818 
MR. F. C. PENROSE ON THE RESULTS OF AN EXAMINATION 
the great Temple of Jupiter at Olympia. On the list it is shown that this temple 
has an orientation angle of 262° 37' 46", which gives the eastern axis an amplitude 
of 7° 22' 14" north. The eastern mountains subtend an angle of 2° 4'. 
I assume that in the climate of Greece no star with which we are concerned in this 
inquiry, excepting Sirius, could be expected to be seen under ordinary circumstances 
heliacally at an angle less than 3° (independent of refraction) above the true horizon. 
1 have indeed myself seen Rigel heliacally, and in the same direction as the Sun, at a 
lower elevation but allowing for variation of weather and the glow which skirts 
the horizon when the sun is about 10° below it, 1 consider the altitude of 3°, as above 
stated, the proper angle to take for the stars generally. When there is a mountain 
high enough to exclude the glow referred to, it is favourable for the detection of the 
star, but that is not the case at Olympia. The Sun, however, is differently situated, 
and in the climate of Greece can be reckoned upon to throw a strong illumination as 
soon as a quarter of his refracted orb is clear of the visible horizon. This at moderate 
altitudes allows the reduction of the apparent height of the mountain by 0° 22'. 
We have then to determine the Sun’s place in the case before us, having the Sun’s 
amplitude 7° 22' 14", an altitude of 1° 42', and the terrestrial latitude. Applying 
the formula 
Sin S = cos zenith dist X cos colat + sin zenith dist X sin colat X sin ampl, 
we obtain for the Sun’s declination + 6° 52' 22". 
This, at the value of the obliquity at, say, 800 years B.C., gives for the Sun’s 
KA., 1 >' 3“ 15^ 
Applying the same formula for a star having the same amplitude, but with an 
altitude of 3°, we obtain for its declination 7° 40'. 
* I made, with such opportunities as presented themselves, naked-eye observations of heliacal stars. 
The following apjjear to be the most valuable. 
Name of Star. 
Magnitude. 
Altitude of 
Star. 
Sun’s 
depression. 
Hifl'ereuce of 
azimuth 
S un and Star. 
Sunset, April 19. At sea. / 
^ Ai'gus 
G 
U / 
9 47 
10 49 
O 
102 
Latitude about 37° 50' \ 
7 Andromeda? 
2 
9 0 
12 
0 
17 
Suni’ise, April 26. Livadia. 1 
Latitude 38° 26' / 
20 Librm . 
o 
9 0 
10 
17 
163 
Sunset, May 1. At Sea. f 
e Can is Major 
1-5 
7 20 
8 
0 
76 
Latitude about 39° 50' \ 
Rigel . 
1 
2 40 
9 48 
41 
The stars on the occasions above recorded were distiirctly seen, and were found in the open sky—in 
most cases with the distraction of ship-lights about. These observations by no means show the limiting 
angles of visibility of heliacal stars by younger eyes looking from a dai’kened chamber through a narrow 
opening and towards points in the horizon Avhere it would be kuoAvn that the stars must rise. Three 
degrees appears to have been about the angle considered necessary by Ptolemy. (See Biot, ‘ Recherches 
sur I’Annee Vague des Egyptiens.’) 
