Before we proceed to consider these results, it is necessary to recollect that they have all been obtained under the free action of an invariable radiation of 30° measured by the thermomultiplier. Now the half degrees of the galvanometer are very distinctly legible. Thus the transmissions are exact to 160th of the incident heat; but the observations being repeated, the hundredth part becomes easily appretiable.
In the quantity of rays transmitted through the same substance there is a variation of several hundredth parts according to its greater or less purity. It was therefore useless in giving the measure of this element to attempt a degree of exactness exceeding the hundredth part of the whole; but it was desirable to ascertain the limits of the insensible transmissions with more precision. In this case therefore I have always carried the approximation to 1200, and sometimes to 1300, so that if the zero does not represent a transmission really equal to nothing, it is at least certain that, if there are any rays of heat transmitted, their amount does not exceed 1200dth of the whole incident quantity.
In order therefore to reduce the probability of error, it has been found necessary to operate on stronger radiations. Now the table of intensities given in my first Memoir does not exhibit the forces which move the galvanometric index beyond the 45th degree. I could have extended it to the higher degrees of the quadrant by the method followed in its construction. But I thought it better to employ at each step a very simple artifice which immediately gives the force of any radiation whatsoever as well as the required limit of error. To make this clear, let us suppose that it is desired to verify a particular case of the transmissions in the table; for instance, that it is requisite to prove that the transmissions of alum, sugar, or ice exposed to the rays emitted by copper heated to 390° are either null or less than 1200dth of the whole of the incident heat.
The table shows that a plate of glass, of rock crystal, or of Iceland spar transmits from five to six hundredths of those rays; that is to say, that for a free radiation of 30° we obtain about 2° through the plate. We know moreover that in this feeble indication there is a possible error of 160th of the whole heat. The limit of error would be 170·6 if we wished to be rigorously exact, for by the table of intensities we see that, in the deviations below 20°, one degree is equivalent to 135·3 of the force which moves the needle to 30°. But let us admit only the limit 160, which will have the advantage of rendering the values independent of a knowledge of the ratios existing between the degrees of the galvanometer and the corresponding forces of deviation. Let us bring the source near, in order that We may obtain through the same plate of glass a deviation exceeding 2°; a deviation, for instance, of 8°. The quantity of incident heat is now increased fourfold, and the pro-
