338 THE PRINCIPLES OF SCIENCE. 



It is obvious that many of the slower changes of the 

 heavenly bodies must require the lapse of large intervals 

 of time to render their amount perceptible. Hipparchus 

 could not possibly have discovered many of the smaller 

 inequalities of the heavenly motions, because there were 

 no previous observations of sufficient age or exactness to 

 exhibit them. And just as the observations of Hipparchus 

 formed the starting-point for subsequent comparisons, so 

 a large part of the labour of present astronomers is di- 

 rected to recording the present state of the heavens so 

 exactly, that future generations of astronomers may detect 

 many changes, which cannot possibly become known in 

 the present age. 



The principle of repetition was very ingeniously em- 

 ployed in an instrument first proposed by Mayer in 1767, 

 and carried into practice in the Repeating Circle of Borda v . 

 The exact measurement of angles is indispensable, not 

 only in astronomy but also in trigonometrical surveys, and 

 the highest skill in the mechanical execution of the gradu- 

 ated circle and telescope will not prevent terminal errors 

 of considerable amount. If instead of one telescope, the 

 circle be provided with two similar telescopes, these may 

 be alternately directed to two distant points, say the 

 marks in a trigonometrical survey, so that the circle shall 

 be turned through any multiple of the angle subtended 

 by those marks, before the amount of the angular revolu- 

 tion is read off upon the graduated circle. Theoretically 

 speaking, all error arising from imperfect graduation might 

 thus be indefinitely reduced, being divided by the number 

 of repetitions. In practice, however, the advantage of 

 the invention is not found to be great, probably because 

 a certain error is introduced at each observation in the 

 changing or fixing of the telescopes. It is moreover in- 



v Young, ' Works,' vol. ii. p. 546. 



