Berthoud found that the spiral spring, in order to be isochronal, must have an ascending force in arithemetical progres sion, and that this property may be affect ed, not only by the length of the spring, but by the number of coils, and the taper ingor decreasing thickness from the cen tre to the extremity, &c. He adds, be sides, the proportions of the tapering in many springs, which he had actually tried, and gives minute accounts of the experiments made with them in several time-keepers.
The late Mr. Arnold applied to the ba lance the cylindrical or helical spring, which had been employed long before to a variety of purposes instead of the spiral, which had been constantly used in watches since the time of Dr. Hooke and M. Huy gens. This is one of the articles of his patent of 1782, whence it would appear, that provided the spring be made of that form, the vibrations cannot fail to be iso. chronal ; but experience is contrary to that, notion, and artists are obliged to at tend to a variety of circumstances in the application of the helical, as well as that of the spiral spring. At present, some watchmakers think that the helical spring does not possess any advantage with re gard to that property ; but as the opi nion of other persons is in the affirmative, while all the manufacturers, as far as our knowledge goes, agree in considering the cylindrical form as more easily managed than the other, its application seems en titled to the merit of a practical improve ment.
Mr. Earnshaw, in the explanation of his time-keepers presented to the board of longitude, after noticing the insufficieny of the cylindrical spring, states, that he had, by long preseverance, found how to make springs increasing in thickness to the outer end, in order to effect the iso chronism of the vibrations. This method of obtaining isochronal vibrations had been long before explained by Berthoud, with regard to the spiral spring, in that part of his treatise on marine time-pieces which we have already quoted.
This artist states as a considerable dis covery, that the balance spring falls off or tires in its strength, and he gives an al lowance for it ; but the fact is neither so constant nor so equable as to admit of his general remedy.
Fig. 7. represents the balance of a chro nometer, or time-piece, as usually made by our artists. A circular groove is turn
ed in the flat face of a piece of steel, and into this groove a piece of good brass is driven, and a little of the solution of bo rax is applied, to prevent oxydation. This compound piece being then put into a crucible, is made sufficently hot to melt the brass ; which in these circumstances adheres firmly to the steel without re quiring any solder. The face of the steel is then cleaned, andby properapplication of the mechanical means of turning, bor ing, and filing, the superfluous steel is taken away, and the balance is left, con sisting of two or sometimes three radii, and a rim, the external part of which is brass, and the internal part steel, the for mer metal being about twice the thick ness of the latter. Some artists solder the metals together ; and others plunge the steel balance into melted brass, and suffer them to cool together, but the method we have described appears to be the best. In this state the arcs of the rim are then cut through and diminished in their length as in the figure ; and near that extremity of each arc which is farthest from its ra dius, a piece or weight is put on, which can be slided along the arm so as to be adjusted at th...t distance, which upon trial shall be found to produce a good performance, under the different changes of temperature. For it scarcely need be observed, that the flexure of these arms, by change of temperature, will carry the weights nearer to the centre in hot than in cold weather ; and the more, the greater the distance of the weights from the radius. The small screws near the ends of the radii afford an adjustment for time, as the balance will vibrate more quickly, the further these are screwed in ; and the contrary will be the case, if they be unscrewed or drawn fur ther out Fig. 8. shews a balance according to a construction used by Arnold, and speci fied by him,to the commissioners of longi tude. The expansion weights are cylin drical, and are adjusted upon the arm by screwing : and there is an inner rim up on which three weights are adjusted by sliding. These serve to regulate the go ing of the time-piece in different posi tions.