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Here place the eighth Figure.
M Q N O, is the Meridian of the Mag∣netick Pole, and S N is the distance of the Magnetick Pole, from the Pole of the Earth 8 d. 30 m. and L S, is the Co-lati∣tude, 52 d. 21 m. And L N is the Mag∣netick Co-latitude 49 d. 18 m.
The Work follows.
| d. | m. | ||
| N L, | 49 | 18 | |
| S N, the residuum Sine of | 08 | 30 | 083029 |
| L S the residuum Sine of | 52 | 21 | 010140 |
| The Sum of the Sides | 110 | 09 | |
| The Sine of the half Sum | 055 | 04½ | 991371 |
| The side opposite to the Angle, substract | 49 | 18 | |
| The Sine of the Difference | 05 | 46 | 900206 |
| The Sum of all | 1984746 | ||
| The Sine of the half Sum | 57 | 02 | 992373 |
The Complement of 57 d. 02 m. is 32 d. 58 m. the double thereof is 65 d. 56 m. the Angle N S L.
So the Angle L S N, being found 65 d. 56 m. that the Magnetick Meridian is to the Westward of the Lizard, whose Complement is the Angle L S C 114 d. 04 m. that the Magnetick Meridian is to the Eastward of the Meridian of the Li∣zard.
But I observe the Co-latitude of the Magnetick Pole in its proportions, does not make out the Longitude in Mr. Bonds Tables to the Meridian of London by 04 d. 4 m. But, I suppose, Mr. Bond did make
choice of the Meridian of the Lizard to be the Meridian in propotion to the Magneti∣cal Co-latitude at Cape Charles, in re∣gard the Magnetical Co-latitude at Cape Charles, would not give the Magnetical Meridian in proportion to the Meridian of London. And here we are to observe, if the Magnetical Co-latitude, with the other proportions, in one and the same Meridian of the Earth, will not give the fame An∣gle at the Pole in all Parallels, that cross that Meridian, then the Inclinatory Nee∣dle cannot perform the Work of finding the Longitude, in regard you cannot tell where to find the Magnetical Meridian, in proportion to any one Meridian of the Earth.
Now we are to prove, that the Angle at the Pole does alter in one and the same Meridian of the Earth, from Mr. Bonds Observations by the Inclinatory Needle, when according to truth every Meridian keeps its Longitude from the Poles in all Parallel.
Cape Charles, and the New Island of Providence, are both under one and the same Meridian. See Mr. Bonds Tables of Longitude 70 d. 00 m. Westward of the Meridian of London.
Now suppose I was at the new Island of Providence, and should observe and find it in the Latitude of 25 d. 25 m. N°. and should find the inclination of the Inclina∣tory Needle 48 d. 39 m. and in the Caro∣line Table, the Magnetick Co-latitude 60 d. 24 m. and the Magnetick Pole di∣stant from the Pole of the Earth 8 d. 30 m. to find the Angle at the Pole of the Earth L S N.
| d. | m. | ||
| L N, | 60 | 24 | |
| S L, the residuum Sine of | 64 | 35 | 004421 |
| N S, the residuum Sine of | 08 | 30 | 083029 |
| The Sum of the Sides | 133 | 29 | |
| The Sine of the half Sum | 66 | 44½ | 996316 |
| The Side opposite to the Angle, substract | 60 | 24 | |
| The Sine of the difference | 06 | 20½ | 904264 |
| The Sum | 1988028 | ||
| The Sine of the half Sum | 60 | 36 | 994014 |
The Complement of 60 d. 36 m. is 29 d. 24 m. the double thereof is 58 d. 48 m. for the Angle at the Pole of the Earth L S N.
Now substract 58 d. 48 m. the Angle at the Pole, that the Magnetick Meridian of New Providence makes with the Meridian of the Lizard, from 65 d. 56 m. the An∣gle at the Pole, that the Magnetical Meri∣dian of Cape Charles, makes with the Me∣ridian of the Lizard, and you have 07 d. 08 m. that the Magnetical Meridians or Angles at the Pole do differ in the same Meridian of Cape Charles, when ac∣cording to truth every Meridian keeps its Longitude from the Poles of the Earth in all Parallels.
So that the Magnetical Co-latitude un∣der one and the same Meridian of the Earth, doth alter the Angles at the Pole, and then the Magnetick Co-latitude, un∣der one and the same Meridian of the Earth, is not in proportion to the Meri∣dian of the Lizard, or any certain Meridi∣an of the Earth.