294 Mr DAVIES on the Equations of Loci 



That is, let L be a point whose co-ordinates are to be changed from 

 origin P and prime meridian PO, to another origin N in that meridian, and 

 prime meridian NP. 





HereNP = a; PL =0; 



Then, 



cos (p = cos <p' cos a + sin <p' sin a cos & ........................... (!) 



sin <p sin Q = sin <p' sin & ................................................. (2.) 



which conditions will enable us to express (f>, 6 as functions of <', &. 

 From (1.) we find 



sin (f> = >Jl (cos <p' cos a + sin <p' sin a cos &)* ........ (3.) 



And from (2.) and (3.) we get readily 



sin (j)' sin & 

 sln ^- ~ VI (cos <' cos a -f. sin <' sin a cos P) 1 ....... "... 



a cos </>' sin a sin 0' sin a sin ^ / K ^. 



cos v -) ' < - ......... t>- 



~ 



*J\ (cos (f)' cos a + sin (j)' sin a cos cf) 2 



Which values of sin 0, cos 0, sin 6, and cos 6, will transform any curve re- 

 ferred to P and PO into one referred to N and NP. 



3. When we wish to transform the origin from P to any point in the 

 equator, as E, we have only to refer the locus to the meridian PE and ori- 

 gin P; and the formulae (1, 3, 4, 5) become in reference to this, 



