28 ELEMENTS OF LABORATORY WORK 



A telescope with a vertical cross-wire is mounted so that 

 it swings in the plane of the meridian. The first apparent 

 contact of the sun with the cross-wire is compared with the 

 chronometer, and the contact again noted the next day. This 

 observation gives the length of a solar day. These, however, 

 vary throughout the year. The year is the period in which the 

 earth completes its orbit round the sun. The mean length of 

 all the days throughout the year is found, and it is called the 

 mean solar day. Time-keepers are constructed so that the 

 seconds, marked by them, are -g-^ J^ of this calculated mean solar 

 day. This second is the unit in all physical measurements. 



The interval between successive transits of the same fixed 

 star is called a sidereal day. A star being practically at an 

 infinite distance, a sidereal day is the accurate period of the 

 earth's rotation. The sidereal day is slightly longer than the 

 mean solar day. 



25. The Resultant of Two Simultaneous Displacements. 

 It is clear that a given displacement may have resulted from a 

 movement along any number and any variety of paths. Ob- 

 servations alone can decide the manner in. which the displace- 

 ment proceeded. A particle may move in a straight line A B, 

 or it may have taken any other path, such as A c, c B (fig. &). 



If the particle reach the 

 position B at the same 

 time by either path, a 

 certain relation must hold 

 between the speed along 

 Fig 8 AB and the speeds along 



the paths AC, c B. The 



numerical value of the one must be the equivalent of the other 

 two speeds, since the same result is obtained in each case, 

 although the equivalence may not be very clear. If the cause, 

 whatever it may be, which produces the displacement along 

 A c co-exists with the cause which would, if it acted upon the 

 body when it is in the position c, produce the displacement 

 along c B, it will be perceived that the displacement will take 

 place along the path A B, but only in those cases where the 

 directions and amounts of displacement during a given time 



