70 .Mr. H. Hilton on the Grajilikal 



Proceed exactly as in (1), marking in the positions of the 

 stars, and then making OU coincide with OC. Now diminish 

 the longitude of all the stars by x x 50*2^^ by moving all the 

 stars along the lines / through this amount. This is readily 

 done with the help of the net : it is best to mark the new 

 positions of the stars on another piece of tracing-cloth laid 

 over the first (the net is readily seen through two pieces of 

 good cloth), and then remove this first sheet, after tracing- 

 through the line OR onto the new piece of cloth. Now 

 turn back the line OR into its original position. Find a point 

 Z such that the angle between the circles AZB and ACB 

 is 70*^, and the arc ZA represents the colatitude ; then Z is 

 the position of a star at the zenith at the given time. Mark 

 on the cloth a star X at the pole A, and turn the diagram till 

 Z lies on the line OC of the net. Move all the stars along 

 the lines / through the number of degrees represented by ZO 

 (preferably on a new sheet of tracing-cloth as before). Let 

 the star X be brought into the position Y by this process. 

 Then the diagram now obtained is the one required, Y being 

 the position of the celestial pole. 



(6) What is the interval between the times of rising of a 

 given star as observed by two men, one at the top of a 

 mountain and the other on a plane at its base ? (The 

 effects of refraction and the ellipticit}^ of the earth are 

 disregarded.) 



On the tracing-cloth trace through the point R coinciding 

 with xl, the line COD, and that one of the lines I which is 



distant 90°H-cos~^ from A (or R), a being the radius of 



the earth and r the height of the mountain. Turn the dia- 

 gram till the angle ROA is equal to the north polar distance 

 of the star. Let that one of the lines I whose distance from 

 A is equal to the colatitude of the mountain cut the two lines 

 on the tracing-cloth in X and Y ; convert the angle between 

 the circles AXB and AYB into time. 



For instance, the interval for a mountain on the earth 

 12,750 feet high in latitude 66° N. is found to be 28 minutes, 

 and for a mountain in latitude 56° N. to be 18 minutes, the 

 star's declination being 20° S. For a mountain on the moon 

 23,000 feet high in latitude 80° N. the interval is 95^ lunar 

 minutes and for a mountain in latitude 70° N. is 46^ lunar 

 minutes, the star's declination being 1° 25' N. These results 

 are not very accurate, but greater exactness could readily 

 be obtained by the use of a larger and more finely divided 

 net. 



