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county of England, “having cut a six sheet map in pieces for that purpose *.” He used “nice scales” but he did not consider that he arrived at more than a certain approximation, which however he chiefly attributed to the imperfection of the maps on which he had to work. The projection, likewise, that was used for them, obliged him to reduce all the parts to the same mean size of the acre, and consequently the experiment best known for the purpose, and described by Dr Long in his Astronomy f, possessed in this respect a decided advantage. He says that by “weighing thus the papers of Mr Senex's globe of 16 inches diameter, the weight of the paper whereon the sea was represented was 349 grains, that of the land 124 grains: so the surface of the sea is almost three times as great as that of the land hitherto discovered. I omitted,” he adds, “weighing the parts contained within the polar circles, because it is not known to any degree of exactness how much of them is land and how much is sea.” Mr Vince refers to this passage f, and observes, that “the conclusion would be more accurate, if the land were cut out from the sea before the paper was put upon the globe;” and he gives his opinion that “after all our modern discoveries, this method would probably give the proportion of land to water, to a considerable degree of accuracy.” Senex died in December 1740, and Dr Long published the first volume of his work (which contains the passage just quoted) in 1742: they may, therefore, be considered as contemporaries; and no difficulty can be well imagined to interfere with the plates being obtained before they had been used. But Mr Vince prints the word “before” in Italics, which seems to indicate that he alludes to some tradition which was credited in his time. Under such circumstances, however, the experiment must have been worth absolutely nothing. The varnish must have been broken off unequally, and the greatest care could not have been sufficient for taking off the paper without some of it remaining in adhesion to the substance of which the globe was formed, or other portions bringing off some of that substance with them. We have, however, no later accounts of such a determination of these quantities. Several persons are said to have repeated the experiment, but as they have not published its results, it seemed desirable to try it again with that care, which might at least ascertain the reliance which can be placed upon the method. The advanced state of modern geography affords a more reasonable expectation of accuracy than could, under the most favourable circumstances, have been attained in the time of Dr Long; and the beautifully distinct manner, in which globe-plates of the largest size have now been executed, gives great advantage to the trial. In 1823 Mr Carey allowed me, for this purpose, to make use of the plates of his 21-inch globe; and when I recently wished to check the results, at which I had then arrived, Mr Addison obliged me with those which he has had engraved for a globe three feet in diameter— he took the trouble, likewise, not only of inserting all the latest discoveries, but of having the impressions expressly worked off for me with every precaution and attention.
* See a Collection for the Improvement of Husbandry and Trade, by John Houghton, F.R.S. Nos. 25, 26. # Article 580. f Astronomy, 4to. Vol. II. p. 112.
There are some difficulties in the pursuit of this inquiry, which make it necessary to proceed with great care. Dr Halley observes, “that the moisture of the air imbibed by the paper, did very notably increase its weight, which made me very well dry the pieces before I weighed them, that so I might be assured there was no error upon this account; and in so doing, I found that in a very few minutes of time, their weight would sensibly increase by their reimbibing the humidity of the air.” This effect is indeed so rapid that artificial drying is possibly the worst thing that can be done; it will occasion the weights to vary while the paper is in the scale, and will thus destroy the precision of the ratio, which may be derived from the examination of parts of the same sheet. A much better method is to lay the paper out for some time in a large room, where there is no danger of much fluctuation in the state of the air, the materials will then reach a nearly saturated state, in which they will generally continue stationary during the time which they are in hand. Such an exposure will of course on different days produce different degrees of dampness; but uniformity in this respect, for any great length of time, is unattainable, and if it can be secured for the interval, which
Wol. VI. PART II. PP
the immediate operation requires, all is gained that can be hoped for. The results, which are now about to be described, were all obtained during the summer in this manner: each piece was weighed before the land was cut from the water, the separate parts were then weighed independently; this was usually repeated," when the second was very seldom found to vary from the first determination by Tor of a grain, and the sum of the parts most commonly made up exactly the weight which had at first been found to belong to the whole.
