Talk:Barlow's law

To do
--Ben Kovitz (talk) 19:10, 23 February 2009 (UTC)
 * Check if there is a Barlow's law for crystallography.

There is indeed a Barlow's law for crystallography. It might be more important than the false law for electricity covered on this page. —Ben Kovitz (talk) 08:26, 7 June 2009 (UTC)

Also, there appears to be a Barlow's law for artillery (the same Barlow). I see a DAB page in our future. —Ben Kovitz (talk) 23:16, 7 June 2012 (UTC)

Why was Barlow's law bad for telegraphy?
Why did Barlow belief that long-distance telegraphy wouldn't work if his law were correct? If the resistance would only increase with the square root of the length of the wire, then long-distance telegraphy would actually be easier!? Icek (talk) 18:49, 20 October 2009 (UTC)


 * An excellent question! I think a good answer will requiring making a correction to the page. Schiffer's book says that he (Schiffer) reformulated Barlow's law to state that the "current strength" varies inversely with the square of the length of the wire. I don't see how to reconcile this with the direct quotations of Barlow's law that are found in other places (like the Report on Mining, etc.). I'm guessing that the answer has something to do with Barlow's terminology, which we should explain in the article. Barlow's law could not have been about conductance (or resistance) in the modern sense of the word, because that concept wasn't established until Ohm's law. —Ben Kovitz (talk) 15:57, 1 June 2010 (UTC)

I think we should discredit and delete the Schiffer reference, because it clearly overstates the case. As Icek says, if resistance were proportional to the square root of distance, this would facilitate rather than impede the sending of electric currents along wires! Barlow was trying to guess the future; he got it wrong; he wasn't the first and he wasn't the last. Perhaps his opinion did slightly delay further advance in the field, perhaps not. Like BenKovitz says, time for a rewrite. 193.60.63.224 (talk) 11:01, 21 April 2011 (UTC)


 * I'm reluctant to delete the Schiffer reference just yet, since he seems to have treated the topic seriously. We might be the ones making a misreading here. Also, I believe I've run across the same analysis in a couple places: Barlow's law persuaded important people that long-distance telegraphy was impossible. I think Barlow's original article even said that he had shown that long-distance telegraphy is unworkable, though I don't have it handy anymore. I can't remember for sure what Barlow was measuring: he might have just been measuring the current, and thought he found that it decreased very quickly with the length of the wire. Can someone get that fact straight? Then we can revisit whether there is a logical disconnect between Barlow's law and "long-distance telegraphy is unworkable". —Ben Kovitz (talk) 21:08, 23 April 2011 (UTC)


 * I think the major issue was that Barlow did not recognize the dependence of current strength on voltage which is discussed in relation to other historical references cited by Schiffer. Schiffer also mentions remodeling as an inverse square law but I am reluctant to include this in the wikipedia page since Schiffer does not detail the rationale for this interpretation. I question the Report on Mining more than Schiffer since it seems to have gotten the year of Barlow's paper wrong and appears to misstate the law based on conductance rather than current strength which was what Barlow was measuring.Blm19732008 (talk) 00:45, 2 June 2012 (UTC)


 * Thanks for tracking down the Barlow paper! I just added a link to it on Google Books. The paper refers to a Plate III, which is not in the Google Books copy. I got hold of a physical copy of the journal from the Indiana University library. It was also missing Plate III. (Perhaps not a coincidence: I understand that Google Books gets a lot of material from the IU library.) Maybe that doesn't much matter, but the article cuts off at p. 113, and I haven't found the rest of the article. Perhaps both of these are printing errors. However, from what I can see, it does appear that Barlow is about to say something to the effect of, "The bigger the wire, the less the diminution of strength." So, for now, I'm thinking to take the Report on Mining at its word, despite its getting Barlow's year of publication wrong. If someone can find a more complete version of Barlow's paper or a better secondary source, that would be great.


 * Barlow has no notion of voltage, but he does explicitly address the effect of battery strength, taking care in his experiments to "guard against the variable power of the battery" and blaming some discrepancies between his observations and the predictions of his law on that variability. He relates all of his measurements to the effect produced by a "standard power of the battery". He appears not to have considered the possibility of using a huge battery to power long-range telegraphy, even though his experiments and law actually seem to suggest that it might work (and work better than real physics allows; see below).


