VOL. I.] PHILOSOPHICAL TRANSACTIONS. 71 



and the consociation of remotest nations, '-, ould attain its full lustre and per- 

 fection. 



Besides that the same rule would also discover a far easier way of making lo- 

 garithms than ever was practised or known, and therefore might serve, when- 

 ever there should be occasion, to extend the logarithms beyond the number of 

 places already known. 



Moreover, such a rule would enable men to draw the meridian line geometri- 

 cally, that is, without tables or scales: which indeed might also be done by- 

 setting off the secants of every whole or half degree, if there were not this in- 

 convenience in it, that a line, composed of so many small parts, would be 

 subject to many eiTors, especially in a small compass. 



The same rule also will serve to find the course and distance between two 

 places assigned, as far as practice shall require it; and that without any table 

 of meridional parts, and yet with as much ease and exactness. 



And as all these things depend on the solution of this question, whether the 

 artificial tangent-line be the true meridian-line ? I undertake, by God's assist- 

 ance, to resolve the said question. And in order to let the world know with 

 what readiness and confidence I undertake it, I am willing to lay a wager against 

 any one or more persons that have a mind to engage, for so much as another 

 invention of mine, which is of less subtlety, but of far greater benefit to the 

 public, may \c of worth to the inventor. 



For the great advantage which all merchants, mariners, and consequently the 

 commonwealth may receive from this other invention, is, in my judgment, 

 highly valuable; as it will often make a ship sail against even a contrary wind, 

 and yet as near to the place intended as if the wind had been favourable : or 

 will enable one to gain something in the intended way whether the wind be fair 

 or not (except only when you go directly south or north), but the advantage will 

 be most where there is most need of it, that is, when the wind is contrary : So 

 that one may very often gain a fifth, fourth, third part, or more of the in- 

 tended voyage, according as it is longer or shorter, but always most in a longer 

 voyage. 



All this the proposer is to make good by the verdict of some able men, who 

 also may give a guess what this latter invention may be worth to the owner : 

 And for so much, and no more, he will stand engaged against any one or 

 more persons, that he will and shall resolve the question above-mentioned, viz. 

 Whether the artificial tangent-line be the true meridian line; and if not, then he 

 will lose, and transfer to the other party the whole benefit of the last men- 

 tioned invention. But if, on the contrary, he prove or disprove the identity 

 of the said two lines, to the judgment of some able mathematicians, that 



