3.9: Conclusions
- Identify successful strategies for writing conclusions
Conclusions
Try to avoid beginning your conclusion with the words “In conclusion”! This section will help you consider ways to write so that readers can clearly see you are ending your piece without your having to announce it in such blunt terms.
A satisfying conclusion allows a reader to finish your paper with a clear understanding of the points you made and hopefully even a new perspective on the topic. As the writer, consider who your readers are and the conclusions you want them to reach.
For example, is your reader relatively new to your topic? If so, you may want to restate your main points for emphasis as a way of starting the conclusion. (Don’t literally use the same sentence(s) as in your introduction, but come up with a comparable way of restating your thesis.)
We want to move, however, beyond the traditional re-statement of the thesis that you learned when you were mastering the five-paragraph-essay format. Ideally, in your paper you have just taken your reader through a strong, clear argument in which you have provided evidence for your perspective. You want to conclude by pointing out the importance or worthiness of your topic and argument. You might describe how the world would be different, or people’s lives would be changed, if they ascribed to your perspective, plan, or idea.
Ask yourself the “So what?” question. Your reader has read through your essay and conclusion. Now, what do you want the reader to think?
What is the “So, what?” or take away from this conclusion?
- In a society fixated on the latest and smartest digital technology, a consumer can easily become confused by the countless options and specifications. The ever-changing state of digital technology challenges consumers with its updates and add-ons and expanding markets and incompatible formats and restrictions–a fact that is complicated by salesmen who want to sell them anything. In a world that is increasingly driven by instant gratification, it’s easy for people to buy the first thing they see. The solution for many people should be to avoid buying on impulse. Consumers should think about what they really need, not what is advertised.
Notice how clearly the final call to action here–insisting that consumer think before they buy instead of being driven by advertising—tells the reader (a consumer) what to take away from this discussion of how consumption is shaped and distorted by ever-changing technology, instant gratification, and relentless advertising.
You might also point out the limitations of the present understanding of your topic, suggesting or recommending future action, study, or research that needs to be done. A strong conclusion does not need to suggest only conclusions or answers; you may, at this stage in your writing, suggest new questions or consideration for further discussion. Note, however, that your conclusion is not the place to question or raise counter-points to your argument.
Below is a list that captures these ideas and other potential goals of a conclusion. Conclusions might
- Summarize the argument in fresh language (especially in longer pieces of writing)
- “Bookend” a story or idea that started in the introduction
- Include an emotional appeal, with which you (explicitly or implicitly) connect the “logic” of the argument to a more passionate reason intended to sway the reader
- Issue a call to action
- Make some sort of prediction or assessment about the future of your topic or future research that needs to be done on the topic
Often, a conclusion will work in tandem with an introduction, having some kind of “call back” element to remind your reader of the powerful opening you provided.
Remember that introductions and conclusions are not independent sections of your writing. They should work together and fit with the rest of your paragraphs or sections. For example, a conclusion should pick up from the final body paragraph and feature an effective transition. Likewise, your introduction should set up the direction of your writing and lead nicely into the first body paragraph.
Consider the “Declaration of Independence” below. Without reading every word of the text, focus on how the introduction and conclusion work together to open and close the piece so strongly.
In Congress, July 4, 1776.
The unanimous Declaration of the thirteen United States of America, When in the Course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another, and to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature’s God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.
We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.–That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, –That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness. Prudence, indeed, will dictate that Governments long established should not be changed for light and transient causes; and accordingly all experience hath shewn, that mankind are more disposed to suffer, while evils are sufferable, than to right themselves by abolishing the forms to which they are accustomed. But when a long train of abuses and usurpations, pursuing invariably the same Object evinces a design to reduce them under absolute Despotism, it is their right, it is their duty, to throw off such Government, and to provide new Guards for their future security.–Such has been the patient sufferance of these Colonies; and such is now the necessity which constrains them to alter their former Systems of Government. The history of the present King of Great Britain is a history of repeated injuries and usurpations, all having in direct object the establishment of an absolute Tyranny over these States. To prove this, let Facts be submitted to a candid world.
- He has refused his Assent to Laws, the most wholesome and necessary for the public good.
- He has forbidden his Governors to pass Laws of immediate and pressing importance, unless suspended in their operation till his Assent should be obtained; and when so suspended, he has utterly neglected to attend to them.
- He has refused to pass other Laws for the accommodation of large districts of people, unless those people would relinquish the right of Representation in the Legislature, a right inestimable to them and formidable to tyrants only.
