THE NEW-YORK EXHIBITION ILLUSTRATED.
largest of these is the office comparing balance for the heavier stan ai weig 1The drawing of it exhibits the characteristics of what is called the ew oc e .We also give a front elevation of the smallest sized State a ance, piesenting the peculiar traits of the “Old Model.” The other two ba ances ex 1 1ed are the large and medium sized State balances of the old model. compartson of the two models in the two largest balances cannot but impress one wit ithe superior grace and merit in the composition of the new one. It was a ^ ® noesimilar to this one which received a medal from the jury of the London Exhibition.We cannot here do better than to cite the substance of Silbermanns lemai s onthese balances, for few men living are as competent to judge of theii ments as emodest and thoroughly scientific administrator of the Paris “ Conservatoire esArts et Metiers." In a letter to M. Vatteinare, relative to the Amencan set o■weights and measures presented through the latter to the French government, lesays: “ I will first make known to you the judgment of connoisseurs re ative othe American collection, and you may rest assured that each piece has een weinspected and thoroughly examined. There is but one opinion as to t e per ec.workmanship of these articles; the two balances especially are the paiticu ar sujects of admiration by connoisseurs and the public. I cannot better testi y e esteem in which I hold these balances than by informing you that I used the sma erone in adjusting the platinum kilogramme for the London Exhibition. constancy and sensibility are above reproach, and its delicacy is such that can weigwith certainty to a half-milligramme. The form adopted for these a ances isonce severe, appropriate for use, and impressed with that noble coquet ene w iicis only found in instruments emanating from a master hand. These aie, w la y
are justly called, instruments of precision. _ „ ,
“What I have said of the small balance is still more strikingy i 00 0larger one. With ten kilogrammes on each scale, the latter shows wit aci 1 yhalf milligramme of difference between the two loads; that is to say, one partwenty millions. This trial has been many times repeated, as wel or my own
gratification as to convince the skeptical.” , .
Mr. Silbermann then proceeds to express his strong preference or e mo elimiting the oscillation employed in them, and to regret that the <ienc 1 government instead of using the same, has adopted the mode of estimating y 10 0801lations themselves. He highly commends the device used in shaping t 0 mericasmall weights, by using wire figures; thus a straight line foi one, a m wo,triangle for three, a square for four, &c. After several other points o appio a 10he indulges in a most natural regret over the yard measure, with its me les antenths. Indeed, one living in the full fruition of the metre system 000 n0lament over such proof of outside barbarianism. Let us not despair o 10days when a universal language of metrology shall purge away the as ves g ^our motley legacy from the primeval chaos of scruples, grains, feet, e •, nleycorns.
LATITUDES AMD LONGITUDES—COAST SURVEY METHODS.
A MONG the great physical problems which have tasked tbe mus (ft> e
A- of the last century, a high rank, both in interest and difficulty, must-be
awarded to the investigations and measurements made to 001 ™ . p
try and dimensions of the earth. As the earth s ra ms is . ^ actual
astronomical measurements of distance, and as the conec ex P' e e j eraentg 0 f
distances between remote points on its surface, and a so 0 + 0
accurately projected terrestrial maps and charts,_ are fun “““J p e oon cededthe grand results of arc measurements, a primary importanc de _
to those geodetic operations, from which the earth’s form an ime “ ' jduced. The time is not far back in the past, when the earth’s raffius w*,known “ within a scantling of the truth ”; but now the accumu a io ^ ^ t p e
and comparable measurements is giving a high degree of precision n , SD ] iero idalvalue of the equatorial radius, but to the fraction expressing teecompression. , . , ] eve ]
The disturbing effect of mountains on the plumb line, zeni. , j rresu iari-
has been repeatedly made out, and also a class of station enor found
ties, not ascribable to any obvious surface inequalities, h bto produce minute but very appreciable’ ^^“"j^o/^sphere or even aAstronomical latitudes and longitudes. The eai no^neousness lead
.pw„id ; ™ «.—,»>< i»
constantly to measurable inconsistencies betwe , th0 ]evel SUI . faoe tracedw actual distances between stations. In other ’ We departnre8 from
J? its continuity around the earth, is a ®^ he eralproblemofahomo-that particular spheroid, which would resultYi on S . which resu l t s
geneous rotating sphere like the earth, as also fl J de when Norwood
from a combination of all the arc measurements i. ,;„<!• and nacing
■was determining the earth’s circumference, by a mixture o ^
between London and York, whose latitudes he had observed, what would Le
thought had he been told that, in the nineteenth century, philosophers would beforced to speculate on the irregular specific gravities of strata, and even be led tohypothecate huge subterranean caves, in order to reconcile astronomical and ac-tual measurements! Now that the amount of probable error in base measure-ment can bo reduced to six-tenths of an inch in seven miles, and that in latitudesand even in longitudes by telegraph, an error of a second of arc has become some-thing gross, it is not wonderful that Bessel’s elements of the earth’s figure, or anygeneral elements which are possible, should bo found to fall sensibly short of re-conciling all discrepancies. Yet it is rather remarkable that station errors or dis-crepancies between geodetic and astronomical results, amounting frequently totwo or three seconds of arc, and in one instance to 9\48, should be found belong-ing to points not far remote, and bearing no obvious relation to any local attractions.
