THE 



POPULAR SCIENCE 

 MONTHLY. 



FEBRUARY, 1875. 



THE PEKSONAL EQUATION. 



By Pbof. EDWAKD S. HOLDEN, 



OF THE UNITED STATES NAVAL OBSERVATORY, WASHINGTON, D. C. 



IN an attempt to explain clearly some of the phenomena which 

 have led to the consideration of what astronomers call the "per- 

 sonal equation," it will, perhaps, he most advantageous to consider 

 the suhject somewhat in an historical manner. In this way we shall, 

 it is true, lose something in directness, hut it will assist in gaining a 

 definite conception of the whole suhject if we consider it in the order 

 in which astronomers have heen forced to do. 



To make the meaning of the term plain, it will be necessary to 

 premise a brief account of the methods of observation with astronomi- 

 cal instruments, and of some of the refinements which have gradually 

 been found necessary in these methods. 



Nearly every astronomical observation has for an object to fix the 

 relative position of two bodies at a given time. If, then, a second 

 observation of a similar kind is made, these two, taken together, will 

 suffice to give some idea of the apparent relative motion of one body, 

 referred to the other. If, for example, the design is to determine the 

 orbit of a new comet, the mode of proceeding is, or might be, some- 

 thing as follows : Some star, whose place is known (or whose place is 

 subsequently determined), is chosen in the vicinity of the comet, and 

 the distance of the comet from this star is measured. This may be 

 done in several ways, by a sextant, with which we can measure this 

 distance directly, or, more usually, by one of the fixed instruments of 

 an observatory, with which we can determine two things: 1. The 

 distance of the comet east or west of the star; and, 2. Its distance 

 north or south of it. The distance north or south is usually deter- 

 mined by a direct measure of the celestial arc included between the 

 respective parallels on which the star and comet are at a given time ; 

 while the distance east or west is usually measured by the interval 

 of time required for the earth's rotation to carry a body from the 

 vol. vi. 25 



