manent current which would flow were the end of the line put to earth.

The effect of a condenser on the signals varies according to the description of instruments used for observing the signals, on the system of currents forming the signals, and on the value of the unit of time a for the particular line under consideration. Thus on an overland line worked on the Morse system with single currents, where the signalling consists in alternately connecting the sending-end of the line with one pole of a battery and to earth, it would be impossible to make dashes, because on land lines the length of a contact is always so great compared with the unit a, even in rapid signalling, that the current at the receiving-end would have come and gone long before the contact at the sending-end was finished. On cables of any considerable length it would be different. There would then be only a shortening of the dashes, its extent depending on the length of the contact; and it would consequently lead to an increase in the speed of working. There would similarly be very little direct advantage, save immunity from earth-currents, in using on land lines the condenser with polarized relays and reversing-keys, although there would be no shortening of the marks, as the armature of a polarized instrument will, if properly adjusted, remain in the position in which it is placed by a transient current. On cables worked with the same instruments, a considerable increase in the speed of working results.

But the condenser is peculiarly applicable to those systems of signalling where the currents sent are of equal duration and alternately positive and negative; for example, Sir C. Wheatstone's automatic system. A succession of reversals, each contact of the length 4a, produces through the receiving instrument reversals alternately 50 per cent. plus and 50 per cent. minus, being a whole range of 100 per cent. Without the condenser the whole amplitude of variation of the current is only 24-42 per cent. On a certain circuit worked by the automatic system, on which the value of a was about 0.0175 second, the speed of working with condenser was 75 per cent. greater than without.

With Sir W. Thomson's mirror and recording instruments there does not at first sight appear any reason why the speed of working should be much raised, as they indicate in the one case and record in the other every change in the strength of the current. Yet the condenser is of great advantage here, as it keeps the spot of light and siphon within very narrow ranges, never departing much from the zero line, and naturally the signals are much more distinct.

It will be found on examination that

dv

when the end of the

dť

line is to earth, reaches its maximum in 3a, as against 7a when the end of the line is insulated. Thus it would appear that a considerable increase in the speed of signalling should result from connecting the line to earth through a resistance, as shown in fig. 4, where ƒ is the battery, A the cable, e the receiving in

strument, Cr the condenser, and R the resistance introduced between the end of the line and earth. This resistance is necessary in order to raise the potential of the end of the cable, and give signals of a workable strength. That this plan does increase the speed, I have verified on the circuit before mentioned, using a polarized instrument and double current key. The increase in speed was about 20 per cent., compared with the speed obtained by making R infinite. The signals were, of course, weaker in the former than in the latter case.

The effects of defective insulation may be traced by giving h different small values in equation (7). In the first place the signals are weakened; and next, the effect of loss is to decrease the time required for the signal to arrive at its maximum strength. Thus when h=7' the maximum is reached in 4a, as against 7a when h=0. This is an extreme case, and would nearly correspond to the French Atlantic cable if its insulationresistance were 3 megohms per knot, instead of more probably 300. Whether loss does or does not increase the speed of working depends on a great many circumstances. It is an undoubted fact that, under some systems of signalling, a cable with a very bad fault in it has worked quicker than when it was perfect; and it is also a demonstrable fact that under other systems the effect of loss is greatly to diminish the speed. In a particular case which I have examined theoretically and practically, the fact that each signal should be more quickly made through a faulty than a perfectly insulated cable is quite consistent with the fact that the speed of working is reduced.

Phil. Mag. S. 4. Vol. 47. No. 314. June 1874.

2 F

Another method of receiving signals has been tried, though not adopted anywhere. The current is passed through the primary wire of an induction-coil, in the secondary circuit of which dC

is the receiving instrument. The signal here depends on dt' the rate of increase of the current; and the arrival-curve has its maximum at about 3.5a, while with condenser pure and simple it is 7a. It does not, therefore, appear evident why, as Mr.Varley states, he found the condenser more satisfactory. Mr. G. K. Winter reinvented this system, and reports very favourably on its effect (British Association, Brighton, 1872).

LV. On the Physical Cause of Ocean-currents.

To the Editors of the Philosophical Magazine and Journal.
GENTLEMEN,

IN

Na lecture at the Royal Institution, and also in the 'Athenæum,' 'Nature,' Philosophical Magazine, and other quarters, Dr. Carpenter has been advancing a somewhat plausiblelooking objection to my views in reference to under-currents. As this objection bears upon a point which in my last communication I omitted to consider, perhaps you will permit me, through your columns, briefly to refer to it. The objection in question, as stated in Dr. Carpenter's own words, is as follows:

"According to Mr. Croll's doctrine, the whole of that vast mass of water in the North Atlantic, averaging, say, 1500 fathoms in thickness and 3600 miles in breadth, the temperature of which (from 40° downwards), as ascertained by the Challenger' soundings, clearly shows it to be mainly derived from a polar source, is nothing else than the reflux of the Gulf-stream. Now, even if we suppose that the whole of this stream, as it passes Sandy Hook, were to go on into the closed Arctic basin, it would only force out an equivalent body of water. And as, on comparing the sectional areas of the two, I find that of the Gulf-stream to be about one 900th that of the North Atlantic underflow; and as it is admitted that a large part of the Gulfstream returns into the Mid-Atlantic circulation, only a branch of it going on to the north-east, the extreme improbability (may I not say impossibility?) that so vast a mass of water can be put in motion by what is by comparison a mere rivulet (the north-east motion of which, as a distinct current, has not been traced eastward of 30° W. long.) seems still more obvious."