- He has called together legislative bodies at places unusual, uncomfortable, and distant from the depository of their public Records, for the sole purpose of fatiguing them into compliance with his measures.
- He has dissolved Representative Houses repeatedly, for opposing with manly firmness his invasions on the rights of the people.
- He has refused for a long time, after such dissolutions, to cause others to be elected; whereby the Legislative powers, incapable of Annihilation, have returned to the People at large for their exercise; the State remaining in the mean time exposed to all the dangers of invasion from without, and convulsions within.
- He has endeavoured to prevent the population of these States; for that purpose obstructing the Laws for Naturalization of Foreigners; refusing to pass others to encourage their migrations hither, and raising the conditions of new Appropriations of Lands.
- He has obstructed the Administration of Justice, by refusing his Assent to Laws for establishing Judiciary powers.
- He has made Judges dependent on his Will alone, for the tenure of their offices, and the amount and payment of their salaries.
- He has erected a multitude of New Offices, and sent hither swarms of Officers to harrass our people, and eat out their substance.
- He has kept among us, in times of peace, Standing Armies without the Consent of our legislatures.
- He has affected to render the Military independent of and superior to the Civil power.
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He has combined with others to subject us to a jurisdiction foreign to our constitution, and unacknowledged by our laws; giving his Assent to their Acts of pretended Legislation:
- For Quartering large bodies of armed troops among us:
- For protecting them, by a mock Trial, from punishment for any Murders which they should commit on the Inhabitants of these States:
- For cutting off our Trade with all parts of the world:
- For imposing Taxes on us without our Consent:
- For depriving us in many cases, of the benefits of Trial by Jury:
- For transporting us beyond Seas to be tried for pretended offences
- For abolishing the free System of English Laws in a neighbouring Province, establishing therein an Arbitrary government, and enlarging its Boundaries so as to render it at once an example and fit instrument for introducing the same absolute rule into these Colonies:
- For taking away our Charters, abolishing our most valuable Laws, and altering fundamentally the Forms of our Governments:
- For suspending our own Legislatures, and declaring themselves invested with power to legislate for us in all cases whatsoever.
- He has abdicated Government here, by declaring us out of his Protection and waging War against us.
- He has plundered our seas, ravaged our Coasts, burnt our towns, and destroyed the lives of our people.
- He is at this time transporting large Armies of foreign Mercenaries to compleat the works of death, desolation and tyranny, already begun with circumstances of Cruelty & perfidy scarcely paralleled in the most barbarous ages, and totally unworthy the Head of a civilized nation.
- He has constrained our fellow Citizens taken Captive on the high Seas to bear Arms against their Country, to become the executioners of their friends and Brethren, or to fall themselves by their Hands.
- He has excited domestic insurrections amongst us, and has endeavoured to bring on the inhabitants of our frontiers, the merciless Indian Savages, whose known rule of warfare, is an undistinguished destruction of all ages, sexes and conditions.
In every stage of these Oppressions We have Petitioned for Redress in the most humble terms: Our repeated Petitions have been answered only by repeated injury. A Prince whose character is thus marked by every act which may define a Tyrant, is unfit to be the ruler of a free people.
Nor have We been wanting in attentions to our British brethren. We have warned them from time to time of attempts by their legislature to extend an unwarrantable jurisdiction over us. We have reminded them of the circumstances of our emigration and settlement here. We have appealed to their native justice and magnanimity, and we have conjured them by the ties of our common kindred to disavow these usurpations, which, would inevitably interrupt our connections and correspondence. They too have been deaf to the voice of justice and of consanguinity. We must, therefore, acquiesce in the necessity, which denounces our Separation, and hold them, as we hold the rest of mankind, Enemies in War, in Peace Friends.
We, therefore, the Representatives of the United States of America, in General Congress, Assembled, appealing to the Supreme Judge of the world for the rectitude of our intentions, do, in the Name, and by Authority of the good People of these Colonies, solemnly publish and declare, That these United Colonies are, and of Right ought to be Free and Independent States; that they are Absolved from all Allegiance to the British Crown, and that all political connection between them and the State of Great Britain, is and ought to be totally dissolved; and that as Free and Independent States, they have full Power to levy War, conclude Peace, contract Alliances, establish Commerce, and to do all other Acts and Things which Independent States may of right do. And for the support of this Declaration, with a firm reliance on the protection of divine Providence, we mutually pledge to each other our Lives, our Fortunes and our sacred Honor.