 * Schiffer is clearly mistaken about Barlow saying that the strength is inversely proportional to distance squared. This just sounds like a careless error, since so many physical laws have distance squared in the denominator. I'm inclined to keep Schiffer as a source on the historical importance of Barlow's Law despite this error.


 * And so, we still have no answer to the mystery raised by Icek! If the current strength were inversely proportional to the square root of distance, that would be better for telegraphy than Ohm's Law, which simply makes the current strength inversely proportional to the distance. Barlow says that he drew his conclusion that telegraphy is impracticable not from the shape of the curve implied by the law, but from a single measurement of a great decrease in current strength at 200 feet in one wire. Then he became curious about the mathematical law by which the current strength decreases, but his erroneous law had nothing to do with his dismissal of telegraphy. Saying this in the article, though, would be original research. Maybe we should publish a tiny paper about it in a history journal. "Telegraphy naysayers had a weaker argument than previously thought."


 * What are your thoughts? —Ben Kovitz (talk) 00:20, 3 June 2012 (UTC)
 * I found Plate III. It's here. Fig. 5 is the diagram of Barlow's experiment with wires of different lengths (reproduced with the letter A omitted in his second paper, here). —Ben Kovitz (talk) 14:33, 14 June 2012 (UTC)
 * Thanks for your efforts tracking down the paper and finding the links.


 * I don't think that this article is the right place for Barlow's opinion on telegraphy; that may fit into the article on Barlow himself. I don't see how anything should be "original research" just because the paper is 187 years old.


 * I think Barlow's actual mistake was to not know about the internal resistance of a battery; the law should be neither 1/dist nor 1/sqrt(dist) but 1/(k+dist). Compare the measurements with the various possible laws. [[Image:Barlow1825.png]]


 * Icek (talk) 10:44, 4 June 2012 (UTC)


 * Thanks, Icek. This graph definitely settles a few things. First, Schiffer speculates that Joseph Henry's "failure to confront Barlow by identifying weaknesses in his experiments may have been based on political calculation." But the graph shows that Barlow performed the experiment competently, and that his proposed law is a very reasonable conjecture to explain it. Barlow actually expresses it with some doubt. I think your guess that Barlow did not understand internal resistance, and thus didn't go looking at possibilities such as 1/(k + dist) when 1/sqrt(dist) seemed to work, is almost certainly correct. Schiffer suggests that internal resistance was the key concept that Barlow was missing, though he doesn't put it quite that way, maybe to avoid getting too technical; on first reading, I thought he was talking about something like impedance-matching (which doesn't seem likely, given that he wasn't describing an AC circuit).


 * Second, Schiffer seems to speculate that Barlow arrived at his law by analogy with other physical laws. "This was a plausible result; after all, inverse-square laws were familiar in physics, for they described the force of gravity as well as magnetic and electrostatic attractions and repulsions." The graph shows, however, that Barlow did just as he said: he found a simple equation to fit the data. —Ben Kovitz (talk) 23:29, 7 June 2012 (UTC)

Searching for other sources on the nature and influence of Barlow's law
Whenever I've come across Barlow's law (admittedly, this hasn't happened often), it's been in the same breath as, "delayed telegraphy a few years". So, I'm reluctant to remove that. I did a little more googling, though, and here's what I found:

The legal deposition that Samuel Morse wrote for his U.S. Supreme Court case regarding his priority in the invention of the telegraph was published in Shaffner's Telegraph Companion, January, 1855, pp. 6–96. Morse argues that Barlow's finding did not hold him back from developing telegraphy, because you could just use a bigger battery, and other scientists had already shown that a big battery could produce mechanical effects at a distance through a long wire. However, the deposition includes an 1848 letter from Morse to a Prof. Walker, in which he says that from 1824–1829, "the result of the experiments of Barlow seem to have effectually palsied all efforts" toward making a telegraph.

