the degrees to the forces was perceptible as far as the twentieth degree of the scale, I have attentively observed the passage of the index through every 4°, by commencing with this position and continuing my observations as far as the forty-fourth degree. There I stopped; for my experiments on calorific transmission were to be confined to radiations considerably weakened by distance.
The arcs 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 arc 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 observations, 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 xes, 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. |
| 20° | 20·0 | 29° | 33·4 | 38° | 55·4 |
| 21 | 21·1 | 30 | 35·3 | 39 | 58·5 |
| 22 | 22·3 | 31 | 37·4 | 40 | 61·9 |
| 23 | 23·7 | 32 | 39·6 | 41 | 65·5 |
| 24 | 25·1 | 33 | 41·8 | 42 | 69·3 |
| 25 | 26·6 | 34 | 44·1 | 43 | 73·4 |
| 26 | 28·2 | 35 | 46·7 | 44 | 78·0 |
| 27 | 29·9 | 36 | 49·5 | 45 | 83·2 |
| 28 | 31·6 | 37 | 52·4 |
The use of a table requires no explanations. All the forces are referred 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 arc the number representing the force is equal to the number of degrees contained in the arc passed over by the index. Thus, for instance, when we look
