194 PROCEEDINGS OF THE AMERICAN ACADEMY 



XIV. 



SUPPLEMENTARY NOTE ON THE THEORY OF THE 

 HORIZONTAL PHOTOHELIOGRAPH. 



Bt Professor William Harkness, U. S. Navt. 

 Presented Doc. 12, 1877. 



Referring to equation (14),* we remark that, if the photographs of 

 the sun are centred upon the measuring engine with moderate care, it 

 will seldom happen that either di/ or 8x amounts to so much as 3", 

 while A will usually exceed 900". It is therefore evident that all 

 three of these quantities cannot be accurately derived from conditional 

 equations of the sumo form as (14), without using logarithms having 

 at least six places of decimals. As the value of A is not required, we 

 eliminate it in the following manner : In equation (14) put 



(58) 



sin (e ^ ^) = a 

 n cos (s ^ 6) = b 



Then the resulting normal equations will be 



= [an] -\- [_aa'] 8y -\- [ai] dx ") 

 = [5»] -f [aJ] d>/ + [i6] dx ) 



If m is the number of equidistant points at which E is measured, the 

 expressions for the required auxiliaries are 



* Proceeding of the American Academy of Arts and Sciences, Vol. XII. 

 (1876-77), p. 194. 



