of Edinburgh , Session 1872-73. 57 
where all the quantities are constants except n, which may be any 
positive integer. 
It is obvious that, as the difference of the squares of p n , q n , is 
constant, while their product varies as n , their values will ulti- 
mately be equal for very great values of n. We may therefore 
assume, as an approximation, for large values of n — - 
Pn~- \/ + 2»=\/ 
where the square of e is negligible. This satisfies the first of our 
conditions, and the second gives 
HT 
e - 47m ' 
This remark does not, of course, affect Angstrom’s deduction of 
the conductivity from the term of full period ; but it must materially 
affect the others, and thus it is certainly remarkable how glosely 
the results he has obtained from the second and third harmonic 
terms agree with these simple forms. 
I have not as yet managed to control by this process my results 
deduced by Forbes’s method {Trans. R.S.E.), though I hope soon 
to do so The difficulties are of two kinds: ls£, in the strictly 
periodic application of very hot sources, without a great range ; 
2d, in the procuring of thermometers which will give with great 
accuracy small differences at very high temperatures. In the 
meantime, with the assistance of several of my laboratory students, 
especially Messrs G-reig and M‘Leish, I have studied the periodic 
state of temperature in bars of copper (of two very different kinds), 
iron, and German silver, produced by applying for fifteen minutes 
at a time, and with fifteen minute intervals, a powerful Bunsen 
burner to one end. The ranges of temperature thus produced are 
so great that the differential equation assumed above can hardly 
be regarded as even a rough approximation to the law of the 
phenomenon. Still, the results possess considerable interest, 
especially in the contrast between the various substances; indicating 
the great differences not merely in conducting power, but also in 
its rate of change with temperature The bars employed were all 
1^-inch square, and the thermometers were inserted at 3-inch 
intervals. 
