294 PROCEEDINGS OF SECTION A. 



These hyperbola;, or time curves, may, however, be described in 

 another and more convenient way by means of a ruler, thread, and 

 pencil, which is, in fact, the usual method of describing a hyperbola. 

 One end of the thread must be fixed in the focus of the hyperbola 

 to be cbawn, and one end of the ruler pivoted in the opposite focus ; 

 the free end of the thread is made fast to the free end of the ruler. 

 The radius line, that is, the line between the centre of the diagram 

 and the focus of the hyperbola, being laid out in a scale of sines, 

 the length of the thread must be such that the pencil will just be 

 able to touch the sine of the hour for which the hyperbola is to be 

 described. If the ruler be then swung round its pivoted end, the 

 pencil kept close to its edge and the thread extended, the curve 

 described will be a hyperbola, and the point at which it intersects 

 each ellipse of latitude will indicate the position of the sun on that 

 ellijjse at the time for which the curve is drawn. 



For convenience in measuring off the azimuth I have put a 

 graduated horizon round the marghi of the diagram, but any other 

 mechanical means may be substituted. 



This completes the diagram as published ; and, before compli- 

 cating it any further, I will explain how it is used for compiiting a 

 time azimuth by reading the description and instructions printed 

 thereon, which description and instructions, I may mention, were 

 written by Sir W. Thomson (now Lord Kelvin), who has taken 

 great interest in the diagram : — " To find the true bearing of a 

 celestial object, the latitude, declination, and time from crossing 

 the meridian (hour angle) being given — 



" Rule. — Change the signs of both latitude and declination ; then 

 from the latitude (on the meridian) follow the ellipse to its point of 

 intersection with the hyperbola of the required hour angle, and 

 mark it ; this may be called the position of the object. (If the 

 hour angle is less than six hours, this intersection Avill be on the 

 same side of the equator as the latitude as used on the diagram ; 

 if more than six hours, it will be on the opposite side, as the amount 

 over six hours must be measured beyond the equator to obtain the 

 position of the required hour-angle hyperbola). Mark the declina- 

 tion on the meridian; this may be called the position of the observer. 

 With the parallel ruler transfer the line joining these positions to 

 the centre © of the meridian ; the point where the edge of the 

 parallel ruler cuts the graduated horizon is the true bearing, to be 

 reckoned north or south, according as the place where the horizon 

 is cut is north or south of the equator, and east or west, according 

 as the heavenly body is east or west of the meridian." 



Although the principal purpose for which the diagram is in- 

 tended is the computation of a time azimuth, it may be used to 

 solve a variety of other problems, a few of which I now propose to 

 bring under your notice. 



Having given the latitude, declination, and hour angle, the true 

 azimuth may be found as I have been endeavoring to explain, but 



