^73-] Th e Planet Mars in 1873. 203 



consideration, it is not important in determining the aspect of 

 the planet at any hour on any day intermediate to those 

 corresponding to the projections of the plate. For we see 

 from the figure that the lines E I M I , E 2 M 2 , &c, are in every 

 case inclined at a small angle to their next neighbour lines. 

 Moreover, by determining the aspect of Mars, from the 

 nearest of the projections in point of time, we are sure of 

 not having more than half even of this difference. Also, by 

 means of a protractor, the angular change of the line of 

 sight can be determined from the figure, and taken duly into 

 account. 



It is convenient to notice that at any given hour on any 

 night the planet presents appreciably the same aspect as on 

 the preceding night, 37m. 22f s. earlier. 



So far as the shapes of the parallels on the different pro- 

 jections are concerned, it is manifest that the change is too 

 slight, from projection to projection, to introduce any diffi- 

 culty. Nor will any draughtsman find any trouble in 

 reducing or enlarging the scale to the proper dimensions, 

 should he think this necessary. I believe that further 

 explanation of these points is unnecessary, but to prevent 

 any difficulty which may arise I will take an example : — Let 

 us suppose the observer desires to know the aspect of the 

 planet at 1 o'clock on the morning of May 1st (that is, in 

 astronomical time, at 13I1. on April 30th). In this case 

 three days and one hour have elapsed after 12I1. April 27th, 

 the epoch of projection 5. Now three Martial days are 

 equal to three of our days and ih. 52m. 8Js. So that Mars 

 at 1 on May 1st will be rotated as much forward, compared 

 with the aspect observed in projection 5, as corresponds to 

 52m. 8Js. ; but from meridian to meridian in the projections 

 corresponds to an interval of 2I1. 3m. 7s. So that each 

 meridian in projection 5 must be shifted forwards by a less 

 distance than that separating it from the next meridian, in 

 the proportion that 52m. 8Js. is less than 2h. 3m. 7s., or 

 that 31283: is less than 7387. This proportion may be taken 

 as the same as 3 to 7. So that, if we trace the parallels 

 and circular outline of disc from projection 5, and shift each 

 meridian (this also can be done in tracing, — that is, there is 

 no occasion to pencil the meridians as they actually are) 

 forwards by three-sevenths of the space separating it from 

 the next to the left, we have the required meridians and 

 parallels. The features can then be drawn in from projec- 

 tion 5, being carried forward by the same amount as the 

 meridians. In most cases the application of this method 

 requires the features to be completed from one of the other 



