504. Mr. J. W. L. Glaisher on the Complete 
that we do not thereby come nearer to a representation of 
the processes which occur. We may say with certainty that 
fluid unequally-heated metals are electrically charged, and that 
by simple inequalities of temperature in a conductor the con- 
ditions for transformation of heat into work are fulfilled, only 
that we cannot obtain the work in the convenient form of a 
closed current. Perhaps this excitation of electricity takes 
place in all fluids, and generally in all substances, 7. e. also in 
the so-called vacuum ; and the further question, important 
in principle, may arise, what influence this hitherto disre- 
garded circumstance has upon physical processes. 
If we return to the facts detailed above, everything indicates 
that thermoelectric excitement is an intermolecular process 
dependent upon the number or arrangement of atoms in the 
molecule. It is thus suggested that all the rough mechanical 
changes, which exert so much influence on the thermoelectric 
behaviour of a solid body, and which consist in drawing, 
bending, hardening, annealing, &c., are also connected with 
intermolecular, and thus in a measure chemical, changes. 
This would be in harmony with the one already known fact, 
that in steel, upon passage from the soft into the hard con- 
dition and vice versé (also by simple drawing), the quantity of 
chemically combined carbon changes. Hard and soft steel 
give, as is well known, a tolerably powerful thermoelectric 
action. 
LVII. On the Expression for the Complete Elliptic Integral 
of the Second Kind as a Series proceeding by Sines of Mul- 
tiples of the Modular Angle. By J. W. L. GuatsHER, 
MOA, LR SS 
Series for K and Hi, §§ 1-4. 
Sie iB vol. xix. pp. 51, 52 of Crelle’s Journal, Guder- 
mann has given the following interesting expres- 
sion for K in a series proceeding by multiples of the modular 
angle 0 :— 
Ke ae lly 3 172830. le. 372152 8 
=n 6+ gp sin 5A + 97 geen 0+ oa aa Ge sin 130+ &e. (1) 
The coefficients are the same as in the well-known fundamental 
formula 
2K Ae a Layne 1? .8 here 
== —JT+ oy sin? 6+ gz ge Sin’ 0+ S356 sin°@+&e. (2) 
* Communicated by the Author. 
