6/0 PHILOSOPHICAL TRANSACTIONS. [aNNO IJS-l. 



whole degree or 6o minutes, in the space of 4 minutes of time ; so that the 

 observer has but one minute, to come within 15 minutes of the truth in his 

 latitude : while in a middle altitude, as 45 deg. he is at noon above 5i minutes 

 in rising or falling one single minute of space, the odds between which is more 

 than 80 to 1 . And yet perhaps no parts of the world require more exactness in 

 taking the latitude, than is necessary in voyages to the West Indies: for it is 

 owing to the difficulty of it, that vessels have so frequently missed the island of 

 Barbadoes, and when got to the leeward of it, have been obliged to run down a 

 thousand mites farther to Jamaica, from whence they can scarcely work up 

 again in the space of many weeks, against the constant trade winds, and there- 

 fore generally decline to try fur, or attempt it. 



But further, as the latitude cannot be found by any other method, that our 

 mariners are generally acquainted with, than by the sun or a star on the meri- 

 dian : in a cloudy sky, when the sun can but now and then be seen, and only 

 between the openings of the clouds for very short intervals, which those who 

 use the sea know frequently happens : as also in high tempestuous seas, when 

 though the sun should appear, the observer can scarcely by any means hold his 

 feet ; it would certainly be of great advantage to have an instrument by which 

 an observation could also be, as it were, snatched or taken in much less time, 

 than is generally required in the use of the common quadrant. 



Tho. Godfrey therefore considering this, applied himself to find out some 

 contrivance, by which the necessity of bringing the rays from the sun, and those 

 from the horizon to coincide, which is the most difficult part of the work, on 

 one particular point or line from the centre, might be removed. In order to 

 which, he considered, that by the 21. 3d Elem. of Eucl. all angles at the peri- 

 phery of a circle, subtended by the same segment within it, are equal, on what- 

 ever part of the circumference the angular point falls ; and therefore, if instead 

 of a quadrant, a semicircle were graduated into QO degrees only, accounting 

 every two degrees but one ; this would effectually answer : for then, if an arch 

 of the same circle were placed at the end of the diameter of the instrument, 

 every part of that opposite arch would equally serve for taking the coincidence 

 of the rays abovementioned. But such an instrument would manifestly be at- 

 tended with great inconveniencies ; for it would in great altitudes be much more 

 unmanageable, and the vanes could not be framed to stand, as they always 

 ought, perpendicular to the rays. He therefore further resolved to try, whether 

 a curve could not be found, to be placed at the centre of a quadrant, which 

 would, at least for a length sufficient to catch the coincidence of the rays, with 

 ease fully answer the intention. 



A curve which in all the parts of it would in geometrical strictness effect this, 

 cannot be in nature, any more than that one and the same point can be found 



