34 
MR. RUiMKER’S OBSERVATIONS 
In the same manner, if from absolute altitudes of the sun we would infer 
the sidereal time of the sun’s culmination, the hour-angle converted to sidereal 
time must be decreased or increased by a proportional part of the daily differ- 
ence of equation of time, according as the apparent time is gaining or losing 
upon mean time, or, which is the same, according as the daily difference of 
right ascension is less or more than 3' 56".6. 
Correction of the assumed Time of the Sun’s Culmination. 
It is clear that the utmost precision in the time is required under such 
circumstances, when the vicinity to noon is indeed the most favourable period 
of the day for determining this very element — the time, which in finding the 
latitude we assume as given. But I believe that both objects can be attained 
at once, and that circummeridional altitudes near the zenith afford the means 
of ascertaining the error in the level of the transit as well as the latitude. 
If we find that with an assumed time of the sun’s culmination from several 
sets of circummeridional altitudes, the deduced respective meridional altitudes 
A, B, C, D, E either gradually decrease or increase, we may suspect that the 
sun’s transit has been assumed too late or too soon. I suppose the correction 
for the change of declination during the hour-angle (which also occasions 
a gradual alteration) to be already applied. With the mean of Delambre’s 
numbers A in an ascending set, take out of his Tables for the Reduction to 
the Meridian the quantity corresponding to a change of one second in time, 
which call m, take also with the mean of A in a descending set a similar 
quantity n. Then is 
■ - A ~ ^ ~ = &c. & c. = x the error by which the sun’s culmi- 
7T m + n" n tt' w! + n m n J 
nation has been assumed too late; and A — tt in x = E + ^ n" x = B — r 1 rri x 
= D + ^“ n 1 x = the true meridional altitude. 
Reduction to the Solstice. 
The reduction to the solstice is computed after the following formula ; 
c x sin 2 i L 
where the constant c — 
2 sin w 
L = complement of sun’s 
p = T7T\ i \ vvnuic tiic liuiiDiaiii c — c ; n in ? 
cos £ (D + oo) sin 1 
longitude ; D the declination ; and u the obliquity of the ecliptic 
