VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 5Q 



Second biennial period, 1777, April 17 d 7 h 50 m s to 1779, J »ne 15 d g h 45 m 

 17 s = 78g d l h 55 m 17 s . The geocentric places 6 s 3 d si' 27" and 7 s 12 d 40' '23' ', 

 the diff. Is Q d 8' 56", turned into time 789 d l h 55 m 17 s , and subtracting 

 2 h 40 m 52 s , leaves 788 d 23 h 14 m 25 s = 768 revol. hence 1 revol. = 24 h 39™ 18 s .94. 



Third biennial period, 1777, April 26 d 9 h 5 m O s to 1779, June 19 d 8 h 40 m 22 s = 

 783 d 23 h 35 m 22'. The geocentric places 6 s 1° 24' 36" and 7 s 12° 31' 48", the 

 diff. I s 11° 7' 12" turned into time gives 783 d 23 h 35 m 22 s , and subtracted 

 2 h 45 m 1 5 s .61eaves 783 d 20 h 50 ra 6 3 .4 = 763 revol. hence 1 revol. = 24 h 39 m 23 5 .04. 



As these 3 periods are supported by observations of equal validity, Mr. H. 

 takes a mean of them all for the nearest approximation to the true sydereal re- 

 volution of Mars on his axis, which therefore is 24 h 39 m 21 '.67. 



It remains now only to see how far we may depend on this determination of 

 Mars's diurnal rotation as coming near the truth ; and looking over those causes 

 which may possibly produce any errors, we find, first of all, that in the long 

 biennial periods a mistake in the number of revolutions would produce a con- 

 siderable deviation from truth. Secondly, in the observations of a spot which 

 moves so slow, we are also liable to some considerable mistake in estimating the 

 time when it comes to a certain place ; and the more so, if that place is not the 

 centre. Lastly, the time itself is liable to inaccuracy. 



As to the 1st, it appears from the 3 monthly periods observed in the year 

 1779, when the proper allowances for the geocentric places are made, that the 

 sydereal revolution of Mars cannot well be less than 24 h 39 m 5 s , nor more than 

 24 h 39™ 22 s ; but if we should divide any one of the 3 biennial periods by a sup- 

 posed number of revolutions, only one more or one less than we have done, the 

 difference would be so considerable, that nothing but a mistake in every one of 

 the 3 monthly periods, of at least one whole hour, could justify such a suppo- 

 sition ; and that such a mistake in the situation of a spot on Mars cannot have 

 been made in those observations, is evident enough from the exactness with 

 which they were made, and from their agreement with each other. 



The 2d cause of error, which is the uncertainty in assigning the exact time 

 when a spot comes to the centre, is of some force/ But it seems highly proba- 

 ble, from the manner in which the spots on Mars pass over the disc of that 

 planet, that there can hardly be so great an error as 10 m in an observation of 

 any remarkable spot's coming to the centre. However, not being willing to 

 trust more to the eye than ought to be done, Mr. H. had recourse to the fol- 

 lowing experiment. He drew several circles of 1 inch radius, taking care to 

 make no visible impression of a centre ; and placed in each a fine point at the 

 several distances of .0424, .0636, .0848, in ten thousands of an inch from the 

 real centre ; some to the right, others to the left. These measures are the sines 

 to radius l, of 2° 26', 3° 39', and 4° 52'; which are the arches a spot on 



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