The objection seems to me to be based upon a series of misapprehensions: (1) that the mass of cold water 1500 fathoms deep and 3600 miles in breadth is in a state of motion towards

the equator; (2) that it cannot be the reflux of the Gulf-stream, because its sectional area is 900 times as great as that of the Gulf-stream; (3) that the immense mass of water is, according to my views, set in motion by the Gulf-stream.

I shall consider these in their order. (1) That this immense mass of cold water came originally from the polar regions I, of course, admit, but that the whole is in a state of motion I certainly do not admit. There is no warrant whatever for any such assumption. According to Dr. Carpenter himself, the heatingpower of the sun does not extend to any great depth below the surface; consequently there is nothing whatever to heat this mass but the heat coming through the earth's crust. But the amount of heat derived from this source is so trifling, that an undercurrent from the Arctic regions far less in volume than that of the Gulf-stream would be quite sufficient to keep the mass at an ice-cold temperature. Taking the area of the North Atlantic between the equator and the tropic of Cancer, including also the Caribbean Sea and the Gulf of Mexico, to be 7,700,000 square miles, and the rate at which internal heat passes through the earth's surface to be that assigned by Sir William Thomson, we find that the total quantity of heat derived from the earth's crust by the above area is equal to about 88 × 1015 foot-pounds per day. But this amount is equal to only 4 that conveyed by the Gulf-stream, on the supposition that each pound of water carries 19,300 foot-pounds of heat. Consequently an undercurrent from the polar regions of not more than the volume of the Gulf-stream would suffice to keep the entire mass of water of that area within 1° of what it would be were there no heat derived from the crust of the earth; that is to say, were the water conveyed by the under-current at 32°, internal heat would not maintain the mass of the ocean in the above area at more than 33°. The entire area of the North Atlantic from the equator to the arctic circle is somewhere about 16,000,000 square miles. An under-current of less than that of the Gulfstream coming from the Arctic regions would therefore suffice to keep the entire North Atlantic basin filled with ice-cold water. In short, whatever theory we adopt regarding oceanic circulation, it follows equally as a necessary consequence that the entire mass of the ocean below the stratum heated by the sun's rays must consist of cold water. For if cold water be continually coming from the polar regions either in the form of under-currents, or in the form of a general under-flow as Dr. Carpenter supposes, the entire under portion of the ocean must ultimately become occupied by cold water; for there is no source from which this influx of water can derive heat, save from the earth's crust. But the amount thus derived is so trifling as to produce no sensible

effect. For example, a polar under-current one half the size of the Gulf-stream would be sufficient to keep the entire water of the globe (below the stratum heated by the sun's rays) at an icecold temperature. Internal heat would not be sufficient under such circumstances to maintain the mass 1° Fahr. above the temperature it possessed when it left the polar regions.

(2) But suppose that this immense mass of cold water occupying the great depths of the ocean were, as Dr. Carpenter assumes it to be, in a state of constant motion towards the equator, and that its sectional area were 900 times that of the Gulf-stream, it would not therefore follow that the quantity of water passing through this large sectional area must be greater than that flowing through a sectional area of the Gulf-stream; for the quantity of water flowing through this large sectional area depends entirely on the rate of motion.

(3) I am wholly unable to understand how it could be supposed that this under-flow, according to my view, is set in motion by the Gulf-stream, seeing that I have shown that the return undercurrent is as much due to the impulse of the wind as the Gulfstream itself.

I am also wholly unable to comprehend how Dr. Carpenter should imagine, because the bottom-temperature of the South Atlantic happens to be lower, and the polar water to lie nearer to the surface in this ocean than in the North Atlantic, that therefore this proves the truth of his theory. This condition of matters is just as consistent with my theory as with his. When we consider the immense quantity of warm surface-water which, as has been proved, is being constantly transferred from the South into the North Atlantic (a quantity which to a large extent is compensated by a cold current from the Antarctic regions), we readily understand how the polar water comes nearer to the surface in the former ocean than in the latter. In fact the whole of the phenomena are just as easily explained upon the principle of under-currents as upon Dr. Carpenter's theory.

Dr. Carpenter lays considerable stress on the important fact established by the Challenger' expedition, that the great depths of the sea in equatorial regions are occupied by ice-cold water, while the portion heated by the sun's rays is simply a thin stratum at the surface. It seems to me that it would be difficult to find a fact more hostile to his theory than this. Were it not for this upper stratum of heated water there would be no difference between the equatorial and polar columns, and consequently nothing to produce motion. But the thinner this stratum is the less is the difference, and the less there is to produce motion. I have been favoured by the Hydrographer to the Admiralty with a series of temperature-soundings taken along the equator;