72 THE BOOK OF NATURE STUDY 



little consideration will show, is that the tangent of the sun's altitude is equal 

 to the height of the stick divided by its shadow. 



-ru stick 



Therefore, as tan angle a 



shadow 



shadow 



stick 

 tan angle a 



The sun's altitude (i.e. angle a) at the equinoxes may be simply calculated. If 

 / be the latitude of the school, then at the winter solstice the sun is distant from 

 the zenith by / + 23^, while at the summer solstice it is distant from the zenith 

 by /-23J. If the result in either case be subtracted from 90 we have the 

 sun's height above the horizon, or altitude. 



For example, taking the latitude of Edinburgh as roughly 56 N., we find that at 

 the winter solstice the sun's altitude is 10 J (56 + 234 = 794 ; 90 - 79i = 10 J) . 

 The tangent of ioj (roughly 0*1853) is easily obtained from a table of logarithms, 

 and if the height of the stick be divided by this tangent the result gives the length 

 of the shadow. By similar reasoning it will be found that the altitude of the sun 

 at the summer solstice at Edinburgh is 57!, and by taking the tangent of this 

 angle (roughly 1*569) and dividing the length of the stick by it, we can obtain 

 the minimum length of shadow, as the former calculation gives us the maximum 

 length. It is prudent to make a rough calculation of this kind, in order to be 

 quite certain that the place chosen gives space enough for the full demonstration 

 of the seasonal variations in lengths of shadows. 



It would seem well in the first instance to rest content with 

 shadow and sunlight observations taken from time to time, and 

 regarded merely as curious facts. If the path of the pin's shadow 

 on a piece of paper, for instance, or on the window-sill, be carefully 

 marked, dated, and preserved, it will be natural to refer to these 

 old records when new ones are made. Comparisons would then 

 crop up quite naturally, and without excessive effort, and without 

 having recourse to globes or any pieces of apparatus, we could 

 make at least the following deductions : Every sunny day we 

 see the sun low in the early morning, and then its rays are not 

 very strong, and it casts long shadows ; in the middle of the day 

 its rays are strongest, and the shadows are shortest. Comparing 

 summer days with winter days we find that the shadows in the 

 middle of the day are shorter in summer than in winter, and by 

 marking the places which the sun reaches in winter and in summer 

 we may show that it is higher up in the sky in summer than in 



