T R I 



tions whilst the planet performs y revolutions; then will Pjrrrpy, 

 .'. = . Now P = 565,256 and for Mercury, p = 87,968, 



therefore, = ^ = z^r; a = (by resolving it into its continued frac- 

 y f 000,^00 



tlons) T* ^ 3? 51* W 1ST- &c ' That is ' *' 7 ' 13 ' ^ 46 ' &c ' re * 



volutions of the earth are nearly equal to 4, 25, 29, 54, 1S7, 191, &c. revo- 

 lutions of Mercury, approaching nearer to a state of equality, the fur. 

 ther you go. The first period, or that of one year, is not sufficiently 

 exact j the period of six years will sometimes bring- on a return of the 

 transit at the same node ; that of seven years more frequently j that of 

 13 years still more frequently, and so on. Now there was a transit of 

 Mercury at its descending node, in May, 1786 j hence by continually 

 adding 1 6, 7, 13, 33, 46, &c. to it, you get all the years when the transit 

 may be expected to happen at that node. In 1789 there was a transit at 

 the ascending node, and therefore by adding the same numbers to that 

 year you will get the years in which the transits may be expected to 

 happen at that node. The next transits at the descending node will 

 happen in 1799, 183?, 1845, 1878, 1891 ; and at the ascending node, in 1802, 

 1815, 1322, 1835, 1848, 1861, 1868, 1881, 1894. For Venus, p = 224,7 ; 



x p 224,7 8 235 713 



hence - = = ^^ = ^ ^, ^ ft* Therefore the periods 



are 8, 235, 713, &c. years. The transits at the same node will therefore 

 sometimes return at 8 years, but oftener in 235, and still oftener in 713, 

 &c. Now in 1769 a transit happened at the descending node in June, 

 and the next transits at the same node will be in 2004, 2012, 2247, 225i>. 

 2490, 2498, 2733, 2741, and 298k In 1639 a transit happened at the ascend, 

 ing node in November, and the next transits at the same node will be in, 

 1874, 1882, 2117, 2125, 2360, 2368, 2603, 2611, 2846, and 2851 These tran- 

 sits are found to happen, by continually adding the periods, and finding 

 the years when they may be expected, and then computing, for each 

 time, the shortest geocentric distance of Venus from the sun's centre at 

 the time of conjunction ; and if it be less than the semidiameter of the 

 an, there will be a transit. 



TRANSIT of a star and planet over the Meridian. Sec Time. 

 TRANSIT instrument, to bring it into the Meridian. See Tdetoop* 

 TRAPEZIUM, area of.See Surveying. 



TRIANGLE, plant and tpherioal area of.See Surveying and Trifo* 

 nometry. 