Dr Halley points out another difficulty, for he says “that the map consisting of several sheets of paper, they were found to be of different thickness or compactness, so as to make a sensible difference, which obliged me to examine the proportion between the weight and acre in each sheet.” Dr Long refers to this where he observes that “the paper whereon it” [the engraving of the globe] “is printed should be of an equable thickness as near as possible.” Mr Addison obligingly endeavoured to obviate any such cause of inaccuracy by taking care that the impressions should be worked off on paper of an uniform texture. It was not possible to succeed in this so far as to have all the equal gores of the same weight, but there were hardly any knots to produce partial inequalities, and, by working out the results separately for each part, as near an approximation to the truth was upon the whole arrived at as the method seemed capable of producing. Relative quantities are all that were required, and by this means they rested on the uniformity of paper only of a small comparative size, a quality which might be assumed without any material error. The plates of Mr Addison's globe cover a plane surface of 4071% square inches, and from the many parts, into which they are of necessity divided, there is a fair chance for compensation, because it may be presumed that if the land were on the thicker part in one instance, it might be on the thinner in another. This compensation, being a general effect, might at first sight appear to be best secured by weighing all the land of the globe together, and all the water; but in addition to other advantages in the different process, there are objections to this method, which make it inexpedient. It would require constant and long attention in keeping the respective parts together after they have been once separated from the whole. To cut up the plates with due care is the work of many days; if suspicion occurred of any part being mislaid, or lost, it would be, in such a mass, impossible to obtain any satisfaction of the truth; and when a number of small islands or lakes were to be cut out and distributed, they could hardly be recovered, if it should be wished, from the divisions in which they had once been placed. These are not imaginary difficulties. We must suppose that the precaution would in this case be taken of ascertaining in the first instance the weight of the whole, and if the sum of what was found for the parts should not be equal to it, there would remain no possibility of determining the cause of error: there might be a deficiency, and there would be no means of discovering whether it was to be assigned to the land or to the water, or to both. But even if all this could be provided against, there would still be an essential obstacle in the different degrees of humidity, which would be imbibed by the several parts of so many pieces of paper, which could not all be equally exposed to the air. These difficulties were almost entirely avoided by the careful and distinct examination of each piece, and the further advantage was gained, that not only the ratio might by this means be determined for the whole, but, as it had been settled in detail, the corrections from future discoveries may, at any time, be introduced, without the necessity of repeating the entire examination.
The gores of Mr Addison's globe are made each for 15 degrees of longitude, and there are five divisions of each for the five zones. The twenty-four for the torrid zone were cut into two at the equator, and examined in forty-eight portions, in order to have the quantities for each of the hemispheres. The forty-eight gores for the two temperate zones, when added to these, make up ninety-six, which may be considered as having been analysed with tolerable completeness. In one or two instances the precise terminations of land and water were of necessity assumed in an arbitrary manner, but this was to a very limited extent, and could not materially affect the general conclusion. In the polar circles there is a much greater degree of uncertainty, and for these it was necessary in some parts to have recourse to conjectural estimates. The southern was taken as consisting entirely of sea. The expedition, about to sail from the United States of America, will make us better acquainted with the constitution of these parts; and if it should discover any lands in them, the correction which this circumstance will require may easily be applied. In the Northern Polar Circle the parts which belong to Europe and Asia seem to be sufficiently distinct; but the land, in high latitude, of North America, admits as yet of no certain measure. It is impossible, in many parts, to tell what belongs to a continent and what are the boundaries of islands, of which seldom more than a portion of the coasts has been traced out. In this state of things nothing more was attempted than a very rough guess, that from 180° to 270° of longitude, one half of the American portion of the circle, might be considered as land, which also (on account of the probable extent of Greenland) might, from 270° to 360°, have to the water a ratio of 2 to I.
Every care was taken to separate the land and sea with accuracy. All the bays, aestuaries, and indentations, were attended to, especially when the precise form of them appeared to indicate the representation of actual surveys. The several weights were taken, to the tenth of a grain, which was considered to be as minute a measure as was consistent with the nature of the experiment.
A table of versed sines gives the ratio of the spherical superficies, to any parts of it which are bounded by given circles. Hence the hemisphere being taken at 1, the portion between the aequator and the tropics will be 1 – 0.6012509 = 0.3987491; that within the temperate zone will be 0.6012.509 – 0.0829399 = 0.51831.10; and that within the polar circle 0.0829399; but for the immediate comparison of the results it seemed most convenient to suppose the surface of the globe to be divided into 1000 parts, and to reduce all the measures to this standard; consequently, under this condition, 0.3987491 x 500–199.37455 will give the relative magnitude of the half torrid zone, and loss = 8.30727 will give the magnitude of each of its gores; in the same manner for the temperate zones 0.518311 × 500 = 259.1555 is the quan
- 259.1555 tity for the whole, and *- 10.79814 for each of its parts;