44.4, TRANSACTIONS OF SECTION A. 
But in industrial apparatus, and even in those for accurate measurement, it 
is apparently always assumed that the cooling of the thermometric detector, 
bolometer wires, or thermo-pile, &c., follows a linear law. Nothing more is 
necessary to show, at least theoretically, that if the Stefan law is verified in 
radio-pyrometry, it must only be approximate. 
It may be of interest to obtain some idea of the magnitude of each of the 
cooling effects. It is practically certain that the principal of these is generally 
the thermal conductivity of the wires of the thermo-junction. I have, however, 
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Constantan Constantan 
i 
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been able to produce thermo-junctions in which an increase of the area S exposed 
to the radiation produces no perceptible increase of voltage, showing that the 
most importaut loss has been eliminated. 
It may be asked what the temperature of the thermo-element would be if it 
were iz vacuo, and thereby removed from the cooling influence of air currents. 
In an industrial instrument the rise of temperature never exceeds 100° C. 
But in these instruments, the diameter of the mirror being equal to its focal 
length, it is easily seen that the surface of this mirror is ;4th of the total surface 
Ss 
of the sphere of which it forms part, and in consequence the ratio of the surface s 
of the mirror to that of the cooling surface 8 is +4. 
If the junction A is 7m vacuo, we have, as the condition of equilibrium, 
T?—a' = 15(a* —#*), assuming that the only loss is that by radiation. Here T is 
the apparent temperature of the mirror s, which ts equal to that of the furnace, 
t that of the telescope body (temperature of the enclosure), and a the temperature 
attained by the junction. From this formula we find that for 'T = 1500° abs. and 
¢ = 300° abs. « = 750° abs. approximately. 
This calculation shows how great must be the loss by convection when, as 
in practice, where the loss by conduction has been rendered very small, the 
temperature of the junction is only 100° C. 
This investigation also explains why the bolometer is so sensitive to the 
smallest air-currents. The temperature of the grid, by the fact of the passage of 
the current, is always much higher than that of a thermo-pile under the same 
conditions, 
On the other hand it shows that, even when the conduction loss is rendered 
negligible, the loss by convection (which may be taken as linear for small 
differences of temperature between the junction and the surrounding air) is so 
great that it masks the loss by radiation. The latter cannot therefore seriously 
affect the proportionality of the indications of the instrument. 
Nevertheless this last form of radio-pyrometer has found much favour in 
factory practice, and I would conclude by mentioning that an apparatus of this 
