, Of Dialing.

vertical plane at Z, declining westward from S (the south) by anangle of 36 degrees; on which plane an erect dial for London at Z isto be described. Make the semidiameter Z D perpendicular to 'Zb,and it will cut the horizon in D, 36 degrees west of the south S,Then, a plane in the tangent HD, touching the sphere in D , willbe parallel to the plane Z h ; and the axis of the sphere will be equallyinclined to both these planes.

Let WQj EJ be the equinoctial, whofe elevation above the horizonof Z (London) is 38- degrees; and PRD be the meridian of theplace D, cutting the equinoctial in R. Then, it is evident, thatthe arc RD is the latitude of the place D (where the plane Zbwould be horizontal) and the arc K^,is the difference of longitudoof the planes Zh and DH.

In the spherical triangle PFDR, the arc WD is given, for it isthe complement of the plane’s declination from S the south ; which,complement is 54 0 (viz. 90°—36°:) the angle at R, in which themeridian of the place D cuts the equator, is a right angle ; and theangle RWD meafures the elevation of the equinoctial above thehorizon of Z, namely, 38^ degrees. Say therefore, as radius is tothe co-sine of the plane’s declination from the south, fo is the co-sineof the latitude of Z to the sine of R D the latitude of D : which isof a different denomination from the latitude of Z, becaufe Z ajidD are on different sides of the equator.

As radius ------ 10.00000

To co-sine 36' o — 9.90796

So co-sine 51 0 30' = QZ 9.79415

To sine 30° 14 ' = DR (9.70211) = the lat. of D, whofehorizon is parallel to the.vertical plane Zb at Z.

N. B. When radius is made the first term, it may be omitted,and then, by fubtracting it mentally from the sum of the -other two,the Operation will be fhortened. Thus, in the prefent case,

To the logarithmic sine of WR=* 54 0 o' 9.90796

Add the logarithmic sine of R D = -f 38° 30' 9.79415

Their sum — radius ------- 9.702 11 gives the

fame folution as above. And we fhall keep to this method in thefoliowing part of the work.

* The co-sine of 36° or of -f The co-sine of 51 0 30', or of Z.