Part 3 (2/2)

Every bent row of sixteen numbers, as shown by the diagonal lines in the figure, makes 2056.

If a square hole be cut in a piece of paper, so as to show through it just sixteen of the little squares, and the paper be laid on the magic square, then, wherever the paper is placed, the sum of the sixteen numbers visible through the hole will be 2056.

[Ill.u.s.tration:

200 217 232 249 8 25 40 57 72 89 104 121 136 153 168 185 58 39 26 7 250 231 218 199 186 167 154 135 122 103 90 71 198 219 230 251 6 27 38 59 70 91 102 123 134 155 166 187 60 37 28 5 252 229 220 197 188 165 156 133 124 101 92 69 201 216 233 248 9 24 41 56 73 88 105 120 137 152 169 184 55 42 23 10 247 234 215 202 183 170 151 138 119 106 87 74 203 214 235 246 11 22 43 54 75 86 107 118 139 150 171 182 53 44 21 12 245 236 213 204 181 172 149 140 117 108 85 76 205 212 237 244 13 20 45 52 77 84 109 116 141 148 173 180 51 46 19 14 243 238 211 206 179 174 147 142 115 110 83 78 207 210 239 242 15 18 47 50 79 82 111 114 143 146 175 178 49 48 17 16 241 240 209 208 177 176 145 144 113 112 81 80 196 221 228 253 4 29 36 61 68 93 100 125 132 157 164 189 62 35 30 3 254 227 222 195 190 163 158 131 126 99 94 67 194 223 226 255 2 31 34 63 66 95 98 127 130 159 162 191 64 33 32 1 256 225 224 193 192 161 160 129 128 97 96 65 ]

In 1754 war with France appeared to be again imminent, and a Congress of Commissioners from the several colonies was arranged for. Of course, Franklin was one of the representatives of Pennsylvania, and was also one of the members who independently drew up a plan for the union of all the colonies under one government, for defensive and other general purposes, and his was the plan finally approved by Congress for the union, though it was not accepted by the a.s.semblies or by the English Government, being regarded by the former as having too much of the _prerogative_ in it, by the latter as being too _democratic_. Franklin wrote respecting this scheme: ”The different and contrary reasons of dislike to my plan makes me suspect that it was really the true medium; and I am still of opinion that it would have been happy for both sides of the water if it had been adopted. The colonies, so united, would have been sufficiently strong to have defended themselves; there would then have been no need of troops from England; of course, the subsequent pretence for taxing America, and the b.l.o.o.d.y contest it occasioned, would have been avoided.”

With this war against France began the struggle of the a.s.semblies and the proprietaries on the question of taxing the estates of the latter.

The governors received strict instructions to approve no bills for the raising of money for the purposes of defence, unless the estates of the proprietaries were specially exempted from the tax. The a.s.sembly of Pennsylvania resolved to contribute 10,000 to a.s.sist the Government of Ma.s.sachusetts Bay in an attack upon Crown Point, but the governor refused his a.s.sent to the bill for raising the money. At this juncture Franklin proposed a scheme by which the money could be raised without the consent of the governor. His plan was successful, and the difficulty was surmounted for the time, but was destined to recur again and again during the progress of the war.

The British Government, not approving of the scheme of union, whereby the colonies might have defended themselves, sent General Braddock to Virginia, with two regiments of regular troops. On their arrival they found it impossible to obtain waggons for the conveyance of their baggage, and the general commissioned Franklin to provide them in Pennsylvania. By giving his private bond for their safety, Franklin succeeded in engaging one hundred and fifty four-horse waggons, and two hundred and fifty-nine pack-horses. His modest warnings against Indian ambuscades were disregarded by the general, the little army was cut to pieces, and the remainder took to flight, sacrificing the whole of their baggage and stores. Franklin was never fully recouped by the British Government for the payments he had to make on account of provisions which the general had instructed him to procure for the use of the army.

After this, Franklin appeared for some time in a purely military capacity, having yielded to the governor's persuasions to undertake the defence of the north-western frontier, to raise troops, and to build a line of forts. After building and manning three wooden forts, he was recalled by the a.s.sembly, whose relations with the governor had become more and more strained. At length the a.s.sembly determined to send Franklin to England, to present a pet.i.tion to the king respecting the conduct of the proprietaries, viz. Richard and Thomas Penn, the successors of William Penn. A bill had been framed by the House to provide 60,000 for the king's use in the defence of the province.

This the governor refused to pa.s.s, because the proprietary estates were not exempted from the taxation. The pet.i.tion to the king was drawn up, and Franklin's baggage was on board the s.h.i.+p which was to convey him to England, when General Lord Loudon endeavoured to make an arrangement between the parties. The governor pleaded his instructions, and the bond he had given for carrying them out, and the a.s.sembly was prevailed upon to reconstruct the bill in accordance with the governor's wishes. This was done under protest; in the mean time Franklin's s.h.i.+p had sailed, carrying his baggage. After a great deal of unnecessary delay on account of the general's inability to decide upon the despatch of the packet-boats, Franklin at last got away from New York, and, having narrowly escaped s.h.i.+pwreck off Falmouth, he reached London on July 27, 1757.

