esUmating theJieight of the clouds, 

 a problem which has already attracted the attention of several 

 eminent philosophers, such as James Bernoulli J, Brice§, Lam- 

 bert ||, and more recently M. Arago^. The following is the 

 method which 1 propose for its solution. 



• Bulletin of the Sittings of the Vaiidois Society of Natural Sciences, 

 tome i.p. 21. (Sitting of February 2, 1842.) See also Pogg. ^/wh., toni. Ivi. 

 |). 635 ; and Geliler's Phi/silcalisckes W'drterbucJt, torn. xi. p. 700. 



+ Note on the Height, Velocity, and Direction of tiie Clouds; Comptes 

 llcndti* of the Academy of Sciences of Paris, tom.xi. p. 717 (Nov. 9, 1840). 



X Acta Eruditorum, 16HH. § Philosophical Transactions, 1706. 



II .Memoirs of the Academy of Berlin, 177'5- ' 



il Comptes Rcndtis, torn. xi. p. .■^23 (August 24, 1840). Annual of the 

 Bureau of Longitudes, 1840, p. 316. 



