deductions to deserve insertion here, as they present only proportional fractions of this number. H. The effect of the variation of temperature being compounded of two, the one in arithmetical ratio for the brass, the other in an increasing ratio (explained above) for the water; the table for these reductions of the gallon is here inserted, for the temperatures near the two minima of this effect; remarking only, that the weighings were never made to so great an extent of variation of temperature as the table reaches. 22. Table of reductions, for the weighing of the gallon to the temperature of maximum density of the water, for a brass gallon, to its absolute value. For the or, &c., gallons, the effect is of course alsoor 4, &c. 23. This necessary limitation in the temperature, without which the proper accuracy would be unattainable, is the cause why these adjustments can be made only in the winter months, when this temperature is obtainable at least for a certain number of hours in the morning; the afternoon hours being employed for the calculation of the reduction of these weighings, and the adjustment of the measures themselves. 24. It will be observed by these tables, that the brass has a particular advantage in these adjustments, namely: while below the maximum density of the water, or about 39.2° Fahrenheit, it continues to contract, while the water expands; from thence to the neighborhood of 52° Fahrenheit, both brass and water expanding, the reduction changes sign from+ to—, and passes a maximum at about 45°, from which the two expansions approach again to each other; there the reduction decreases again until to about 520 Fahrenheit they are again equal, thence the reduction becomes= O again, after which the increase of the expansion of the water goes on rapidly, while that of the metal increases only in arithmetical proportion. Thus, at the two limits of this change of about 39.2°, and at about 52° Fahrenheit, there are two points of temperature equally favorable for the adjustment, where namely the variation of the effect of temperature is at its minimum. 25. It is evident that the temperature of 52° is most favorable for the work, and affords a relief in the operation; between the two temperatures, 39° and 52° the reduction never amounts to so much for the about 64° of variation, as it does after a few degrees of deviation from them, either above or below the two points of minimum variation, or rather of the 0 of variation, for one single degree. 26. By thus organizing the works of such a nature in the practical application of natural philosophy, the greatest accuracy is obtained, which is entirely unobtainable if a point of temperature is selected, where the variations are large, and in the same direction. I have therefore no doubt of this arrangement having been one of the main causes of the extreme accuracy which has been obtained in the present operation, which exceeds all that I have ever found in any similar operation. 27. This mode of proceeding will therefore be so much more approved by the men of science, who have been practically engaged in such works, and are acquainted with the difficulties which these operations have; while on another hand it adds more stability to the system itself, besides that the operation itself is very much easied, and therefore accelerated. 28. The tables of the ultimate results, inserted hereafter, present both the last comparisons, under the temperature by which they were made, and the ultimate results corresponding, when reduced to the temperature of the maximum density of the water, which administers the fullest proof of their accuracy. 29. Weights were made of the same brass employed for all the standards, exactly equal to what the calculations exposed in my report of 1832, indicated for each of the capacity measures; these were used for all equally in the whole operation. Also, in all the weighings, brass was used of the very same proportion of copper and zinc as the standard weights, the length measures, and the capacity measures, were made of; thence all compensation for difference of metal was made by the very organization of the operation, which otherwise would necessitate very complicated reductions, thereby lengthening the work, and, by the increase of the difficulties endangering the accuracy. 30. By thus compensating practically the many accessary influences, which pretend to take share in these delicate operations of natural philosophy, many corrections, and even the reduction to the vacuum, were avoided; thence also, all those possible errors that might arise from insufficiency of the elements which guide these reductions, and complicate so much the operations, were avoided. 31. A special distillery was established to obtain the distilled water employed, always pure and new, which is well known to be the essential quality required; the water employed every day in weighing was never over twenty-four hours old. 32. No more than one-third of the water can be distilled over, to be taken for use, to obtain it pure; the two-thirds remaining become useless for this purpose, and the greatest cleanliness is required in the whole operation, to avoid all extraneous matter in the water employed for that purpose. 33. It may be observed here again in passing, that all weights whatsoever, made in this office, are full; not any hollow parts, nor addition of other metal is allowed, to complete or adjust any weight. 34. In the weighing operation itself, the capacity measure being placed in one basin of the balance, with its glass cover upon, the weight which represents the quantity of distilled water of the measure to be weighed, is placed upon the glass, and the whole is counterbalanced, in the other basin, with brass weights of the same metal as the measure, and the weight in the other basin, so that all the buoyancy of the brass is exactly balanced, which is as well, for accuracy and uniformity, as if all was reduced to the vacuum. 