The latitude and longitude of a point are but the terrestrial co-ordinates of itsposition, by which it is referred to the equator and prime meridian. These terres-trial great circles are usually reputed to be planes, but we doubt if more difficultsurfaces ever courted mathematical skill than these very surfaces of reference.The Greenwich meridian and equatorial circumferences must be indeed curves ofdouble curvature, and their corresponding surfaces, if traced through the earth’smass, would exhibit a most ingenious and delicate complication of minute doublecurvatures. It is the same with all parallels and meridians. Yet this astronomi-cal system of co-ordinates for positions can by no means be dispensed with,—be-cause terrestrial positions must either be determined and defined by their use, orby the slow and laborious process of actual measurement, combined with computa-tions necessarily involving a neglect of these same minor irregularities of the earth’sform and substance. No practical inconvenience beyond the limits of geodeticdiscussion can ever be felt from disagreements of so minute a character, unless it \be in some very transcendental age. But geodetically it is of high importance to'bring out, with all possible cle '.mess, tho exact amount by which a map projectedastronomically would differ from one based on geodetic elements. Of course, allmaps must necessarily be constructed on goodetic projections—hence points intro-duced in these with their astronomical co-ordinates, are liable to be sensibly mis-placed. But, if geodetic co-ordinates are used, so as to give the actual relations be- 1tween natural objects, any new astronomical determinations will seem to accuse themap of error. In the British Ordnanoe Survey, the discrepancy of 9’.5 amountsto an inch on the scale (i-jr.Vsir) °f the larger map. In the Coast Survey, the sta-tion error sometimes amounts to five seconds, the ordinary error being from twoto three seconds. Are latitude and longitude, then, to mean what is so generallyunderstood by them, or are they to refer to absolute distances ? We presume thatthe geodetic co-ordinates must ultimately bo universally adopted as tho true ones,and that the difference between them and the astronomical, will be regarded asan error, for which tho astronomical must be corrected. Yet the nautical com-munity may say that as they use astronomical co-ordinates, their charts should bebased on them alone. This plea would be-entirely valid, if the quantity in ques-tion were not too small to become sensible im tlm nautical mode of observing—asin fact it is and will be. On land, a geodetic survey fixes, once for all, tho posi-tions of its stations, so as to supersede the necessity of continuing observations.
The British Ordnance Survey has recontly published its Astronomical Obser-vations at twenty-six stations, at most of which is exhibited somewhat of a sta-tion error. This has had the effect to call special attention to the subject of localdisturbances. The attraction of Schehallion Mountain on the plumb line, the de-viation of the plumb line through 47'8 seconds in Lombardy ; the deviation ofseven seconds observed in Peru; the three seconds of attraction by Table Moun-tain, and two seconds by Pikel Berg, observed by Maclear; and like effects foundin the East India Survey, had rendered quite familiar the measurable character oflocal attractions by mountains; but the effect of irregular densities in strata,though, of course, undoubted, had not generally been regarded as sensible or im-portant. That it is so in fact, is now clearly seen. In 1844, Prof. Bacho de-tected evidences of station errors of this kind, and was thus induced to adopt theplan which has since prevailed in the Coast Survey, of making accurate latitudeand longitude observations at a series of stations running through the entire pri-mary triangulation, with the express view and purpose of developing these stationerrors, and all the facts bearing on the earth’s figure. No less than 70 latitude and46 longitude stations have already been occupied, giving a mass of observationsbearing on geodesy, the value of which can only become fully known by theirpublication. So far from their testifying to a symmetrical spheroid, they areladen with a series of well-defined station errors which may almost furnish anearth crust sounding line to the geologists. We long to see these results consignedto fair type, while the observers are still living to detect errors and divine conclu-sions. We hope the special appropriation for this purpose, whioh has been twiceasked, will be granted by Congress, while this subject has a fresh interest, andbefore the British, Russian, and llindostan surveys have made an old story ofwhat would now reflect so much honor on our country.
There is already a considerable store of geodetic measurements proper for usein discussing the earth’s figure. The French arc of 12° 22' comes first in order oftime, and is of great value. Connecting with this, the British Ordnance arc ofnear 11°, botween 49° 53' and 60° 49'north latitude, although only just published,