56 
Proceedings of the Royal Society 
Angstrom writes this in the form — 
dv 
dt 
assuming the conductivity to be unaffected by temperature, so that 
it is necessary that the range of temperature in his experiments 
be small. As the method consists essentially in so applying the 
heat as to bring the bar to a periodic state of temperature at each 
point, the solution must be of the form — 
v=Y + cos (» ^ - q „ x + pj , 
where T is the period, and V is the mean temperature or non- 
periodic part of the solution. Substituting in the equation, we 
have — 
d 2 Y 
0 = Kjf-RV, 
~ (ji — — ) 
0 = K(rf- 2 2)-H. 
The second of these is equivalent to Angstrom’s exceedingly simple 
expression for K in terms of the experimental data. Angstrom, 
however, goes farther than this, for instead of the formula for v 
just given, he uses a more restricted one, which assigns very simple 
forms for the quantities jp w , q n , viz., — 
Vn^gjn, q n = g'Jnf 
where g and g f are absolute constants, depending on K, H, T alone. 
If this were admissible, it seems that we should have not only, 
with Angstrom, 
but also the impossible relation, 
0 = Kn (g 2 - g' 2 ) - H , 
* There are several serious misprints, both in the original {Pogg. 1862) and in 
the English translation (Phil. Mag. 1863, I.) In fact, in the expression for v, 
V x appears instead of x , alike in the exponential and in the argument of the 
cosine. 