On arriving in London, Franklin was introduced to Lord Granville, who told him that the king's instructions were laws in the colonies.

Franklin replied that he had always understood that the a.s.semblies made the laws, which then only required the king's consent. ”I recollected that, about twenty years before, a clause in a bill brought into Parliament by the Ministry had proposed to make the king's instructions laws in the colonies, but the clause was thrown out by the Commons, for which we adored them as our friends and the friends of liberty, till, by their conduct towards us in 1765, it seem'd that they had refus'd that point of sovereignty to the king only that they might reserve it for themselves.” A meeting was shortly afterwards arranged between Franklin and the proprietaries at Mr. T.

Penn's house; but their views were so discordant that, after some discussion, Franklin was requested to give them in writing the heads of his complaints, and the whole question was submitted to the opinion of the attorney- and solicitor-general. It was nearly a year before this opinion was given. The proprietaries then communicated directly with the a.s.sembly, but in the mean while Governor Denny had consented to a bill for raising 100,000 for the king's use, in which it was provided that the proprietary estates should be taxed with the others.

When this bill reached England, the proprietaries determined to oppose its receiving the royal a.s.sent. Franklin engaged counsel on behalf of the a.s.sembly, and on his undertaking that the a.s.sessment should be fairly made between the estates of the proprietaries and others, the bill was allowed to pa.s.s.

By this time Franklin's career as a scientific investigator was practically at an end. Political business almost completely occupied his attention, and in one sense the diplomatist replaced the philosopher. His public scientific career was of short duration. It may be said to have begun in 1746, when Mr. Peter Collinson presented an ”electrical tube” to the Library Company in Philadelphia, which was some time after followed by a present of a complete set of electrical apparatus from the proprietaries, but by 1755 Franklin's time was so much taken up by public business that there was very little opportunity for experimental work. Throughout his life he frequently expressed in his letters his strong desire to return to philosophy, but the opportunity never came, and when, at the age of eighty-two, he was liberated from public duty, his strength was insufficient to enable him to complete even his autobiography.

It was on a visit to Boston in 1746 that Franklin met with Dr. Spence, a Scotchman, who exhibited some electrical experiments. Soon after his return to Philadelphia the tube arrived from Mr. Collinson, and Franklin acquired considerable dexterity in its use. His house was continually full of visitors, who came to see the experiments, and, to relieve the pressure upon his time, he had a number of similar tubes blown at the gla.s.s-house, and these he distributed to his friends, so that there were soon a number of ”performers” in Philadelphia. One of these was Mr. Kinnersley, who, having no other employment, was induced by Franklin to become an itinerant lecturer. Franklin drew up a scheme for the lectures, and Kinnersley obtained several well-constructed instruments from Franklin's rough and home-made models. Kinnersley and Franklin appear to have worked together a good deal, and when Kinnersley was travelling on his lecture tour, each communicated to the other the results of his experiments. Franklin sent his papers to Mr. Collinson, who presented them to the Royal Society, but they were not at first judged worthy of a place in the ”Transactions.” The paper on the ident.i.ty of lightning and electricity was sent to Dr. Mitch.e.l.l, who read it before the Royal Society, when it ”was laughed at by the connoisseurs.” The papers were subsequently published in a pamphlet, but did not at first receive much attention in England. On the recommendation of Count de Buffon, they were translated into French.

The Abbe Nollet, who had previously published a theory of his own respecting electricity, wrote and published a volume of letters defending his theory, and denying the accuracy of some of Franklin's experimental results. To these letters Franklin made no reply, but they were answered by M. le Roy. M. de Lor undertook to repeat in Paris all Franklin's experiments, and they were performed before the king and court. Not content with the experiments which Franklin had actually performed, he tried those which had been only suggested, and so was the first to obtain electricity from the clouds by means of the pointed rod. This experiment produced a great sensation everywhere, and was afterwards repeated by Franklin at Philadelphia. Franklin's papers were translated into Italian, German, and Latin; his theory met with all but universal acceptance, and great surprise was expressed that his papers had excited so little interest in England. Dr. Watson then drew up a summary of all Franklin's papers, and this was published in the ”Philosophical Transactions;” Mr. Canton verified the experiment of procuring electricity from the clouds by means of a pointed rod, and the Royal Society awarded to Franklin the Copley Medal for 1753, which was conveyed to him by Governor Denny.

We must now give a short account of Franklin's contributions to electrical science.

”The first is the wonderful effect of pointed bodies, both in _drawing off_ and _throwing off_ the electrical fire.”

It will be observed that this statement is made in the language of the _one_-fluid theory, of which Franklin may be regarded as the author.