Contributors and Attributions
- Introductions and Conclusions. Authored by : Jay Jordan. . Provided by : The University of Utah University Writing Program. Project : Open2010. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
- Image of painted hands. Authored by : stokpic. Provided by : Pixabay. Located at : https://pixabay.com/photos/hands-world-map-global-earth-600497/ . License : Other . License Terms : https://pixabay.com/service/terms/#license
- Sample Paragraph. Provided by : Minnesota Libraries Publishing. Located at : https://open.lib.umn.edu/writingforsuccess/chapter/9-4-writing-introductory-and-concluding-paragraphs/ . Project : Writing For Success. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike


9.3A: mRNA Processing
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Eukaryotic pre-mRNA receives a 5′ cap and a 3′ poly (A) tail before introns are removed and the mRNA is considered ready for translation.
LEARNING OBJECTIVES
Outline the steps of pre-mRNA processing
Key Takeaways
Pre-mRNA Processing
The eukaryotic pre-mRNA undergoes extensive processing before it is ready to be translated. The additional steps involved in eukaryotic mRNA maturation create a molecule with a much longer half-life than a prokaryotic mRNA. Eukaryotic mRNAs last for several hours, whereas the typical E. coli mRNA lasts no more than five seconds.
Pre-mRNAs are first coated in RNA-stabilizing proteins; these protect the pre-mRNA from degradation while it is processed and exported out of the nucleus. The three most important steps of pre-mRNA processing are the addition of stabilizing and signaling factors at the 5′ and 3′ ends of the molecule, and the removal of intervening sequences that do not specify the appropriate amino acids. In rare cases, the mRNA transcript can be “edited” after it is transcribed.
5′ Capping
While the pre-mRNA is still being synthesized, a 7-methylguanosine cap is added to the 5′ end of the growing transcript by a 5′-to-5′ phosphate linkage. This moiety protects the nascent mRNA from degradation. In addition, initiation factors involved in protein synthesis recognize the cap to help initiate translation by ribosomes.
3′ Poly-A Tail
While RNA Polymerase II is still transcribing downstream of the proper end of a gene, the pre-mRNA is cleaved by an endonuclease-containing protein complex between an AAUAAA consensus sequence and a GU-rich sequence. This releases the functional pre-mRNA from the rest of the transcript, which is still attached to the RNA Polymerase. An enzyme called poly (A) polymerase (PAP) is part of the same protein complex that cleaves the pre-mRNA and it immediately adds a string of approximately 200 A nucleotides, called the poly (A) tail, to the 3′ end of the just-cleaved pre-mRNA. The poly (A) tail protects the mRNA from degradation, aids in the export of the mature mRNA to the cytoplasm, and is involved in binding proteins involved in initiating translation.
Poly (A) Polymerase adds a 3′ poly (A) tail to the pre-mRNA. : The pre-mRNA is cleaved off the rest of the growing transcript before RNA Polymerase II has stopped transcribing. This cleavage is done by an endonuclease-containing protein complex that binds to an AAUAAA sequence upstream of the cleavage site and to a GU-rich sequence downstream of the cut site. Immediately after the cleavage, Poly (A) Polymerase (PAP), which is also part of the protein complex, catalyzes the addition of up to 200 A nucleotides to the 3′ end of the just-cleaved pre-mRNA.
Pre-mRNA Splicing
Eukaryotic genes are composed of exons, which correspond to protein-coding sequences ( ex -on signifies that they are ex pressed), and intervening sequences called introns ( int -ron denotes their int ervening role), which may be involved in gene regulation, but are removed from the pre-mRNA during processing. Intron sequences in mRNA do not encode functional proteins.
Discovery of Introns
The discovery of introns came as a surprise to researchers in the 1970s who expected that pre-mRNAs would specify protein sequences without further processing, as they had observed in prokaryotes. The genes of higher eukaryotes very often contain one or more introns. While these regions may correspond to regulatory sequences, the biological significance of having many introns or having very long introns in a gene is unclear. It is possible that introns slow down gene expression because it takes longer to transcribe pre-mRNAs with lots of introns. Alternatively, introns may be nonfunctional sequence remnants left over from the fusion of ancient genes throughout evolution. This is supported by the fact that separate exons often encode separate protein subunits or domains. For the most part, the sequences of introns can be mutated without ultimately affecting the protein product.
