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XI. On the true Measure of a Ltmar Cycte^ as compared 

 tu'ith the Lunar Tables in the Nautical Almanacki By Mrt 

 Thomas Yeates. 



To Mr. TillocL 



Sir, — X n e true quantity of a mean lunation is obtained by 

 taking the piecise number of days^ hoars, &c. between two di- 

 stant solar or lunar eclipses, or the known times of new or full 

 moons, and dividing the elapsed period by the number of luna- 

 tions from the one to the other. Bv this means, whatever errors 

 may be committed hv stating the times of the mean conjunctions 

 or oppositions, those errors will become divided among so many 

 lunations, as will, render insensible the error of one or any small 

 number of lunations atfected thereby, so that the greater the 

 distance of time and number of lunations, the precise quantity of 

 one mean lunation is the more safely ascertained. 



But this measure of time between any two distant eclipses, 

 conjunctions, or oppositions of the sun and moon must be limited 

 within reasonable and well defined bounds, or the calculation 

 will be subject to fatal mistake. The space of one hundred years 

 seems preferable to any smaller number, and is certainly prefe- 

 rable to that of a thousand years. It is on this principle, and on 

 the indubitable method of computing by the weekly cycle, that 

 I have attempted to ascertain the mean quantity of a lunation 

 from an indisputable epoch, one hundred years distant from its 

 corresponding new moon, a quantity I have stated at 29 days, 

 'J'J min. 38 sec. 51 thirds, which is the solar measure as com- 

 puted by the Julian reckoning imequated. 



A lunar cycle of 19 years, containing 2.j5 lunations, compared 

 with the aforesaid quantity, brings the sun and moon within one 

 hour of Julian time. D. H. M. S. T. Days. II. M. S. 

 235 Lunations at 29 12 4-J 38 51 = 6939 18 52 10 ' 

 19 Julian years =6939 18 



Diff. ~52~Y() 



The difference of 52 minutes, 10 seconds, by which the moon's 

 motion is slower than the sun in this period, if multiplied into 

 100 Julian years, will scarcely amount to five hours, which may 

 he attributed to the known variation of the moon in every luna- 

 tion. 



Having fairly stated these simple principles, and showed my 

 reason for correcting the above quantity, viz. by subtracting the 

 excess, 52' 10", D. H. M. S. T. F. 



Common measure 29 12 44 38 51 00 



Julian measure 29 12 44 25 31 51 



VoJ. 56". No. 2t)8. y^7<i'. 1820. L I i'«o- 



