Jussit, & erectos ad sidera tollere vultus.

Ovid. Metam. L. 1. car. 84.

[e] If any should be so curious, to desire to know how far a Man’s Prospect reacheth, by Means of the Height of his Eye, supposing the Earth was an uninterrupted Globe; the Method is a common Case of right-angled plain Triangles, where two Sides, and an opposite Angle are given: Thus in [Fig. 4.] A H B is the Surface, or a great Circle of the terraqueous Globe; C the Center, H C its Semidiameter, E the Height of the Eye; and foreasmuch as H E is a Tangent, therefore the Angle at H is a right Angle: So that there are given H C 398,386 Miles, or 21034781 English Feet, (according to [Book II. Chap. 2. Note (a)];) C E the same Length with the Height of the Eye, on the Mast of a Ship, or at only a Man’s Height, &c. added to it; and E H C the opposite right Angle. By which three Parts given, it is easy to find all the other Parts of the Triangle. And first, the Angle at C, in order to find the Side H E, the Proportion is, As the Side C E, to the Angle at H; so the Side H C, to the Angle at E, which being substracted out of 90 gr. the Remainder is the Angle at C. And then, As the Angle at E, is to its opposite Side H C, or else as the Angle at H is to its opposite Side C E; so the Angle at C, to its opposite Side E H, the visible Horizon. Or the Labour may be shortned, by adding together the Logarithm of the Sum of the two given Sides, and the Logarithm of their Difference; the half of which two Logarithms, is the Logarithm of the Side requir’d, nearly. For an Example, We will take the two Sides in Yards, by Reason scarce any Table of Logarithms will serve us farther. The Semidiameter of the Earth is 7011594 Yards; the Height of the Eye is two Yards more, the Sum of both Sides, is 14023190.

Logar. of which Sum is,7,1468468
Logar. of two Yards (the Differ.) is,0,3010300
Sum of both Logar.7,4478768
The half Sum,3,7239384

is the Logar. of 5296 Yards = three Miles, which is the Length of the Line E H, or Distance the Eye can reach at six Feet Height.

This would be the Distance, on a perfect Globe, did the visual Rays come to the Eye in a strait Line; but by Means of the Refractions of the Atmosphere, distant Objects on the Horizon, appear higher than really they are, and may be seen at a greater Distance, especially on the Sea; which is a Matter of great Use, especially to discover at Sea the Land, Rocks, &c. and it is a great Act of the divine Providence, in the Contrivance and Convenience of the Atmosphere, which by this Means enlargeth the visible Horizon, and is all one, as if the terraqueous Globe was much larger than really it is. As to the Height of the Apparent above the true Level, or how much distant Objects are rais’d by the Refractions, the ingenious and accurate Gentlemen of the French Academy Royal, have given us a Table in their Measure of the Earth, Art. 12.

[f] See [Book VI. Chap. 5. Note (g).]

[g] See [Book IV. Chap. 8. Note (c).]

[h] The Mechanism of the Foot, would appear to be wonderful, if I should descend to a Description of all its Parts; but that would be too long for these Notes; therefore a brief Account, (most of which I owe to the before-commended Mr. Cheselden,) may serve for a Sample: In the first Place, It is necessary the Foot should be concave, to enable us to stand firm, and that the Nerves and Blood-Vessels may be free from Compression when we stand or walk. In order hereunto, the long Flexors of the Toes cross one another at the Bottom of the Foot, in the Form of a St. Andrew’s Cross, to incline the lesser Toes towards the great One, and the great One towards the lesser. The short Flexors are chiefly concern’d in drawing the Toes towards the Heel. The transversalis Pedis draws the Outsides of the Foot towards each other; and by being inserted into one of the sesamoid Bones, of the great Toe, diverts the Power of the abductor Muscle, (falsly so call’d,) and makes it become a Flexor. And lastly, the peronæus Longus runs round the outer Ankle, and obliquely forwards cross the Bottom of the Foot, and at once helps to extend the Tarsus, to constrict the Foot, and to direct the Power of the other Extensors towards the Ball of the great Toe: Hence the Loss of the great Toe, is more than of all the other Toes. See also Mr. Cowper’s Anat. Tab. 28. &c.

[] It is very well worth while to compare here what Borelli saith, de motu Animal. Par. 1. cap. 18. De statione Animal. Prop. 132, &c. To which I refer the Reader, it being too long to recite here.