VOL. LXXVII.] PHILOSOPHICAL TRANSACTIONS. 253 



But whatever might be the mode adopted as the best for conducting ex- 

 periments of this nature, the observers must not only be very attentive and dili- 

 gent, but also quick-sighted, have their clocks nicely regulated indeed, and the 

 trials must be many times repeated before the uncertainty, even in this way, 

 which seems to be the best mode, could be reduced to less than -aV^h part of a 

 second of time, to which it may infallibly be brought by trigonometry. 



Having in this manner shown what probable degree of exactness may be ex- 

 pected in the various, but usual, ways of ascertaining the difference of longitwde 

 between the Observatories of Greenwich and Paris, and compared the results 

 with the uncertainty that seems yet to exist in this matter from the state of 

 astronomical observations; let us next see how Mr. Ramsden's instrument is 

 likely to perform, when actually applied to the determination in question, by 

 the observed angle between the pole star in its eastern or western azimuth, and 

 a very remote station, whose distance from the instrument is known by the 

 series of triangles, and distinguishable by the Indian lights at night, for the 

 purpose of this particular observation. 



With an instrument, carrying telescopes so good that the pale star may be 

 seen in daylight, it is obvious, that the bisected angle between the star in its 

 eastern and western azimuths will give at once the polar distance of the star, 

 and the true meridian of the place, as referred to any known stations visible at 

 the time of observation. But as cloudy weather may often prevent a complete 

 observation of this sort from being obtained, and since much time might be lost 

 in attempting it, therefore the declination of the star settled for any particular 

 period being accurately known, its apparent distance from the pole may, by the 

 established rules, be readily computed for any proposed day, as well as the pre- 

 cise times of its greatest elongations, twice in 24 hours, when in its eastern and 

 western azimuths, at which times it will, for several minutes, appear, as to 

 sense, stationary or without motion, except in altitude. These are therefore 

 the best times for taking the angle between the star and any particular station, 

 since the observations may be repeated frequently in the space of a few minutes, 

 or until it shall be perceived that the star has again approached towards the pole. 

 Now suppose the station of the instrument to be at Tatterlees, whose distance 

 from the perpendicular to the meridian of Greenwich, and consequently from 

 its parallel, is known by the trigonometrical operation. The latitude of the 

 station becomes known also; and let the co-latitude be 38° 54' 20". Let us 

 next suppose the distance of Bottle-hill on one side to be 44100 fathoms, equal 

 to 43' 28''.6 of a great circle; and that of the Brunemberg on the other to be 

 38250 fathoms, equal to 37' 42".6 of a great circle; and further, that on these 

 two stations the Indian lights are exhibited for the time proposed. Now, let the 

 angle between the meridian and Bottle-hill, and that between it and the Brunem- 



