vs. 17-19 ] 51 It can be easily seen from the celestial sphere that, whatever be the position of the Sun, the aikuagra will always lie to the south of the rising setting line A rule for the determination of the tropical longitude of the rising point of the ecliptic at any given time with the help of the time elapsed since sumrise and the corresponding tropical longi 17-19. The residue (i.e., the untraversed portion) of the Sun's (tropical) sign (in minutes of arc) should be multiplied by the time of its rising at the local place and divided by the num ber of minutes in a sign (i.e., 1800): the result should be sub tracted from the given (time elapsed since sumrise, in) 0545 (Then)having added the residue of the (Sun's) sign to (the tropi cal longitude of) the Sun, one should (further) add successively the (subsequent) signs whose times of rising, in 25us, at the local place can be subtracted from the remaining (time in) 0545. That (further) increased by the de8rees and minutes obtained on multiplying the remainder (in 0545) by 30, etc., and dividing by the time of rising at the local place of the (tropical) sign occupied by the rising point of the ecliptic should be declared as the (tropical) longitude of the rising point of the ecliptic. We shall illustrate this rule by an example. Suppose that 14 ghags after sunriseat Lucknow (lat.26°55' E, long. 80°45'B.) the tropicallongitude of the Sun is 3 4°20'. Then to find the longitude of the rising point of the cliptic we shall proceed as follows: The Sun lies in the 4* sign, the untraversed portion of that sign being 25० 10' (=1510'). The time of rising of this sign at Lucknow is 20054 15us (See the table of times of risings of signs at Lucknow on page 46). There fore, we multiply 1510' by 2054 and divide the product by 1800; thus we get 1510x2054 172 05us approx 1800 This is the time of rising of the untraversed portion of the Sun's sign Subtracting this from 14 gats, i.e., 5040 05us, we get 3317 25us. Sub tracting from this the 25us of rising of the 5b sign, i.e., 2085 25u, we get 232 ८45us. The atus of rising of the 62 sign cannot be subtracted from it, so we