The deposition quotes "Professor Page's clear statements" of the two competing laws. Barlow's law comes out as "the conductibility was inversely proportionate to the square of the lengths, and directly as the diameters of the wires, (or as the square roots of their sections)." That is not Barlow's law, and if it were true, it would seem to bode ill for telegraphy. Morse doesn't give the full name of Dr. Page, but I assume he means Charles Grafton Page. Did Morse get it wrong? Did Page get it wrong? Did Shaffner or his typesetter transcribe it incorrectly? Morse doesn't cite the work by Page that he quotes from, and I haven't been able to find it by searching for "Barlow's law" on Google Scholar.

Later, in 1869, Morse's Examination of the Telegraphic Apparatus and the Processes in Telegraphy, pp. 9–10 quotes Barlow's law in the square-root version. Morse appears to have copied this from his deposition, with some editing. It still refers to "Dr. Page" without citing the work.

Does anyone know what writing by Page that is, or have access to it? That might clarify matters once and for all. The IU library appears to have only one work by Page, a debunking of psychomancy, which I assume isn't relevant.

—Ben Kovitz (talk) 23:14, 7 June 2012 (UTC)

More sources
As we find more sources and quotations regarding Barlow's law, please collect them here. (No need for conversation or signatures.) —Ben Kovitz (talk) 13:19, 8 June 2012 (UTC)

inverse square "History of Electric Telegraphs." Donald Mann (apparently). American Telegraph Magazine, Vol. 1, No. 2, p. 58. November, 1852.
 * "The law deduced by Barlow was, that the conductibility of wires of the same metal is inversely as the squares of the lengths, and directly as their diameters; but in view of experiments conducted with some care about the same time, the law was not generally received."

Also says that "Lenz's law" (same as Ohm's law) is generally received, based on experiments by six other scientists listed.

inverse square root "On the Electro-magnetic conducting Power of Wires of different Qualities and Dimensions and an Inquiry into the Efficiency of the Galvanometer for determining the Laws of its Variation." Peter Barlow. London and Edinburgh Philosophical Magazine, Vol. 11, pp. 1–11. July 1837.

Barlow tries to explain the discrepancy between his results and those of other scientists. He proposes that the other scientists used thicker wires and wires of different metals, which were capable of carrying more "fluid" than their batteries could supply. This would have thrown off their measurements of the wire's conductibility, since the readings on the galvanometer would only reflect the conductive capacity of the wire if that capacity were at least exceeded by the battery.


 * "On examining the errors arising from the assumption that the deflection varies inversely as the square root of the length, we find them amount on an average to about a degree the maximum exceeding 2º; and Mr Christie properly observes, that with such errors we cannot admit the law of the square roots These errors however, employing the law of the inverse of the length, would amount to 18º; and it is, therefore, very desirable to trace the cause of the discrepancy to its source."


 * "I doubt very much whether the deflection of a compass needle, either from the action of a single wire or from that of what is called the galvanometer is any certain measure of the relative conducting power of a wire without reference to the intensity and productive power of the battery employed whether our inquiries relate to their length diameters or natural qualities."

This appears to settle the matter of whether Barlow thought that the strength of the battery made no difference. Throughout the article, Barlow even carefully distinguishes between the battery's "intensity" and "productive power"—presumably corresponding to emf and peak current in modern terminology.


 * "To take the case of wires of the same kind and same length, it may perhaps be possible, where the productive power is great and the intensity inconsiderable, to employ a wire so small that it shall not be able to carry off the whole of the fluid the battery is competent to supply; and when this is the case a larger wire may be advantageously used, and if it does not greatly exceed the other, the power of conduction and the indications of the galvanometer may be consistent; but after employing a wire capable of conducting away the fluid as fast as it can be supplied by the battery, it will be useless to expect to produce a greater effect on the galvanometer by employing a greater wire."


