14 M. MELLONI ON THE FREE TRANSMISSION 
the degrees to the forces was perceptible as far as the twentieth degree 
of the scale, Ihave attentively observed the passage of the index through 
every 4°, by commencing with this position and continuing my obser- 
vations as far as the forty-fourth degree. There I stopped; for my ex- 
periments on calorific transmission were to be confined to radiations 
considerably weakened by distance. 
The ares passed once in virtue of the forces acting on the system of 
the needles at different points of their course are in the following ratios 
to one another: 
The are comprised between 
20° and 24° is equivalent to 5°12, commencing at zero. 
24 — 28 6 °44 
28 — 32 ——— 8 -00 
32 — 36 — 9 92 
36 — 40 —_———. 12 °44: 
40 — 44 — 19 -04 
Each number in the third column represents the mean of eight obser- 
vations, which agreed with one another as exactly as could be expected 
from the nature of the instrument. Often equal, sometimes differing 
by 0%5, their greatest disagreement never exceeded 1°. A better proof 
cannot be given of the exactness of the method. 
The linear construction of these results, which gives a very regular 
curve convex towards the axis of the ves, has enabled me to obtain the 
values of the intermediate forces, degree by degree, from 20° to 45°. 
By connecting them with the fundamental observations, I have formed 
the following table of the intensities : 
Degrees. | Forces. | Degrees. | Forces. | Degrees. | Forces. 
29° 38° 
30 39 
31 40 
32 41 
33 42 
34 43 
35 44, 
36 45 
37 
The use of a table requires no explanations. All the forces are re- 
ferred to that which makes the index describe the first degree of the 
scale. The values corresponding with the first twenty degrees are not 
exhibited in it; for through the whole extent of this are the number 
representing the force is equal to the number of degrees contained in 
the are passed over by the index. Thus, for instance, when we look 
