8 PHILOSOPHICAL TRANSACTIONS. [aNNO ] 694-5. 



SO that we may conclude the moment of the tropic to have been June lod. 

 17h. 20m. in the meridian of Marseilles. 



Now that these two tropical times thus obtained, will be found to confirm 

 each other's exactness from their near agreement, appears by the interval of 

 time between them, viz. id. 2h. 30m. less than 136 Julian years; of which 

 id. ih. Sm. arises from the defect of the length of the tropical year from the 

 Julian, and the rest from the progression of the sun's apogeeon in that time ; so 

 that no two observations made by the same observer in the same place, can 

 better answer each other, and that without any the least artifice or force in the 

 management of them. 



What were the methods used by the ancients to conclude the hour of the 

 tropics, Ptoleuiy has no where delivered ; but it were to have been wished that 

 they had been aware of this, that we might have been more certain of the mo- 

 ments of the tropics we have received from them, which would have been of 

 singular use to determine the question, whether the sun's apogaeon be fixed in 

 the starry heaven ; or if it move, what is its true motion ? It is certain, that if 

 we take the account of Ptolemy, the tropic said to be observed by Euctemon 

 and Meton, Junii 27 mane, Ann. 432 ante Christum, can nowise be recon- 

 ciled, without supposing the observation made the next day, or June 28 in the 

 morning. And Ptolemy's own tropic observed in the third year of Antoninus, 

 Anno Christi 140, was certainly on the 23d, and not the 24th day of June ; as 

 will appear to those that shall duly consider and compare them with the length 

 of the year deduced from the diligent and concordant observations of those two 

 great astronomers, Hipparchus and Albatani ; established and confirmed by the 

 concurrence of all the modern accuracy. For these observations give the length 

 of the tropical year such, as to anticipate the Julian account only one day in 300 

 vears ; but we are now certain that the said period of the sun's revolution anti- 

 cipates very nearly 3 days in 400 years ; so that the tables of Ptolemy founded 

 on that supposition, err about a whole day in the sun's place, for every 240 

 years. Which principal error in so fundamental a point, vitiates the whole 

 superstructure of the Almagest, and serves to convict its author of want of dili- 

 gence, or fidelity, or both. 



But to return to our method : the great advantage we have hereby, is, that 

 any very high building serves for an instrument, or the top of any high tower 

 or steeple, or even any high wall that may be sufficient to intercept the sun, 

 and cast a true shade : nor is the position of the plane on which you take the 

 shade, or that of the line therein, on which you measure the recess of tiie sun 

 from the tropic, very mriterial ; but in what way soever you discover it, the 

 said recess will be always in the same proportion, by reason of the smallness of 



