And seeing the lines TS, TQ, reduced to minutes of a degree, are 6255.189 and 3255.189 respectively, and the angle STV is 63° 5´⅗, the right line SQ on the map will be 5594´, exceeding its just value by 132´ or ¹⁄₄₂ of the whole. 7. The errors on the parallels increasing fast towards the north, and the line SQ having, at last, nearly the same direction, it is not to be wondered that the errors in our example should amount to ¹⁄₄₂. Greater still would happen, if we measured the distance from O to Q by a straight line joining those points: for that line, on the conic surface, lying every-where at a greater distance from the sphere than the points O and Q, must plainly be a very improper measure of the distance of their correspondent points on the sphere. And therefore, to prevent all errors of that kind, and confine the other errors in this part of our map to narrower bounds, it will be best to terminate it towards the pole by a straight line KI touching the parallel OQ in the middle point K, and on the east and west by lines, as HI, parallel to the meridian thro’ K, and meeting the tangent at the middle point of the parallel SV in H. By this means too we shall gain more space than we lose, while the map takes the usual rectangular form, and the spaces GHV remain for the _title_, and other inscriptions. VII. Another, and not the least considerable, property of our map is, that it may, without sensible error, be used as a sea-chart; the rumb-lines on it being logarithmic spirals to their common pole _t_, as is partly represented in the figure: and the arithmetical solutions thence derived will be found as accurate as is necessary in the art of sailing. Thus if it were required to find the course a ship is to steer between two ports, whose longitudes and latitudes are known, we may use the following RULE. _To the logarithm of the number of minutes in the difference of longitude add the constant logarithm[29] -4.1015105, and to their sum the logarithm sine of the mean latitude, and let this last sum be_ S. _The cotangent of the mean latitude being_ T, _and an arithmetical mean between half the difference of latitude and its tangent being called_ m, _from the logarithm of_ T + m _take the logarithm of_ T - m, _and let the logarithm of their difference be_ D; _then shall_ S - D _be nearly the logarithm tangent of the angle, in which the ship’s course cuts the meridians_. _Note_, We ought, in strictness, to use the ratio of _tx_ + _x_R to _tx_ - _x_R instead of T + _m_ to T - _m_; but we substitute this last as more easily computed, and very little different. EXAMPLE 1. Let the latitudes, on the same side of the equator, be 10° and 60°; then the middle latitude and its complement are 35° and 55°, and half the difference of the latitudes is 25°: and the difference of longitude being 110°, the operation will stand as below.