THE 



PHILOSOPHICAL MAGAZINE 

 AND JOURNAL. 



30^" NOVEMBER 1822. 



LXII. On the Measurement of the Progress of an Eclijne 

 of the Moon '^nth a Sextant or Reflectiiig Circle. By 

 T. E. BowDicH.* 



It is impossible to observe the beginning of an eclipse of the 

 sun or moon on ship-board with precision ; but by measuring 

 the progress of either with a sextant, at intervals of five mi- 

 nutes, advantage may still be taken of these phaenomena for 

 the determination of the longitude. 



This meUiod offers the gi'eat advantage of multiplying the 

 angles, and consequently of diminishing the errors by which 

 the partial observations may be affected. 



It was first proposed, for eclipses of the sun, by Wales, who 

 thus observed that of 1774; King, who accompanied Captain 

 Cook in 1777, also availed himself of it; but in both instances 

 the mere observations are recorded, without calculation, for- 

 mula, or result. 



Kiihler appears to have been the first who recommended, 

 and Humboldt the first who put in practice, the application of 

 this mediod to eclipses of the moon ; the latter thus determined 

 the longitude of Ibague, within one-fifth of a degree: but as 

 Oltmans, who calculated this observation, has merely given 

 us the result without the formula, and as I do not know of any 

 formula being in print, I thought it might be useful as well as 

 interesting to submit the following, which is general, until a 

 neater oiie may be discovered. 

 Let A = longitude 1) — long. © — 1 80° 

 A = latitude of J> 



A^ = augmentation of the relative longitude of D 

 A^ = nujvemcnt in latiludevof ]) 



(1 = demi-diameter of O 



r/ = . . . . do. . . . }) 



/; = parallax of © 



p' = . . do. . . ]) 



e = enlightened part oi ]) in minutes 



* Communicatcil l>v P. BAni.ow, Esq., Roya\ Military Acndcni}'. 

 Vol. CJO. No. 29r,. Nov. 1822. T t / =■ 



