and Rate of a Chronometer. 413 
I am unacquainted with any means of appreciating. I frequently 
observe the edge of the sun’s disk in a state of apparent undula- 
tion, at altitudes at which that appearance is never observed in 
high and open situations. 
The observations of which I shall subjoin an abstract were 
made, like General B.’s, with a sextant of Troughton’ s divided 
on platina to 10”; and the telescope applied to it magnified 
eight times. The rate of the clock and its error for apparent 
time at noon were carefully determined, and the times were noted 
and written down with the altitudes, by a young gentleman on 
whom, from experience, I knew | coulil rely. Several altitudes 
of the sun’s upper and lower limbs alternately were taken near 
the meridian, and the several altitudes were reduced to the me- 
ridian by the following theorem. Let P, S, and Z, be the pole, the 
sun’s centre, and the zenith; then, sine sy = vers. P. sine PS. 
~ 
~ 
sine PZ, cosect. ZS. This theorem was published two or three years 
ago by Dr. Evans in a slightly different form, in Leybourn’s Ma- 
thematical Repository ; and as I know not whether the number 
of that work is published which containsthe demonstration, I may 
as well give it here. By spherics, vers. ZS —vers. ZP—PS= 
vers. P. sine PS. sine PZ. Now ZP<PS is the meridian zenith 
distance; and when P is small, it is evidently nearly =ZS. 
Hence ——~~ = sin. => sin. ZS = vers. P, sine PS. sine PZ; 
rs. 2S v4 
or sin. z= vers. P. sine PS, sine PZ. cosect. ZS. 
The declination of the sun was reduced to the Greenwich time 
of each altitude, and the latitude found from each altitude sepa- 
rately. The mean of the latitudes resulting from the altitudes of 
the snn’s lower limb was then taken, and also the mean of those 
resulting from the altitudes of the upper limb, and half the sum 
of these two means was taken as the latitude resulting from the 
observations of that day. By taking nearly au equal number of 
altitudes of the sun’s upper and lower limbs, any error that might 
have arisen from a faulty habit of estimating the contact was ef- 
fectually obviated. 
This method of observing is also useful in sencinlinw the 
time. 
The following will require no further explanation, and will be 
sufficient to exemplify what I have said: 
Trinity 
