C 74 3 
VII. A Method of finding the Latitude of a Place , by Means of 
two Altitudes of the Sun and the Tune elapsed betwixt the 
Observations. By the Rev. W. Lax, A. M. Lowndes's Pro- 
fessor of Astronomy in the University of Cambridge. 
Read January 10, 1799. 
I hope the following method of determining the latitude, by 
means of two altitudes of the sun and the time elapsed betwixt 
the observations, will be found not less convenient for nautical 
purposes than the rules which are commonly employed. But 
I would rather recommend it in those cases where rigid accu- 
racy is required, and the astronomer is provided with no better 
instrument for taking the sun's altitude than a Hadley's sextant 
of the most improved construction. The process will be neither 
difficult nor tedious; and, if the observations are made with 
proper exactness, I conceive the latitude will generally be ob- 
tained within a few seconds of the truth. With these expecta- 
tions, I have ventured to reduce the method into its present 
form ; and submit it, with the utmost deference, to this learned 
Society. 
In the spherical triangle, whose sides are the complements of the 
latitude, declination, and altitude, let z represent the angle at the 
pole, and t its tangent; Z the azimuth, and T its tangent: L the la- 
titude, and x its cosine, radius being unity; then, if the altitude and 
declination remain constant, we shall have L = xT z, and, con- 
sequently, L will vary as T z, when the increment of x, com- 
