THE METHOD OF MEANS. 425 



the simplest possible case in the determination of the 

 latitude of a place by observations of the Pole-star. 

 Tycho Brahe suggested that if the elevation of any cir- 

 cumpolar star were observed at its higher and lower 

 passages across the meridian, half the sum of the elevations 

 would be the latitude of the place, which is equal to the 

 height of the pole. Such a star is as much above the 

 pole at its highest point, as it is below at its lowest, so 

 that the mean must necessarily give the height of the 

 pole itself free from doubt, except as regards incidental 

 errors of observation. The Pole-star is usually selected 

 for the purpose of such observations because it describes 

 the smallest circle, and is thus on the whole least affected 

 by atmospheric refraction. 



Whenever several causes are in action, each of which 

 at one time increases and at another time decreases the 

 joint effect by equal quantities, we may apply this method 

 and disentangle the effects. Thus the solar and lunar 

 tides roll on in almost complete independence of each 

 other. When the moon is new or full the solar tide coin- 

 cides, or nearly so, with that caused by the moon, and the 

 joint effect is the sum of the separate effects. When the 

 moon is in quadrature, or half full, the two tides are 

 acting in opposition, one raising and the other depressing 

 the water, so that we observe only the difference of the 

 effects. We have in fact 



Spring tide = lunar tide + solar tide 

 Neap tide = lunar tide solar tide. 

 We have only then to add together the heights of the 

 maximum spring tide and the minimum neap tide, and 

 half the sum is the true height of the lunar tide. Half 

 the difference of the spring and neap tides on the other 

 hand gives the solar tide. 



Effects of very small amount may with great approach 

 to certainty be detected among much greater fluctuations, 



