COMMON THINGS THE ALMANACK. 



54. Another effect of transparent media, and the air among the 

 rest, is to change the apparent direction of objects seen through 

 them. Every one can verify this by looking at distant objects 

 through pieces of glass having curved or angular surfaces. They 

 are never seen in their true directions. 



The effect produced by the air is to make all objects appear at 

 greater altitudes than they really have, or than those at which 

 they would be seen if the air had not been interposed. The effect 

 of this is greater at low than at high altitudes. When an object 

 is very near the horizon, which it is just before it sets or just 

 after it rises, its apparent altitude is greater than its true alti- 

 tude by something more than half a degree : now half a degree 

 is equal to the apparent diameter of the sun or moon. 



If an object, therefore, were in such a position, that without 

 the interposition of the atmosphere it would be seen exactly on 

 the horizon, as when it rises or sets, the atmosphere would cause 

 it to appear at more than half a degree above the horizon. 



In the same manner, if an object were half a degree below the 

 horizon, and therefore having already set or not yet risen, and 

 being consequently invisible, it would by the effect of the 

 atmosphere be seen above the horizon, and would therefore be 

 visible. 



It is evident, therefore, that the atmosphere makes all objects 

 appear to rise sooner and to set later than they would rise or set if 

 the atmosphere were absent; and consequently, in calculating 

 the rising and setting of the sun and moon, this must be taken 

 into account. 



55. It may be asked whether it be really true, as would appear 

 from what has been just explained, that the air enables us to see 

 the sun before it has risen, and after it has set ? There can be no 

 doubt that such is the case, and that at the moment indicated in 

 the almanack, as that of sunrise or sunset, the sun is really below 

 the horizon and not upon it. These circumstances, which are not 

 only interesting in themselves, but affect in a very considerable 

 degree the calculations of the almanack, will be rendered more 

 easily intelligible by reference to figs. 1 and 2. 



The horizon is represented by the line H o, the dark part being 

 below, and the shaded part above it. The moment of sunset or 

 sunrise is, properly speaking, that at which the centre of the 

 sun's disc is seen upon the horizon H o, and, when consequently, 

 the horizon would pass across the middle of the disc, one half of 

 which would be above it, and therefore visible, and the other 

 half below it, and therefore invisible, as shown at s, fig. 1. 



The moment at which the centre of the sun would be seen at 

 , fig. 1, in the absence of the atmosphere, is called the moment 

 2S 



