734 PHILOSOPHICAL TRANSACTIONS. [anNO 1776. 



if CE have to cd any multiplicate proportion m of cb to AC, al will have to lb 

 such a multiplicate proportion of cb to ac, as is expressed by the number 

 m — 1. 



IF". A new Method of Finding Time by Equal Altitudes. By Alex. Aubert, 



Esq., F. R. S. p. 9'2. 



Among the various methods practised for finding time, that by equal altitudes 

 of the sun or of a star, has hitherto been esteemed the most eligible for observers, 

 who are not furnished with a good and well-adjusted transit instrument. But 

 this method, though one of the best, is generally attended with inconveniencies, 

 which render the practice of it more difficult, and the result less perfect than 

 could be wished. If the sun or stars near the equator be employed, as usual, 

 and the altitudes be taken near the prime vertical, where the change of altitudes 

 is the quickest, the interval of time between the observations must, in most lati- 

 tudes, be of so many hours, that the observer cannot always attend to the cor- 

 responding altitudes : the weather may prove variable, so as to disappoint him at 

 last; the clock or watch may go irregularly during so long an interval; and if 

 the altitudes cannot, on account of their great distance from the meridian, be 

 taken very high ; an alteration in the state of the atmosphere may produce a va- 

 riation of the refraction, and occasion the horary arcs to be different, though 

 the apparent altitudes will be the same. To which may be added, the difficulty 

 of making the instrument follow the object in its motion in azimuth, without 

 danger of disturbing its adjustment in regard to altitude. To remedy all these 

 inconveniencies, the following method was thought of; and having been prac- 

 tised with constant success, it is presumed the communication of it may be ac- 

 ceptable to astronomers. 



If a star be selected, of which the polar distance is very little less than the 

 complement of the latitude of the place of observation, it will, at equal dis- 

 tances from the meridian, come to vertical circles, -which touch its parallel of 

 declination. The star, when in these vertical circles, will be near the meridian, 

 near the prime vertical, and near the zenith ; and consequently, if it be ob- 

 served there, the interval between the eastern and the western altitudes will be 

 short; the alteration in altitude will be quick; the star cannot be affected by a 

 different refraction; besides, it will have no motion in azimuth. To observe the 

 star in these vertical circles, 2 things are necessary: the first is, to be provided 

 with an astronomical quadrant, having 3 or more horizontal wires in the tele- 

 scope, and if it has also a speculum at the eye-end of the telescope, to bring the 

 vertical ray horizontal, it will be found very convenient. The next thing is, to 

 make a computation of the apparent zenith distance of the star in the vertical 

 circles which touch its parallel of declination; for if the telescope be fixed to 



