92 PHILOSOPHICAL SOCIETY OF WASHINGTON. 
mean value of the latitude and its weight in the most general case 
of entanglemept in terms of the results from individual pairs of 
stars and their symbolical weights. To find the numerical values 
of these symbolical weights he made use of the principle that 
the weights of the individual results must be such as to make the 
probable error of the weighted mean a minimum. After treating 
the most general case he considered some of the special.cases occur- 
ring most commonly, and deduced practical formulas for computing 
the weights of individual results. In illustration of his methods he 
gave the details of the numerical operations in one of the more com- 
plex cases presented in actual work. 
In the discussion which followed, Mr. HArKNeEss derived, by a 
different and less complex process, some of the formulas given by 
Mr. Fuint. Others participating in the discussion were Messrs. 
Pau, FArRquHAR, STONE, and WoopWARD. 
Mr. E. B. Ex.iorr began the presentation of a paper on 
THE MUTUAL ACTION OF ELEMENTS OF ELECTRIC CURRENTS. 
30TH MEETING. May 11, 1887. 
The Chairman presided. 
Present, ten members and two guests. 
Mr. E. B. Exxiorr continued his paper on 
THE MUTUAL ACTION OF ELEMENTS OF ELECTRIC CURRENTS. 
He stated that Ampére’s theory of such currents involves the 
assumption that the action between the elements is limited in direc- 
tion to the line joining them. In conformity with this assumption 
the result reached by Ampére, and now usually given in text 
books, is that the action is proportional to 
4 cos 0 cos 6 — sin @ sin & cos a, 
in which 6 and @’ are respectively the angles between the directions 
of the elements and the line joining them, and » is the angle be- 
tween the two planes defined by the directions of the elements and 
the line joining them. 
