Astronomical Methods of Observation. 43 



The rudest example of the gnomon was an upright pole, 

 placed perpendicularly to the horizontal plane by means of 

 a plumb line, though there are instances of some of them 

 constructed of masonry of considerable heights, but these 

 could not properly be called instruments. The altitudes of 

 the heavenly bodies were from these calculated by com- 

 paring the length of their shadows with their heights. In 

 modern mathematical language, the height of the gnomon 

 divided by the length of its shadow, gives the natural tan- 

 gent of the altitude of the celestial body, such as the sun, 

 whence by means of a table of natural tangents the angular 

 measure of that altitude becomes known in some conven- 

 tional measure, such as degrees. Thus let the height of the 

 gnomon be 5 feet, and the length of its shadow 10 feet, 

 then -^Q or 0*5 being found in a table of natural tangents 

 will give the angle equal to about 26° 30', the altitude of the 

 sun at that time. 



This method was found to be inconvenient, because the 

 length of the shadow was required to be measured each 

 time an observation v/as made. It, therefore, occurred to 

 the ancient astronomers to form an instrument of moderate 

 dimensions on similar principles, like the artizan's square, 

 having the horizontal side divided into equal parts as it 

 was at first, and afterwards into the natural tangents called 

 by the Arabians shadows, to the radius, and by this means 

 the angle of elevation became known in degrees and parts 

 of a degree by inspection, though not to any great ac- 

 curacy. 



This gave place in its turn to the quadrant, divided into 

 degrees and parts of a degree by means of a radius turning 

 round its centre, in which were placed fine pins or sight 

 vanes. It was with such instruments as these that Eratos- 

 thenes and Ptolemy attempted the measurement of the 

 figure and magnitude of the earth, and the determination of 

 the obliquity of the ecliptic. Ptolemy states that the dis- 

 tance between the tropics in his time was found by such an 

 instrument to be ^ of the whole circumference, that is ^ 

 of 360°=47° 42' 40", and the half of this or 23° 51' 20' con- 

 stitutes what is called the obliquity of the ecliptic. 



The accuracy of observations made with the quadrant 

 could not be great till the invention of the telescope and 

 the vernier or reading microscope. The quadrant though 



