324 LENZ ON THE CONDUCTIBILITY OF WIRES FOR ELECTRICITY. 
Supposing therefore that the conductibility is in a direct, and the con- 
ducting resistance in an inverse ratio to the thickness of the wires, and 
that a, a', a! represent the angles of deviation, we have the following 
equations : 
Ab se 
eon 
A = prsin (a) 
‘a 
1 
* + 7787 
a. 
2 + 
= p' sin ($ a’) 
; = p'sin(Z a") 
5,025 
&e. 
Dividing the first equation by all the following seven, and putting 
for brevity sake 
ae anal ' al pte " 
sin (4 a') = a’, &c. and a737 = BS 5005 = a", &e., 
we obtain the following equations : 
ax—y =0 
ax—yt+s =0 
a'x—y+o6' =0 
a"e—y+o"=0, 
&e. 
From these equations were determined, according to the method of 
the least squares, the values 
a = 040679 y = 029146. 
and finally the values a, a’, a’, by substituting the foregoing values in 
the equations, and developing a, a’, a”....or sin } a, sin $a’, sin $ a”, 
&c. These values are placed in the above table under the head “ Cal- 
culated Deviations.” The differences between these and the observed 
angles of deviation, contained in the last column, are greater than 
those of the preceding observations, and even greater than can be as- 
cribed to mere errors of observation ; but the reasons of this have been 
.already explained. Their agreement, however, is in every case great 
enough to remove every doubt with respect to the correctness of the 
hypothesis (which is the basis of the calculation), that the conductibility 
of wires is in a direct ratio to their sections. 
