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Sailing by the Ark of a great Circle.
For this purpose the tangent lines on the index will be a ready help, using the lesser for small, and the greater tangent line, for great latitudes. The way is thus,
Account the pont 60/0, on the outward limb of the moveable piece to be the point, or port of your departure; thereto lay the fiducial edge of the index, and reckoning the latitude of the Port you departed from upon the index, strike a pin directly touch∣ing
it, into the table your instrument lies upon. This pin shall represent the Port of your departure. Therefore hanging a thread, or hair, on the center, whereon the index moves; and winding it about this pin. Count the difference of longitude 'twixt the port of your departure, and the Port you sail to∣ward, from 60/0 on the moveable piece to∣ward 0/60, on the loose piece; and thereto laying the same fiducial edge of the index, reckon the latitude of this last Port upon the index, directly touching of it, strike down another pin upon the table, and draw the thread strait about this pin fastening it there∣to. This done, the thread betwixt the two pins represents the ark of your great Circle; and laying the fiducial edge of the index to any degree of difference of longitude ac∣counted from 60/0 on the moveable piece, the thread shows upon the index what lati∣tude you are in, and how much you have raised, or depressed the pole since your de∣parture. On the contrary, laying the lati∣tude you are in (numbred upon the index) to the thread, the index shows the difference of longitude upon the limb; counting from 60/0 on the moveable piece. So, that were it possible to sail exactly by the ark of a great Circle, it would be no difficulty to deter∣mine
the longitude in any latitude you make.
But I intend not a treatise of Navigation; wherefore let it suffice, that I have already shown how the most material Problems therein, may easily, speedily, and (if the in∣strument be large) exactly, be performed by the instrument without the trouble of Cal∣culation, or Projection.