Intron Processing
All introns in a pre-mRNA must be completely and precisely removed before protein synthesis. If the process errs by even a single nucleotide, the reading frame of the rejoined exons would shift, and the resulting protein would be dysfunctional. The process of removing introns and reconnecting exons is called splicing. Introns are removed and degraded while the pre-mRNA is still in the nucleus. Splicing occurs by a sequence-specific mechanism that ensures introns will be removed and exons rejoined with the accuracy and precision of a single nucleotide. The splicing of pre-mRNAs is conducted by complexes of proteins and RNA molecules called spliceosomes.
Each spliceosome is composed of five subunits called snRNPs (for small nuclear ribonucleoparticles, and pronounced “snurps”.) Each snRNP is itself a complex of proteins and a special type of RNA found only in the nucleus called snRNAs (small nuclear RNAs). Spliceosomes recognize sequences at the 5′ end of the intron because introns always start with the nucleotides GU and they recognize sequences at the 3′ end of the intron because they always end with the nucleotides AG. The spliceosome cleaves the pre-mRNA’s sugar phosphate backbone at the G that starts the intron and then covalently attaches that G to an internal A nucleotide within the intron. Then the spliceosme connects the 3′ end of the first exon to the 5′ end of the following exon, cleaving the 3′ end of the intron in the process. This results in the splicing together of the two exons and the release of the intron in a lariat form.
Key Points
- A 7-methylguanosine cap is added to the 5′ end of the pre-mRNA while elongation is still in progress. The 5′ cap protects the nascent mRNA from degradation and assists in ribosome binding during translation.
- A poly (A) tail is added to the 3′ end of the pre-mRNA once elongation is complete. The poly (A) tail protects the mRNA from degradation, aids in the export of the mature mRNA to the cytoplasm, and is involved in binding proteins involved in initiating translation.
- Introns are removed from the pre-mRNA before the mRNA is exported to the cytoplasm.
Key Terms
- intron : a portion of a split gene that is included in pre-RNA transcripts but is removed during RNA processing and rapidly degraded
- moiety : a specific segment of a molecule
- spliceosome : a dynamic complex of RNA and protein subunits that removes introns from precursor mRNA


11.0: Prelude to Mendel's Experiments and Heredity
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Genetics is the study of heredity. Johann Gregor Mendel set the framework for genetics long before chromosomes or genes had been identified, at a time when meiosis was not well understood. Mendel selected a simple biological system and conducted methodical, quantitative analyses using large sample sizes. Because of Mendel’s work, the fundamental principles of heredity were revealed. We now know that genes, carried on chromosomes, are the basic functional units of heredity with the capability to be replicated, expressed, or mutated. Today, the postulates put forth by Mendel form the basis of classical, or Mendelian, genetics. Not all genes are transmitted from parents to offspring according to Mendelian genetics, but Mendel’s experiments serve as an excellent starting point for thinking about inheritance.


1.7.7: Compressions- Isentropic- Salt Solutions
An extensive literature describes the isentropic compressibilities of salt solutions prompted by earlier studies by Passynski [1] described by Owen [2].
The isentropic compression of a given aqueous salt solution \(\mathrm{K}_{\mathrm{s}}(\mathrm{aq})\) is determined using the Newton-Laplace Equation in conjunction with speeds of sound and densities. An apparent molar compression of salt \(j \phi\left(K_{s} ; \text { def }\right)\) is calculated using equation (a).
\[\mathrm{K}_{\mathrm{S}}\left(\mathrm{aq} ; \mathrm{w}_{1}=1 \mathrm{~kg}\right)=\left(1 / \mathrm{M}_{1}\right) \, \mathrm{K}_{\mathrm{S} 1}^{*}(\ell)+\mathrm{m}_{\mathrm{j}} \, \phi\left(\mathrm{K}_{\mathrm{s}} ; \operatorname{def}\right) \nonumber \]
Here \(\mathrm{K}_{\mathrm{S} 1}^{*}(\ell)\) is the isentropic compression of the solvent at the same \(\mathrm{T}\) and \(\mathrm{p}\). For salt solutions, particularly aqueous salt solutions, the dependence of \(\phi\left(\mathrm{K}_{\mathrm{Sj}} ; \text { def }\right)\) on the molality of the salt is generally examined in the light of equations describing the role of ion-ion interactions [3; see also reference 4]. For dilute salt solutions, equation (b) forms the basis for examining the dependence of \(\phi\left(\mathrm{K}_{\mathrm{Sj}} ; \text { def }\right)\) on \(\left(\mathrm{m}_{\mathrm{j}}\right)^{1 / 2}\) where \(\mathrm{m}_{j}\) is the molality of the salt-\(j\).
\[\text { