Dr. Carpenter’s method of measuring the mean velocity of the Gulf-stream is equally objectionable. He takes the mean annual rate at the surface in the “Narrows” to be two miles an hour and the rate at the bottom to be zero, and he concludes from this that the average rate of the whole is one mile an hour—the arithmetical mean between these two extremes. Now it will be observed that this conclusion only holds true on the supposition that the breadth of the stream is as great at the bottom as at the surface, which of course it is not. All admit that the sides of the Gulf-stream are not perpendicular, but slope somewhat in the manner of the banks of a river. The stream is broad at the surface and narrows towards the bottom. It is therefore evident that the upper half of the section has a much larger area than the lower; the quantity of water flowing through the upper half with a greater velocity than one mile an hour must be much larger than the quantity flowing through the lower half with a less velocity than one mile an hour.
His method of estimating the mean temperature of the stream is even more objectionable. He says, “The average surface temperature of the Florida Channel for the whole year is 80°, and we may set the average of the entire outgoing stream down to the plane of 60° at 70°, instead of 65°, as estimated by Mr. Croll.” If 80° be the surface and 60° be the bottom temperature, temperature and rate of velocity being assumed of course to decrease uniformly from the surface downwards, how is it possible that 70° can be the average temperature? The amount of water flowing through the upper half of the section, with a temperature above 70°, is far more than the amount flowing through the under half of the section, with a temperature below 70°. Supposing the lower half of the section to be as large as the upper half, which it is not, still the quantity of water flowing through it would only equal one-third of that flowing through the upper half, because the mean velocity of the water in the lower half would be only half a mile per hour, whereas the mean velocity of that in the upper half would be a mile and a half an hour. But the area of the lower half is much less than that of the upper half, consequently the amount of water whose temperature is under 70° must be even much under one-third of that, the temperature of which is above 70°.
Had Dr. Carpenter taken the proper method of estimating the mean temperature, he would have found that 75°, even according to his own data, was much nearer the truth than 70°. I pointed out, several years ago,[91] the fallacy of estimating the mean temperature of a stream in this way.
So high a mean temperature as 75° for the Gulf-stream, even in the Florida Channel, is manifestly absurd, but if 60° be the bottom temperature of the stream, the mean temperature cannot possibly be much under that amount. It is, of course, by under-estimating the sectional area of the stream that its mean temperature is over-estimated. We cannot reduce the mean temperature without increasing the sectional area. If my estimate of 65° be taken as the mean temperature, which I have little doubt will yet be found to be not far from the truth, Dr. Carpenter’s estimate of the sectional area must be abandoned. For if 65° be the mean temperature of the stream, its bottom temperature must be far under 60°, and if the bottom temperature be much under 60°, then the sectional area must be greater than he estimates it to be.
Be this, however, as it may; even if we suppose that 60° will eventually be found to be the actual bottom temperature of the Gulf-stream, nevertheless, if the total quantity of heat conveyed by the stream from inter-tropical regions be estimated in the proper way, we shall still find that amount to be so enormous, that there is not sufficient heat remaining in those regions to supply Dr. Carpenter’s oceanic circulation with a quantity as great for distribution in the North Atlantic.
It therefore follows (and so far as regards the theory of Secular changes of climate, this is all that is worth contending for) that Ocean-currents and not a General Oceanic Circulation resulting from gravity, are the great agents employed in the distribution of heat over the globe.
CHAPTER XII.
MR. A. G. FINDLAY’S OBJECTIONS CONSIDERED.
Mr. Findlay’s Estimate of the Volume of the Gulf-stream.—Mean Temperature of a Cross Section less than Mean Temperature of Stream.—Reason of such Diversity of Opinion regarding Ocean-currents.—More rigid Method of Investigation necessary.
At the conclusion of the reading of Dr. Carpenter’s paper before the Royal Geographical Society, on January 9th, 1871, Mr. Findlay made the following remarks:—