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in the course of the present and the former survey; Punnae the south extremity; Putchapoliam, Dodagoontah, Bomasundrum and Paughur, the northernmost point. The amplitude of the whole arch was 5° 56′ 47′′.32, and its length 359595.4 fathoms. From this and the other points named above, the following degrees are deduced :
In these degrees we perceive the same anomalies which have been observed in France and in England, and which will probably always occur, where contiguous parts of the same arch are compared with one another. The degree in the parallel of 11° 6′ 23′′ is 60465.5 fathoms, which is less than that in the parallel of 9° 34′, a degree and a half farther to the south. This is similar to what appears in the degree in England; and there is an instance of the same species of retrogradation, when the parts of the arch between Dunkirk and Formentera are compared with one another. Some part of this irregularity, but certainly a very small one, may be ascribed to error of observation; the
greatest part must, we think, be placed to account of the irregularities in the direction of gravity, arising from the inequalities at the surface, or in the interior of the earth; the attraction of mountains, for example, or the local variations of density in the parts immediately under the surface. On the ef fect of these last, Major Lambton remarks, "That between Dodagoontah and Bomasundrum, (13o and 14°,) there is a vein of iron ore which might be supposed to have affected the plummet." A more particular description, however, of the country would be necessary to enable us to judge of the probability of this hypothesis. A mere vein, in the strict sense of the word, would be a cause inadequate to such an effect as is here ascribed to it; but a great mass of iron ore, or a body of ferruginous strata, might be sufficient to produce the effect. We long ago remarked, in speaking of the trigonometrical survey of England, that it would have been of great importance to have added to it a mineralogical survey, as the results of the latter might have thrown some light on the anomalies of the forThe same thing is suggested by the objects now under consideration. It would be extremely
desirable also to have a vertical section in the direction of the meridian and of the perpendicular, at those places where observations for the latitude are made. This might afford a satisfactory solution of many difficulties which at present are sufficiently
perplexing, and seem to increase just in proportion to the extent and accuracy of the observations. Major Lambton goes on to remark, "That the arc between Putchapoliam and Dodagoontah gave the length of the degree in latitude 11° 59′ 54′′, equal to 60529 fathoms, while the arch between Putchapoliam and Bomasundrum gave the same degree only 60449. Both these stations are sufficiently remote from mountains, to remove all suspicion of a disturbance from that cause; but as no doubt remained as to the existence of some disturbing cause, I attributed it to the effects of the bed of ore, and concluded that the plummet had been drawn to the northward at Dodagoontah, and to the southward at Bomasundrum, which would give the celestial arc between Putchapoliam (to the south of both) and Dodagoontah too little, and that between Putchapoliam and Bomasundrum too great; making, of consequence, the length of a degree too great in the first case, and too little in the second. Being," he adds, "confident as to the accuracy the observations at both places, in consequence of the circumstances just mentioned, I thought it reasonable to take the mean of the two degrees, which gave 60490 fathoms for the degree in latitude 11° 59′ 54′′."
In the conclusion of the paper, the Major reduces the degrees into a consistent form, and apparently cleared of all irregularity, (p. 94,) but on a
principle of which we cannot entirely approve, as it involves in it too much theory. The mathematical reasoning is correct; but the introduction of a degree measured in another latitude, though it is quite legitimate in a general inquiry into the figure of the earth, prevents the results of the Indian measurement from appearing as independent facts, resting on the foundation of experiment alone.
The simplest and most unexceptionable way of deducing from a large arch, (the parts of which, as actually measured, are not perfectly consistent,) the results that may be accounted the nearest approximation to the truth, is to consider, that if the elliptic hypothesis be true, whatever be the compression, the successive degrees of the meridian must increase, on receding from the equator, by a quantity proportional to the sine of the double latitude. Thus, if x be the degree in the latitude L, the next degree is an sin. 21; the next to that is an sin.2L + n sin. (2L + 2o), &c. where n is a constant quantity, to be determined without the assistance of theory, by assuming different values for it, and adopting that which agrees nearest with the observations. This is easy, because n sin. 2L is always a small quantity. In the southernmost point of Major Lambton's arch, it is between 2 and 3 fathoms: the value that seems to us to answer best, is 3.1 fathoms; and in this way we deduce the first degree of the arch, that which be
gins at Punnae, in lat. 8° 39′ 38′′, and has its middle in 9° 9′ 38", equal to 60473 fathoms. This is derived from a comparison of the arch between Punnae and Putchapoliam, which consists of 2° 50′ 10", and is certainly, as far as observation can go, very accurately determined. In this way, the successive degrees are as follows:
These are a little different from Major Lambton's results, to which they would have been brought nearer, if we had employed the arch between Punnae and Dodagoontah, in the determination of the first degree. But as the latitude of Dodagoontah is in all probability affected by the attraction of the plummet toward the north, so that its zenith is carried too far to the south, the arch between it and Punnae must be too small ; and therefore we thought it best to avoid this arch in the fundamental determination. *
* To deduce the mean degree from a large arch, such as one of nearly three degrees, by dividing the length of the arch by its amplitude or number of degrees, is not exact, as the degrees increase each above the preceding by the quantity n sin.(2L +2°.) The length of the arch