66 PRACTICAL EXERCISES IX CEOGRAI'HY 



unit of time which civilized nations divide into 24 liours. It is im- 

 portant to notice tliat the sun's return to its original position has not 

 Ijeen accomi>lished b}' going backward, but by continuous motion as 

 if in a circuit. The idea of rotation is thus clearly presented in spite 

 of the fact that much of the sun's diurnal ])ath is out of sight. It 

 should not be understood that these observations give school children 

 their first knowledge of the movement of the sun in the sky ; that 

 tliey have long known. But the vagueness of ordinary' knowledge 

 on this |)oint is now advanced to well defined knowledge, and this is 

 an imi)ortant ste}). 



Regularity in the movement of rotation is easily shown by making 

 observations at regular intervals of one or two hours and noting that 

 equal angles are moved over by the pointer, or tliat equal arcs are 

 measured between tlie stake tops in equal time intervals. It is, I 

 believe, well understood by teachers today that no preparatory study 

 of formal geometry is needed as a basis for inspectional geometry of 

 this kind. A little more advanced treatment is given by making 

 observations at irregular periods, noting the time intervals between 

 them, and pnjving by a continued ]>ro[)ortion that angles and times 

 bear a constant ratio. The angle of complete rotation (;^60°) will be 

 found to bear the same ratio to the time of a complete rotation (24 

 hours)as that which obtains between partial angles and times ; hence 

 the movement of the sun while it is beneath the horizon must be at the 

 same angular velocity as while it is within reach of observation alcove 

 the horizon. Day-time observations of the old moon (about third 

 quarter) and evening observations of stars at home may be used to 

 extend the results gained from the observations of the sun. If the 

 moon is studied, the teacher should be prepared to explain the 

 questions that may rise if the difference in length of solar and lunar 

 days is detected. The chief point to be determined by star observa- 

 tion is that a star must make a circuit of the sky in about 24 hours, 

 because on the second evening it comes from the eastward to the 

 position from which it departed with a westward motion the night 

 before — an elementary matter truly, but one which is less clearly 

 known to many civilized adults than it was to their barbarous an- 

 cestors. 



Axis and Meridians. — ks a result of these observations it is recog- 

 nized that "something" must turn. Whether it is the earth or the 

 sky that turns need not be decided at once, if the teacher has the 

 patience to let this archaic i)roblem really take possession of the 



