671 PHILOSOPHICAL TRANSACTIONS. [aNNO 1734. 



navigators in their voyages entirely slight a difference of one minute in latitude. 



This radius is the true one for the circular locus to an arch of 77° 15', and 

 the variation from it is nearly as great at CO degrees as at any arch below it, the 

 greatest below being at about 44 degrees, which is owing to the differences ex- 

 pressed by the last figure above, and not to those of the curvatures or circular 

 loci. Yet this variation of 57 seconds arises only when the spot or coincidence 

 falls at the extremity of the horizontal sight or vane, or a whole inch, in an 

 instrument of 20 inches radius, from the centre, and then only in the altitudes 

 or arches of about 44 or gO degrees. And in these, at the distance of half an 

 inch from the centre, the variation is but -i- so much, viz. about 14"; and at 4- 

 of an inch, not 4"; at the centre it is precisely true. Therefore as an observa- 

 tion may be taken with it in one fourth of the time, that Davis's quadrant, on 

 which 3 things must be brought to meet, in a general way requires: I say, con- 

 sidering this, and the vast importance of such dispatch, in the case of great 

 altitudes, or of tempestuous seas, or beclouded skies, it is presumed the instru- 

 ment thus made, will be judged preferable to all others of the kind yet known. 

 Some masters of vessels, who sail from hence to the West Indies, have them 

 made as well as they can be done here ; and have found so great an advantage 

 in the facility and in the ready use of them, in those southerly latitudes, that 

 they reject all others. And it can scarcely be doubted, but when the instru- 

 ment becomes more generally known, it may on the Royal Society's approba- 

 tion, if it appear worthy of it, more universally obtain in practice. 



It is now 4 years since Tho. Godfrey hit on this improvement ; for his ac- 

 count of it, laid before the Society last winter, in which he mentions two years, 

 was written in 1732. And in the same year, J 730, after he was satisfied in 

 this, he applied himself to think of the other, viz. the reflecting instrument by 

 speculums, for a help in the case of longitude, though it is also useful in taking 

 altitudes, and one of these, as has been abundantly proved by the maker, and 

 those who had it with them, was taken to sea, and there used in observing the 

 latitude, the winter of that year, and brought back again hither before the end 

 of February, 1730-1. It was unhappy indeed, that as lie had no acquaintance 

 nor knowledge of persons there, that no account of it was transmitted sooner. 

 But it was owing to an accident which gave Mr. Logan some uneasiness, viz. 

 his attempting to publish some account of it in print here, that he did it at that 

 time, viz. in May 1732, when he transmitted it to Dr. Halley ; to whom he 

 made not the least doubt but the invention would appear entirely new. 



The bow had best be an arch of about 100 degrees, well graduated, and 

 numbered both ways; the radius of 20 or 24 inches; the curve at the centre 

 to be -^ of the radius on each side, that is, -'-o "^ it in the whole ; the radius 

 of that curve ,Vo- parts of the radius of the instrument ; that the glass for the 



