The longitude not found, or, An answer to a treatise written by Henry Bond, Senior, shewing a way to find the longitude by the magnetical inclinatory needle wherein is proved that the longitude is not, nor cannot be found by the magnetical inclinatory needle / by Peter Blackborrow, Gent.

To Demonstrate this Sphere upon the Globe.

THe Brass Meridian, in which the Globe moves, is the Meridian of London; so bring any Meridian upon the

Globe to the Brass Meridian; and from the Poles make a Mark upon the Meridian of the Globe, just under 8 d. 30 m. of the Brass Meridian, for the Magnetick Pole. So take 72 d. 33 m. the Magnetick Pole Distant from the Parallel of 22 d. 30 m. No Latitude from the Equator; and fix one point of your Compasses in the Mag∣netical Pole 8 d. 30 m. turning the Globe Eastwards, until 72 d. 33 m. will cut in the Parallel of Ballasore 22 d. 30 m. just under the Brass Meridian of the Globe, so make a Mark, and let the Globe stand, then is L N the Magnetick Pole Distant from the Meridian of London 72 d. 33 m. and L S is the Co-latitude of Ballasore 67 d. 30 m. and N S is the Distance of the Magnetical Pole, from the Pole of the Earth 8 d. 30 m. and the Angle L S N, is what the Magne∣tick Meridian is gone from the Brass Me∣ridian, or the Meridian of London, and I D is the Magnetick Latitude 32 d. 10 m. and L A is the Latitude of Ballasore 22 d. 30 m.

By this Demonstration you may see the Distance of the Magnetick Poles, and the

Magnetick Co-latitude, and the Co-lati∣tude of the Place will hold their De∣monstrations in Proportion to the Poles of the Earth; then why should we fancy the Magnetick Poles in the Air?

Upon the Sphere M, Q, N, O is the Me∣ridian of the Magnetick Poles, and Q O is the Magnetick Equator, and E W is the Equator to the Poles of the Earth, and M L N is the Magnetick Meridian, crossing the Brass Meridian, or the Meridian of London, in the Parallel of 22 d. 30 m. So is S N the Magnetick Pole Distant from the Poles of the Earth, and L S is the Co-la∣titude of Ballasore, and N L is the Magne∣tick Pole Distant from the Meridian of London 72 d. 33 m. in the Parallel of 22 d. 30 m. and S L P is the Meridian of London, and not the Meridian of Ballasore, yet I place L in the Parallel of Ballasore, in the Meridian of London, in regard I did take the Inclination of the Inclinatory Needle in that Parallel.

For it is supposed, if I would find the Difference of Longitude from London; I have Sailed into unknown Parts, and ob∣serve

and find my Latitude, and my Mag∣netick Latitude; and now I would find how far I am East or West of the Meridi∣an of London: So I ought not to say S L P, is the Meridian of Ballasore, in regard I am to find it; but to make S L P the Me∣ridian of London, from whence I came; so the Magnetick Co-latitude will be in pro∣portion to what the Magnetick Meridian I am in, is from the Meridian of Lon∣don.

So is L S the Co-latitude of Ballasore 67 d. 30 m. in the Meridian of London; and S N, the Distance of the Magnetick Pole, ftom the Pole of the Earth 8 d. 30 m. And L N is the Magnetick Co-lati∣tude 72 d. 33 m. Now the Angle at the Pole N S L, will be found 125 d. 00 m. that the Magnetick Meridian of Bal∣lasore is, from the Meridian of Lon-don Eastwards, which should be the Magnetick Meridian of Ballasore at B, from the Me∣ridian of London L, the complement of 125 d. 00 m. out of 180 d. is the Angle A S W 55 d. 00 m. that the Magnetick Me∣ridian is West of the Meridian of London.

The Angle is drawn from the Sphere: the Work follows.

