382 



Mr. F. C. Penrose. On the 



[Apr. 27, 



taken as 1° 42', but that of the star, 3°. Combining these values 

 with the latitude, viz., 37° 38', and using the formula 



sin t> = cos zen. disfc. X cos colat-fsin zen. dist. X sin colat X sin ampl., 



we obtain for the star a declination of +7° 40', and for that of the 

 Sun +6° 52' 22". This latter, with the ecliptic obliquity of about 

 800 years B.C., determines the Sun's right ascension to have been 

 l h 3 m 15 s . 



The next step is to enqnire if there be any bright star or star 

 group which, at a date consistent with archaeological possibility, 

 would have had a declination near to the above-named place, and 

 would also have been heliacal. 



Such a star would have required about 6 h 8 m to pass from 3° 

 altitude to the meridian, and it would have required to have been 

 about lj h in advance of the Sun to allow it to be seen. The ap- 

 proximate R.A. of such star would therefore be about 23 h 40 m , and 

 its declination, as already stated, must be about 7° 40' N. 



For trials I have used a stereographic projection of the sphere 

 taken on the pole of the ecliptic, but showing also R.A. hours and 

 parallels of declination. Any place on this projection may be chosen 

 and marked on a superimposed sheet of tracing paper, and then if the 

 tracing paper is turned round upon the pole of the ecliptic as a 

 centre, so that the straight line drawn upon it, which in the first 

 instance joined the two poles marked on the projection, is carried 

 round to an angle equal to the amount of precessional movement 

 under consideration, if there be a suitable star marked on the pro- 

 jection the point selected for trial will pass over it or near it, and 

 after the star has been thus roughly pointed out the more exact 

 calculations may be proceeded with. By this process in the case 

 before us the tracing-paper mark coincided almost exactly with the 

 place of a. Arietis, and for this star the particulars were carefully 

 computed which have been given in the list of elements. 



It should be noticed that there are in every case of intra-solstitial 

 temples four possible solutions of this step. The Sun's amplitude 

 may be due either to the vernal or the autumnal place, and the star 

 might have been heliacal either at its rising or setting. In every 

 instance all these four alternatives have been tried by the pre- 

 liminary search method, and in every case in temples of old founda- 

 tion an heliacal star has resulted from one or other of the trials, but 

 never more than one. 



The star which has been found as above for the Temple of Jupiter 

 is no other than the brightest star of the first sign of the Zodiac, and 

 therefore peculiarly suited to that god. The same star is connected 

 with the early temple of Jupiter Olympius at Athens. 



In intra-solstitial temples, by the nature of the case, the stars are 



