You may do the same thing by the Quadrant, without the help of the Rectifier before spoken of, if you will remember, That this Quadrant hath eight Points, or ¼ of the whole Compass, by which you may orderly reckon the whole, and set the Index to the greatest difference either from the East, Southward, or Northward, or West. In like manner as in the foregoing Proposition, the true Amplitude of Rising and Setting was 2 Points, or 22 Deg. 34 Min. E. N. E. Set the Index to the Degrees and Points, reckoning the Deg. from D on the Arch of the Quadrant, toward E the Scale of Leagues of the Index; then reckon the Point and Degree taken by Observa∣tion, which is 11 Deg. and 15 Min. a just Point of the Compass: therefore it being but E. by N. short a Point of the true Amplitude, therefore the E. b. N. of the Steer∣ing-Compass, respecteth the true E. N. E. and the N. b. E. respecteth the true N. and so account all round the Compass a Point more than the Steering-Compass sheweth: And if you would know which way the Variation is, you see it is a Point more from the E. than your Compass sheweth Northerly.
But if the Steering or Azimuth-Compass, had shewn a Point more than the true Amplitude found by the Quadrant and true Point, the Variation had been Westerly.
But suppose the Amplitude found had been a Point Southerly, E. b. S. and the Sun's Rising and Setting had been a Point Northerly; by Observation of the Ship-Com∣pass, you see there is two Points difference: therefore set the Index to two Points, from M the East or West side of the Quadrant, as in this Proposition you must reckon it, and you may see plainly that the East Point by the Steering-Compass is the true East-South-East Point; and the South Point is the true South-South-West Point; and the North is the true North-North-West Point; and so of all the rest: And the Va∣riation is Southerly. So that you see how readily this Quadrant doth these things, when the Points of the Compass is imprinted in a Mans mind, which must be, and is in all Masters and Mates.
Suppose I would know by the Quadrant the true Point of the Compass, when Bootes Arcturus riseth and setteth: In the Latitude of 40 Deg. Bootes Arcturus De∣clination is 20 Deg. 58 Min.
Set the Side of the Index and Sine to the Latitude of 40, and count the Declina∣tion 21 Degrees almost, from M on the Arch; and run your Eye up the Parallel, and it will cut the Index about 27 Deg. 50 Min. which is reduced into Points and Quar∣ters by allowing Gr. 15 Min. to a Point, his Rising will be almost E. N. E. ½ a Point Northerly, his Setting W. N. W. ½ Westerly. But if the Declination of a Star of the South side the Aequinoctial, the Rising had been E. S. E. ½ Southerly, and his Setting W. S. W. ½ Southerly.
In the like manner you may know the Rising and Setting of any Star in an instant, by this Quadrant and Index, which I hold to be as necessary an Instrument as Seamen can use, in respect of its plainness, and brevity, and portability, so made as you see the Figure, the larger the better: And on it you may work all manner of Travisses to the distance of 60 Leagues or Miles which is on the side of the Index. It being so plain and easie, I need not write any thing thereof; but for the Learner's sake, take these few Rules following.