 * "According to the idea I have advanced, the galvanometer only measures the conducting power of a metal while the wire is so small as to be insufficient to carry off the generated electricity; beyond that point it only measures the intensity of the battery. Now this intensity certainly varies with the length of the conductor."

inverse square root "On some of the Phænomena and Laws of Action of Voltaic Electricity and on the Construction of Voltaic Batteries." Christopher Binks. London and Edinburgh Philosophical Magazine, Vol. 11, p. 69. July–December 1837.
 * "Of such statements we have one recent instance among many in which the previously admitted law of the con of wires of different lengths is called in question by E Lenz who substitutes in its place another law of which the expression is that their conductibilities are in an inverse ratio to their lengths in contradiction to that formerly held their conducting power being inversely as the square root of their lengths I would submit that many other such laws are not yet decided since it has not been shown generally in what way provision was made to guard against the irregular operation of the exciting battery employed or that experimenters generally were aware that such irregularities prevailed or at least prevailed to so great an extent as has now been shown."

inverse square and inverse square root "On the Laws of the Conducting Powers of Wires of different Lengths and Diameters for Electricity." Emil Lenz. Taylor's Scientific Memoirs, Vol. 1, pp. 311–324 (1837).

This paper seems to be the one that settled the matter once and for all. It explains Ohm's work clearly, and goes through just about all previous research on this topic, showing how Ohm's law explains the varying results of all the experimenters. It's actually a transcript of a talk given in 1834—possibly with transcription errors, judging by the weirdness below and Lenz's reputation for thoroughness and rigor.
 * "Barlow and Cumming consider, according to their experiments, that the conductibility is inversely proportionate to the square of the lengths [wrong], and directly as the diameters of the wires (or as the square roots of the sections)."


 * "[Barlow] supposed that the conducting power was inversely as the square root of the length, and directly as the section [wrong]. Such a proportion may indeed easily be found between the resistance of the pile and the two wires employed for the experiment, that, according to Barlow's calculation, nearly such a law may be obtained. Had he employed, for instance, two wires of the same diameter, the lengths of which were $$m$$ and $$n$$, his view must have been confirmed, when the conducting resistance of the pile itself was reduced to that of one wire of the same diameter and the length:
 * $$\frac{m \sqrt{n} - n \sqrt{m}}{\sqrt{m} - \sqrt{n}}$$
 * "It is indeed not very probable that such would have always been the condition of the pile, but the experiments agree so little with the calculations performed according to his principle, that differences of 6º and 7º may be found in them."

This last remark seems very inaccurate. The worst discrepancy between Barlow's law and his observed compass deflections was 2º15'.

Is Barlow's law actually true?
After reading Barlow's 1837 paper, I am now wondering if Barlow's law might actually be true and consistent with modern theory. This is totally WP:OR, but I hope you'll forgive my asking about it here. (This question might even lead us to a source that ought to be summarized in the article.) Can someone more knowledgeable about electricity tell me, do conductors usually have a current-carrying capacity, above which they offer much greater resistance? Or was he actually describing a non-ohmic property of batteries (rather than a property of the wire)? —Ben Kovitz (talk) 13:47, 8 June 2012 (UTC)
 * I don't think there is anything non-ohmic going on here. Resistance does indeed increase with large currents: the shorter wires in the experiment will be subject to greater heating due to the larger current, hence the resistance will be higher and the current measured will be less than predicted with a linear resistance law.  It would be difficult to calculate the magnitude of this effect - to do so I would need to convert Barlow's units to modern ones and since he used compasses to measure current details such as the weight and magnetization of the compass needles would be needed.  However, my gut feeling is that it is not a very significant effect and I agree with Icek above that his error is entirely due to not taking into account the internal resistance of his source.  Ohm, on the other hand expressed his result for the current in the wires as;


 * $$ I = \frac {a}{b + l}$$


 * This is entirely consistent with the modern expression for current from a source with internal resistance:


 * $$ I = \frac {E}{r + R}$$


 * where r is assumed constant and R is assumed proportional to length.  Spinning Spark  16:28, 8 June 2012 (UTC)

Another Ohm-compatible theory: If Barlow had a high-voltage, low-power battery (I'm pretty sure he did), then at low resistances (like when your entire circuit consists of a battery shorted to itself through a long wire), the power $$P=I^2R$$ supplied by the battery is a constant. (Some basis for doubt: I don't have much experience shorting out batteries.) Solving for $$I$$ yields:
 * $$I=\sqrt\frac{P}{R}$$

Since resistance is really a linear function of distance, this would explain his inverse square-root law as well as the fact that the inverse-distance law diverged from observation the most at shorter distances. I think it also explains the direct variation with the square root of cross-sectional area, which he also observed, and which also contradicts Ohm's Law.

