Page:Philosophical Transactions - Volume 001.djvu/226

 Mr. Oughtred in the VI. Chap. of his Navigation, annexed to the Book, entituled, The Circles of Proportion, and the Horizontal Instrument, &c. mentions an Artifice, by himself discover'd, by which it may be effected, that the small Parts of the Meridian be not one minute (which on the face of the Earth answers to above an English Mile) but the hundred-thousanth, or, if need be, the millioneth part of a minute, scarce exceeding one fifteenth part of an Inch: Which thing, he saith, he is able to perform in Tables unto the Radius 10000000; yet nothing at all differing either in their form or manner of working from those that are now commonly in use.

But which way this is to be done, this Author hath not made known to the Publick. And, though such Tables unto the Radius 10000000, had been brought to light, yet would they not be sufficient to prove the identity or sameness of the said two Lines, as to continue the comparison between them as far, as the one of them, videl. the Logarithmicall Tangent-line, is already calculated, that is, to Ten places, besides the Charactoristick.

Now therefore, if a certain Rule could be produced, by which the Agreement or Disagreement of the said two Lines might be shew'd, not only to that Extent of places, to which that Tangent Line is already calculated, but also to as many more, as the same maybe yet further extended unto, in infinitum usque; surely that rule would not only save us the labour of making Tables unto the Radius 10000000; but also the Helix or Spiral Line of the Ships Course would be reduced to a more precise exactness, than ever was pretended by Him: and this most Noble and Useful Science (as He justly calls it) which is the Bond of most disjunct Countries, and the Consociation of Nations farthest remote, would attain its full lustre and perfection.

Besides, that the same Rule would also discover a far easier way of making Logarithmes, than ever was practised or known; and therefore might serve, when ever there should be occasion, to extend the Logarithmes beyond that number of places, that is already extant.

Moreover such a rule would enable men to draw the Meridian line geometrically, that is, without Tables or Scales: which indeed Rh