35. The temperature of the measure is ascertained, and that of the water also; then the standard weight is removed, and the measure is filled with the water carefully, so as to occasion the least possible air bubbles; then the temperature of the water is tried again and recorded, when that of the measure is generally found equal with it; the few air bubbles that may be unavoidable, are carefully wiped off, by means of a thin whale bone, with a small rag at the end. The glass cover is again slided over the vessel, and, when near its end for covering, the superfluous water is sucked out by a syringe; the glass fully slided over leaves very little, if any, of the water to be wiped off around the glass cover. 36. Thus the standard measure is ready for weighing by the counterpoises that have been placed in the opposite basin of the balance, and the smaller complementary weights that have been needed, the enumeration of these smaller weights is then made and registered; when the measure is removed the temperature is again observed and recorded; if any difference is found from the first observed temperature, a mean between the two is taken, which was, however, seldom of any amount. 37. Thus was proceeded with every one of the three hundred and fortyone brass vases, here rendered account of, as the standard liquid capacity measures; and there are a number of gallons still under adjustment. 38. This task is the most fatiguing and trying for all faculties of a man in attention and care; it has been executed with the same minute, faithful care and accuracy, as I have described in rendering account of the weights, and the result has rewarded the exertions by its extreme accuracy. 39. It must be evident that these measures cannot be brought to their required accuracy at once; the operation is therefore a successive approach to the truth. The measures are worked out sufficiently large to admit in any case reducing them down, by successive steps, to their proper capacity, their state being successively ascertained, each time, by the weighing. 40. The quantity of reduction in the height, which will correspond to a certain overplus of content of the one or the other kind of measure, is ascertained at first approximately, by pouring the water of one measure, nearly adjusted, in the new vessel, the scale of this reduction is easily deduced from the content of the whole by measurement, compared with its weight. A particular tool has been made to trace within the measure that circle at equal distance from the top, which is considered nearest, but still rather above, the dimension required. 41. Then the measure is brought upon a plate of lead, in the inverted position; upon this it is worked in a kind of epicycloidic revolving motion, with emery upon the plate, by which means the cylindric edge is ground down to the mark made by the guide of the preceding trial, always in an exact perpendicular position. 42. Thus alternately weighing and grinding down, the measure is brought every time nearer to the truth, until it is considered within the limit, which it is found sufficient to allow to abide by, and only to register the ultimate result; it is these last weighings, and their result, which are found in the table hereunto joined. 43. These weighings are of course always made under the existing temperature of the time of weighing, which forms the first column of the table, after the number with which each set is marked; the third column contains the difference found at that temperature; and the fourth column is the final result therefrom arising, for the individual measure, at the temperature of the maximum density of the water, under the direction given by the table presented in section 22; this forms of course the ultimate reduction. 44. It is upon these grounds that I may be allowed to claim, that the determination of standards, made in this office, will stand the test of future times more than could have been expected otherwise. 45. I am, however, unable at this moment, nor is it proper in this special report, to expose the whole philosophical system, its elements and consequences; this belongs more particularly to an ultimate final report upon the whole of the establishment for the uniformity of standards for so extensive a union of country as the United States; the results of which must, by their nature, extend to ages, and of which I understood so well the high importance, in accepting the trust of their execution, at the very beginning. 46. I might yet quote here the result of the reweighing of the English and French standards of liquid capacity measures, which has so strikingly shown the accuracy of the comparison which I have made formerly for the object of my report of 1832, and published therein; but, as this investigation and comparison will be carried on upon the larger scale of embracing also the comparison of the weights, &c., it is much more proper to defer this subject to the final report upon the whole work. 47. But as it may be of interest and importance to make known some of the means employed, the utility of which may extend further to other useful applications, I take the liberty to join here: 1st. The description of the thermometers, constructed purposely for determining the temperature with more accuracy, than the thermometers habitually used give, as it is so essential an assistance in this case. 2d. The description of the kind of barometer of my invention, and of my own construction, which was employed in this work, as well as for all astronomical observations, &c., in the coast survey works. 3d. The description of the balance, constructed in this office, for the next operation of the standard establishment, namely: the adjustment of the bushels and half bushels, which, with a weight of about 130 pounds, to 150 pounds in each basin, will present a sensibility of one-tenth of a grain-an accuracy which I dare assert has never heretofore been obtained, and without which I should consider the results of my works degraded. Hon. WALTER FORWARD, F. R. HASSLER.. Secretary of the Treasury. |