[ 340. ] 
LIII. On the Properties of a Line of shortest Distance traced 
on the Surface of an oblate Spheroid. By J. Ivory, Esg. 
M.A. FRS.* 
(Concluded from p. 249.) 
| continuing the subject of my last communication, I shall 
now examine particularly the case of a geodetical line di- 
rected at right angles to the meridian. For this purpose I 
resume the formula before found, viz. 
sin uw = sin 1 cosz, 
eS J/1 + & cos?l. dx 
(1 + e® — e? sin? 7 cos? z)a° 
/ being the latitude at the commencement of the line, and 
the latitude at its termination. We rejected this formula, be- 
cause the are x cannot be safely determined by means of the 
latitudes. But this objection will be of no force if the same 
are can be ascertained with sufficient exactness either by the 
difference of longitude, or the change in azimuth. In reality 
the formula is extremely proper for finding s: for so long as 
is not very considerable the denominator varies slowly, and 
is almost proportional to s. We may likewise illustrate the 
ae 
to 64°5. At sunrise on the 31st, when at 26 miles west of Cape Verd, the 
dew-point was 61°'5, and lowered to 57°:5 on nearing the land, the tem- 
perature of the air not being sensibly affected. Off the entrance of the 
Gambia, on the Ist of February, and in the river on the 2d and 3rd and 4th, 
the dew-point was never higher than 51°, and occasionally as low as 48°°5, 
the air over the water and in the shade being generally during the day 
from 69° to 70°. When about to quit the Gambia on the morning of the 
5th of February, we experienced, although in a very slight degree, the pe- 
caliar wind called the Harmattan, of which the season was nearly over : its 
direction was one or two points to the north of the trade wind, or about 
N.N.E.; the air during its influence fell to 66°°5, and the dew-point to 
37°°5; affording a reasonable inference, that in a genuine Harmattan, and 
before it reaches the sea, the constituent temperature of the vapour may 
be at least as low as 32°. In the progress toCape Roxo, on the afternoon 
of the same day, we lost the Harmattan, and with it the continuance of the 
trade wind. ‘ke sea breeze which followed, raised the temperature of 
the air to 70°, and of the dew-point to 61°'5. 
It appears, therefore, that when the north-east wind first comes off the 
continent of Africa it contains only 53 parts in 100 of the moisture which 
would be required for repletion at the existing temperature ; that in blowing 
over the sea its proportion of moisture rapidly augmeats, until at fifty miles 
{rom the land, it has acquired 80 parts in 100; which proportion is not 
subsequently increased by its passage over 350 additional miles of ocean, 
In the Harmattan the air contained only 38-parts in 100 of the proportion 
of moisture required for its repletion. 
* Communicated by the Author, 
~ same 