Assuming this is right, then Barlow's law was definitely false. He wasn't measuring the conductive capacity of the wire, but the reduction in current with increasing resistance under constant power. I'm not sure how to tell if this explanation is better or worse than "Barlow neglected internal resistance". The present explanation also neglects internal resistance. The correct explanation of Barlow's law may be that it resulted from two simultaneous sources of confusion: the low power of his battery (producing a genuine square-root law in most of the range he observed), and the unexpected phenomenon of internal resistance (not found because no observation prompted Barlow to consider equations of the form $$\frac{1}{k+d}$$).

It seems unlikely that once Ohm's Law was established, no one would point this out. Maybe Morse does; he seems to go to some lengths in his deposition to address Barlow's Law. Also, there is a much-cited paper by Lenz in Taylor's Scientific Memoirs (1834), which reviews all the experiments to date, and is said to explain the discrepancies between the results. I haven't found a copy yet; Google Books has it, but it's not freely available.

—Ben Kovitz (talk) 16:59, 8 June 2012 (UTC)


 * You cannot possibly model a battery as a constant power source. That would imply that the terminal voltage went infinite as the current went to zero.  It is only even approximately constant power for a small range of load resistances close to the battery internal resistance, and that is clearly not the case in Barlow's experiment.  Taylors Scientific Memoirs are available on the Internet Archive.  I'm not sure if this article is the one you are referring to (volume and date don't match), but it discusses this subject and basically agrees with me and Icek - its all about internal resistance.  Spinning  Spark  17:40, 8 June 2012 (UTC)


 * Thanks, Spinningspark! That is indeed the paper I'm looking for. If, after reading it, I don't grok the reason Barlow got a square-root law well enough to write something on the article page, I'll ask a more-detailed question about the upper limit on the power that a battery can supply and/or internal resistance. —Ben Kovitz (talk) 17:51, 8 June 2012 (UTC)


 * Since no one else has tackled this, I have added something to the article. Comments welcome.  Spinning  Spark  13:19, 10 March 2014 (UTC)


 * It's been a long time since I've looked at this article, but I just read what you added. I think that's exactly what the article needed. Now it seems complete, since it includes an explanation of Barlow's error—the missing piece of the puzzle. It also leads the reader to find out more about internal resistance, which turns out to be the "moral" of the story. Thanks! —Ben Kovitz (talk) 03:16, 21 August 2016 (UTC)

The internal resistance varied throughout the experiment
I read up a bit on the "Hare calorimotor": the battery that Barlow used. Contrary to my assumption above, it had low voltage but could supply a huge amount of current. However, it also drained very quickly. Two questions now:

1. Does this invalidate Icek's graph above, which assumes a constant internal resistance in all the measurements? Barlow's measurements of the power of the battery in his experiments to measure the effect of the diameter of the wire show that the power of the battery drained measurably each time he measured a new size of wire (except the last couple measurements with brass wires).

2. During the measurements of wires of varying lengths, the power of the battery as measured with Barlow's two-foot "standard wire" increased during most of the measurements, and started to decrease only toward the end of the experiment. Barlow remarks that he thought it odd that the measurements decreased instead of continuing to increase; I think it odd that they ever increased at all. Does anyone know what could have caused this? (He measured shorter wires toward the end of the experiment, so this would explain why they drained the battery more than the long wires; however, it doesn't explain why the power was increasing at all. Maybe the acid was heating up?)

—Ben Kovitz (talk) 16:27, 24 June 2012 (UTC)


 * Hare calorimotor is just a redirect at the moment. Can we give more details on his 'battery' (estimated voltage, chemistry, internal resistance) ? and his measurements - are they a single series (eg as Icek graphed above, left to right, 838 ft to 98 feet ) ? What different wires did he use: iron?, brass ? - Rod57 (talk) 12:52, 2 September 2018 (UTC)

"Conducting power" versus "electrical conductance"
There has been an impressive amount of research for this article but I think something which is unclear from the article is the distinction between "conducting power" as measured by Barlow (presumedly using some sort of galvanometer) and the concept of "electrical conductance" which is usually associated with Ohm's law and is denoted by the letter G.