[illustration] geometrical diagram

Fig: 3

	d.	m.
LN,	72	33
NS, the residuum Sine	08	30	083029
SL, the residuum Sine	67	30	003438
The Sum of the sides	148	33
The half Sum	74	16½
The Sine of the first difference	65	56	995993
The Sine of the second difference	6	46	907124
The Sum			1989584
The half Sum			994792

994792 the sine thereof is 62 d. 30 m. the double thereof is 125 d. 00 m. the An∣gle at the Pole of the Earth N S L, which should be the Difference of Longitude: But since Mr. Bond makes London the first Meridian, from whence Longitude shall take its beginning, as in the Question be∣fore, Ballasore should have Longitude 125 d. 00 m. East of the Meridian of London; let the Table of Longitude say what it will, for the Table of Longitudes is no other than the difference of Meridians by Jour∣nal: But if I find the difference of Longi∣tude by the Magnetick Co-latitude, and the distance of the Magnetick Pole, and the Co-latitude of the place, it should correct what has been laid down by Jour∣nal; for I do not take what has been laid down by Journal to be true, in regard there is no certain Observation to lead us to it: For if London be not the Meridian, from whence the Magnetick Co-latitude takes its beginning towards the Magnetick Poles; then the distance of the Magnetick Meridian from the Meridian of London, cannot give the difference of Meridians.

Mr. Bonds way to prove what the Mag∣netick Meridian is gone to the Eastwards, is thus: First, he knows his Magnetick Co-latitude at Ballasore, and the Co-la∣titude of the place, and the distance of the Magnetick Pole; and so finds the di∣stance of the Magnetick Meridian, from the Meridian of London 125 d. 00 m. so then finding 125 d. 00 m. doth not an∣swer the Longitude by Journal; he pro∣ceeds to find what the Magnetick Meridi∣an is gone to the Eastwards: thus, he gives the Co-latitude, and the distance of the Magnetick Pole, and the Longitude by Journal 119 d. 12 m. and to this he adds 6 d. which makes 125 d. 12 m. the distance of the Magnetick Meridian, to find the Magnetick Co-latitude: This is but turning the Question.

So that you must know your Longitude by Journal 119 d. 12 m. before you can find what the Magnetick Meridian is gone to the Eastwards.

Mr. Bonds way is thus: Substract 119 d. 12 m. the Longitude by Journal, from 125 d. 12 m. the distance of the Magne∣tick

Meridian, from the Meridian of Lon∣don, and you have 6 d. 00 m. that the Magnetick Meridian is gone to the East∣wards: So by this Mr. Bond produced the Longitude by Journal, to correct the distance of the Magnetick Meridian, from the Meridian of London.

Mr. Bond must know that Longitude by Journal in all the World is laid down by Judgement; and then how rare is it for any one man, who hath been at any one Port in the World, somewhat remote, that hath found it in the very same Meridian, in regard of the many accidents that at∣tend the Practical part of the Mathematicks at Sea?

And then how is it possible to know the Longitude I am in, by the distance of the Magnetick Meridian? If I must first know the Longitude by Journal, which I cannot prove to be certain, and so correct the Observation by it, so that by this way of practice, the Inclinatory Needle is of no use; for the Magnetick Latitude, with the other proportions before, should give the Longitude without the help

of a Journal to correct his Observa∣tion.

The next thing we are further to consi∣der of is, how Mr. Bond finds what the Magnetick Meridian is gone to the East∣wards of Ballasore.

We may observe from Mr. Bonds own Sphere and Words; let the Angle W P N, be 6 d. 00 m. but this Angle W P N is not to be passed by, with a let it be so; but it must be found in proportion to the several sides, and Angles given in the Sphere. First I shall give the Co-latitude of Ballasore 67 d. 30 m. P B, and the Angle B P N 125 d. 12 m. and the Mag∣netick Co-latitude 72 d. 33 m. to find the Angle P N B.

Now to find the Angle P N B.

[illustration] geometrical diagram

Fig: 4

			d.	m.
As the Sine of the side	NB,	997953	72	33
Is to the Sine of the Angle	N P B,	991229	54	48
So is the Sine of the Side	P B,	996561	67	30
To the Sine of the Angle	P N B,	989837	52	19

So the Angle P N B, is found to be 52 d. 19 m.

