Olbers's Essay on Comets. 147 



alone are scarcely ever sufficient for the purpose. In this case 

 it is much easier to compute the proper times immediately from 

 B and D. This may be done very conveniently by the formulas 

 Log s'— Log B + i log B + 1.4378117 and Log s"=Log D 

 + 1 log D + 1.4378117, the time T, in which the space in 

 question is described, being expressed by s — s", in days. If, 

 for instance, we take r, as in the last article, =1,01262, r"'= 

 1.19773, and A"=:. 18546, the computation will stand thus 

 r'= 1.01262 

 + r'"= 1.19773 



= 2.21035 



Half 1.10517 

 Ih!' .09273 



B= 1.19790 



Dz= 1.01244 



LogB .078421 Log D .005369 



|LogB .039211 JLogD .002685 



Const Log 1.437812 Const Log 1.437812 



Logs' 1.555444 Logs" 1 .445866 



s 35.9290 s" 27.9169 



Hence s' — s"=T=8.0121 days. If we require the time to 

 seconds, we must take out the fifth place of decimals, for 1"= 

 .0000116, and .0001 day is 8".64. 



§ 51. 

 In calculations of any length, it is always an advantage to 

 have some check by which we may from time to time examine 

 their accuracy. In the present instance we have several such 

 expedients. At the end of the calculation it will be also of 

 advantage to compute % again from the elements which have 

 been determined, and thence to find the geocentric longitude 

 and latitude for the time of the middle observation : the one of 

 these steps checks the calculation, at least the latter part of it, 

 the other serves as a test of the accuracy of the elements of 

 the orbit. I find, for instance, from the elements of the comet 

 of 1769 determined in §§ 47, 48, for the 8 September 14h, the 

 true anomaly 138°.19'.55", and the logarithm of the distance 

 from the sun 9.969155, whence the geocentric longitude is 

 3«.10°.5'.57", the latitude 22°.5'.52" S. The error of longitude 

 L 2 



