2 6 JVlifceUanea Curiofa. 



ridian, whereon the faid Canon oiFakq pre- 

 cifely anfwers to the differences of Longitude, 

 putting Unity for one minute thereof, as in 

 the Common Meridian Line. Now, the mo- 

 mentary augment or fluxion of the Tangent Line 

 at 45 degrees, is exactly double to the fluxion 

 of the arch of the Circle, (as may eafily be 

 proved ) and the Tangent of 45 being equal to 

 Radius, the fluxion alfo of the Logarithm Tan^ 

 gent will be double to that of the arch, if the 

 Logarithm be of JSTapier\ form .* but for Briggs\ 

 form, it will be as the fame doubled arch, mul- 

 tiplied into o, 43429, &c. or divided by- 2, 

 30258, &c. Yet this muft be underftood only 

 of the addition of an indivifible arch,for it cea- 

 fes to be true, if the arch have any determi- 

 nate magnitude. 



Hence it appears, that if one minute be fup- 

 pofed Unity, the length of the arch of one mi- 

 nute being ,000290888208665721 5961 54, &c. 

 in parts of the Radius, the proportion will be 

 as Unity to 2,908882, &c. fo Radius to the 

 Tangent of 71 0 1/ 42" whofe Logarithm is 10. 

 4637261 1720718325204, &o and under that 

 angle is the Meridian interfe&ed by that 

 Rhumb Line,on which the differences of Napier's 

 Logarithm Tangents of the half Complements 

 of the Latitudes are the true differences of Lon- 

 gitude, eftimated in minutes and parts, taking 

 the firfb Four Figures for Integers. But for 

 VUcc(% Tables, we muft fay. 



As .2302585, &c. to 2908882, &c. So Ra- 

 dius to 1,26331 14387424456921 2, &c. which 

 is the Tangent of 5 1 0 38' 9", and its Logarithm 

 10,101510428507720941162, &c. wherefore in 

 the Rhumb Line, which makes an angle of 51° 

 38' 9" with the Meridian, Vlaccf% Logarithm 



Tan- 