Now let fall the Perpendicular in the foregoing Angle, as P W; so with the An∣gle W N P 52 d. 19 m. and the side P N 8 d. 30 m. we are to find the Angle W P N, which Mr. Bond saith, let it be 6 d. 00 m.

The Work follows.

[illustration] geometrical diagram

Fig: 5.

		d.	m.
As the Sine of	P Q,	81	30	999520
Is to the Tangent of	Q T,	37	41	988785
So is the Radius	P A,	90	00	1000000
To the Tangent of	A. g.	37	59	989265

So that A. g. 37 d. 59 m. is equal to the Angle A. P. g. or to the Angle W P N, 37 d. 59 m. de∣manded.

Now in the foregoing Angle, substract the Angle W P N, 37 d. 59 m. out of the Angle N P B 125 d. 12 m. and you have the Angle W P B, 87 d. 13 m.

And from hence it may be observed, that the Angle W P N, is 37 d. 59 m. and not 6 d. 00 m. that the Magnetick Meridian is gone to the Eastward, and the Angle W P B, is 87 d. 13 m. and not 119 d. 12 m. by Journal.

So that Mr. Bond has committed a gross error in offering to beg the Question; let the Angle W. P. N. be 6 d. 00 m. and the Angle W P B, be 119 d. 12 m. when it is contrary to all Demonstration and Practice in the Mathematicks, as it is proved in the foregoing Question.

So that by Mr. Bond's Practice, he would make the Longitude by Journal to be the certain difference of Meridians, since he corrects his Observation, from the Longi∣tude by Journal, by substracting 6 d. 00 m. from the Angle at the Pole 125 d. 12 m. to make it equal to the Longitude by Jour∣nal 119 d. 12 m. and then what need is there of finding the Longitude by the In∣clinatory

[illustration] geometrical diagram

Fig: 6.

Needle, when it is found by Journal, or to find what the Magnetick Meridian is gone to the Eastwards, when we have it by imagination; let the Angle W P N be 6 d. 00 m. that the Magnetick Pole is gone from the Meridian of London, when it is 37 d. 59 m.

The Sphere on the other side, is ac∣cording to Mr. Bonds own De∣monstration, to prove the fore∣going Work.

Here place the Sixth Figure.

And before I proceed any further, I shall make one Observation between the Me∣ridian of London and Bourdeaux. Bour∣deaux being but 20 Minutes Eastwards of the Meridian of London: See Mr. Bonds Tables of Longitude.

The Magnetical Latitude 69 d. 26 m. Bourdeaux Latitude N° 45 d. 16 m. the

Magnetick Co-latitude 36 d. 54 m. the di∣stance of the Magnetick Pole, from the Pole of the Earth 8 d. 30 m. to find the Angle of the Pole of the Earth.

The Demonstration of this Sphere upon the Globe, is according to my former.

Here place the seventh Figure.

	d.	m.
N L,	36	54
S N, the residuum Sine	08	38	083029
L S, the residuum Sine	44	50	015178
The Sum of the Sides	90	14
The half Sum of the Sides	45	07
The Sine of the first Difference	36	37	977558
The Sine of the second Difference	00	17	769417
The Sum			1845182
The Sine of the half Sum	09	41	922591

Which 9 d. 41 m. being doubled, you have 19 d. 22 m. for the Angle at the Pole

[illustration] geometrical diagram

Fig: 7

of the Earth, then substract 6 d. from it, as in the case of Ballasore, Bourdeaux be∣ing Eastward of the Meridian of London, and you have 13 d. 22 m. for the difference of Longitude, between London and Bourde∣aux, which is 13 d. 00 m. more than the truth by Journal. See in Mr. Bonds Tables of Longitude.

And from hence you may observe, that the Magnetical Needle, or Inclinatory Needle, cannot give the Magnetical La∣titude in proportion to any one Meridian of the Earth.