This theory will be again referred to presently. Franklin electrified a cannon-ball so that it repelled a cork. On bringing near it the point of a bodkin, the repulsion disappeared. A blunt body had to be brought near enough for a spark to pa.s.s in order to produce the same effect. ”To prove that the electrical fire is _drawn off_ by the point, if you take the blade of the bodkin out of the wooden handle, and fix it in a stick of sealing-wax, and then present it at the distance aforesaid, or if you bring it very near, no such effect follows; but sliding one finger along the wax till you touch the blade, and the ball flies to the shot immediately. If you present the point in the dark, you will see, sometimes at a foot distance or more, a light gather upon it like that of a fire-fly or glow-worm; the less sharp the point, the nearer you must bring it to observe the light; and at whatever distance you see the light, you may draw off the electrical fire, and destroy the repelling.”

By laying a needle upon the shot, Franklin showed ”that points will _throw off_ as well as _draw off_ the electrical fire.” A candle-flame was found to be equally efficient with a sharp point in drawing off the electricity from a charged conductor. The effect of the candle-flame Franklin accounted for by supposing the particles separated from the candle to be first ”attracted and then repelled, carrying off the electric matter with them.” The effect of points is a direct consequence of the law of electrical repulsion. When a conductor is electrified, the density of the electricity is greatest where the curvature is greatest. Thus, if a number of spheres are electrified from the same source, the density of the electricity on the different spheres will vary inversely as their diameters. The force tending to drive the electricity off a conductor is everywhere proportional to the density, and hence in the case of the spheres will be greatest for the smallest sphere. On this principle, the density of electricity on a perfectly sharp point, if such could exist, on a charged conductor, would be infinite and the force tending to drive it off would be infinite also. Hence a moderately sharp point is sufficient to dissipate the electricity from a highly charged conductor, or to neutralize it if the point is connected to earth and brought near the conductor so as to be electrified by induction.

Franklin next found that, if the person rubbing the electric tube stood upon a cake of resin, and the person taking the charge from the tube stood also on an insulating stand, a stronger spark would pa.s.s between these two persons than between either of them and the earth; that, after the spark had pa.s.sed, neither person was electrified, though each had appeared electrified before. These experiments suggested the idea of _positive_ and _negative_ electrification; and Franklin, regarding the electric fluid as corresponding to positive electrification, remarked that ”you may circulate it as Mr. Watson has shown; you may also acc.u.mulate or subtract it upon or from any body, as you connect that body with the rubber or with the receiver, the common stock being cut off.” Thus Franklin regarded electricity as a fluid, of which everything in its normal state possesses a certain amount; that, by appropriate means, some of the fluid may be removed from one body and given to another. The former is then electrified negatively, the latter positively, and all processes by which bodies are electrified consist in the removal of electricity from one body or system and giving it to another. He regarded the electric fluid as repelling itself and attracting matter. aepinus afterwards added the supposition that matter, when devoid of electricity, is self-repulsive, and thus completed the ”one-fluid theory,” and accounted for the repulsion observed between negatively electrified bodies.

It had been usual to employ water for the interior armatures of Leyden jars, or phials, as they were then generally called. Franklin subst.i.tuted granulated lead for the water, thereby improving the insulation by keeping the gla.s.s dry. With these phials he contrived many ingenious experiments, and imitated lightning by discharging them through the gilding of a mirror or the gold lines on the cover of a book. He found that the inner and outer armatures of his Leyden jars were oppositely electrified. ”Here we have a bottle containing at the same time a _plenum_ of electrical fire and a _vacuum_ of the same fire; and yet the equilibrium cannot be restored between them but by a communication _without_! though the plenum presses violently to expand, and the hungry vacuum seems to attract as violently in order to be filled.” The charging of Leyden jars by cascade, that is by insulating all the jars except the last, connecting the outer armature of the first with the inner armature of the second, and so on throughout the series, was well understood by Franklin, and he knew too that by this method the extent to which each jar could be charged from a given source varied inversely as the number of jars. The discharge of the Leyden jar by alternate contacts was also carried out by him; and he found that, if the jar is first placed on an insulating stand, it may be held by the hook (or k.n.o.b) without discharging it.

Franklin, in fact, appears to have known almost as much about the Leyden jar as is known to-day. He found that, when the armatures were removed from a jar, no discharge would pa.s.s between them, but when a fresh pair of armatures were supplied to the gla.s.s, the jar could be discharged. ”We are of opinion that there is really no more electrical fire in the phial after what is called its _charging_ than before, nor less after its _discharging_; excepting only the small spark that might be given to and taken from the non-electric matter, if separated from the bottle, which spark may not be equal to a five-hundredth part of what is called the explosion.

”The phial will not suffer what is called a _charging_ unless as much fire can go out of it one way as is thrown in by another.

”When a bottle is charged in the common way, its _inside_ and _outside_ surfaces stand ready, the one to give fire by the hook, the other to receive it by the coating; the one is full and ready to throw out, the other empty and extremely hungry; yet, as the first will not _give out_ unless the other can at the same time _receive in_, so neither will the latter receive in unless the first can at the same time give out. When both can be done at once, it is done with inconceivable quickness and violence.”

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