To my understanding Barlow did not understand the linearity between current and voltage which is what Ohm's law is famous for and thus did not understand the concept of "electrical conductance" (i.e. G=I/V) for conductors. It is therefore misleading to use the symbol G and the concept of electrical conductance in describing Barlow's Law. Blm19732008 (talk) 15:57, 24 June 2012 (UTC)


 * Indeed Barlow did not understand Ohm's law. He didn't have our modern concept of conductance as the reciprocal of resistance. However, he and the other sources I've found called it "conductibility", and Barlow's law is usually compared with Ohm's law in regard to this very quantity that today we call "conductance". Barlow got wrong what Ohm got right, implying that they're comparable (or else there'd be no contrariety between them). Can you think of a way to do justice to the actual facts simply and clearly? —Ben Kovitz (talk) 16:08, 24 June 2012 (UTC)


 * Also, do you have any suggestion regarding removing or altering the sentence about Barlow not recognizing that stronger batteries would produce stronger effects? (In light of Barlow's remarks about this, especially in the second source under "More Sources" above.) —Ben Kovitz (talk) 16:08, 24 June 2012 (UTC)


 * My understanding from reading Barlow's original paper is that what he called "conducting power" is a measurement of current strength not conductance. These two concepts should not be confused especially since it seems to me to be at the crux of what differentiates Barlow's Law from Ohm's Law. Perhaps Barlow recognized some relationship between the current and the voltage but there is no indication that he understood the linear effect as implied by G=I/V. Incidently, there are many different (non-linear) ways that current can depend on voltage in materials other than metallic electrical conductors. For example, in semiconductors and metal-insulator junctions the linearity between current and voltage is not correct (i.e. even Ohm's Law is not generally true for all materials and there are other "Laws" in relation to space charge effects such as Child's Law and the Mott-Gurney Law). I think the article would be more accurate to use a neutral symbol representing current strength (or deflection of a galvanometer as described by Barlow) rather than "G" or "electrical conductance". The way the article is written now seems to imply Barlow understood the modern concept of electrical conductance (which he did not).Blm19732008 (talk) 17:22, 24 June 2012 (UTC)


 * Incidently Barlow may be getting somewhat of a raw deal. At the time he published his original paper it was apparently not recognized that there was any dependence at all between current in a telegraph wire and the length of a wire and thus many people may have assummed that telegraph wires of hundreds or thousands of miles long could exist with no problem. Barlow CORRECTLY proved that there was a dependence between telegraph wire length and current in the wire (although the precise mathematical form of his result was not correct). So he was RIGHT that there was a significant problem with long distance telegraphy (and YES the correct dependence of G = kA/L makes the problem even WORSE). However, ultimately it was not an insurmountable problem especially when one understood Ohm's Law stating the linear relationship between voltage and current allows technical solutions such as high-intensity batteries and repeaters which could amplify the current over long distances.Blm19732008 (talk) 18:25, 24 June 2012 (UTC)


 * It is noteworthy that Ohm did not express his law in terms of G or R either. Both laws have been restated in this article in a form directly comparable to the modern statement of Ohm's law.  Spinning  Spark  23:47, 24 June 2012 (UTC)


 * I replaced electrical conductance "G" with current "I" for both Barlow's and Ohm's Law. I think this is a better basis for comparison since Barlow never determined electrical conductance (i.e. G=I/V) but rather measured the deflection of a compass needle used as a galvanometer to measure current. Blm19732008 (talk) 17:34, 27 June 2012 (UTC)

Keeping voltage constant
On the sentence about Barlow keeping voltage constant, User:ChristianSmay removed the citation needed tag and added this source. While that is an interesting historical paper, it is not about Barlow, it's about Henry's work. It mentions Barlow's result, but does not go into the details of his experiment. If you think I am wrong, please give the page number and passage that supports this claim. SpinningSpark 08:18, 30 March 2020 (UTC)

That source does make the interesting comment that Barlow was right that the electromanetic telegraph was impossible, but because the technology of his day was not up to it, not because the law was wrong. SpinningSpark 08:52, 30 March 2020 (UTC)