674 PHILOSOPHICAL TRANSACTIONS. [aNNO 1734. 



of the arches, by which means the distance of the said intersection from the 

 equator, or its latitude, is found. The degrees and minutes may likewise be 

 shown by diagonal lines. 



The Use of the Instrument is asfoUoivs. — Prop. 1. From two observations of 

 the height of the sun, and the distance of the said observations in time, being 

 given by a watch, as also the declination of the sun ; to find the latitude of the 

 place, and the hour of the day. 



1. When the ship is at rest, that is, at anchor, or in a calm, so as to have 

 little or no progressive motion. 



Case 1 . — Suppose the sun in the equator on the day of observation : fix tlie 

 centre of the beam-compass at O degree, or at the equator, and move the point 

 k to the zenitii distance, the complement of the altitude taken by the usual in- 

 struments, and from any hour, as from c, describe an arch of a circle with the 

 said point, as be, Ex. 1. Suppose 8 hours after, by the watch, you have an- 

 other observation ; move the meridian 8 hours farther, to d, and fix it there ; 

 and with the zenith distance then observed describe another arch, 3« ef ; the 

 point where it cuts the former, is the place of observation, and its distance 

 taken on the meridian from the equator, shows its latitude ; and the minutes 

 reckoned on the equator, from the meridian to c and d, the times of observa- 

 tion, show what tiiose hours were. 



Cd^^f, 2. — When the sun has declination : fix the centre of the beam-compass 

 on the meridian, to the proper degree of declination for the day of observation, 

 and proceed as before. 



Case 3. — When the observations are at a greater distance than 12 hours, but 

 in the same day : make use of the complement to 24 hours of the distance in 

 time, and take the declination on the contrary, or lower side, of the equator ; 

 and instead of the zenith distances, take the nadir distances or altitudes in- 

 creased by 90 degrees. 



Thus you will find the latitude, and the time of each observation from 

 midnight. In this case the beam-compass must extend to more than 90 deg. 



CfMe4.— When the observations are Tnore than a day asunder ; as for in- 

 stance a day and 2 hours, or 26 hours : place the centre of the beam-compass 

 2 hours farther than it was the day before ; but in different declinations, ac- 

 cording to the table of declination for the several days. 



Case 5.— When the observations are made by a star: the centre of the beam- 

 compass must be set to the declination of the star; then proceed as before. To 

 find the hour in this case, the right ascension must be likewise given. 



Scholhm. — The same method may be useful at land, when no meridian ob- 

 servation offers. 



II. JVken the Ship is in Motion. — Case 1. Suppose the sun in the equator: the 



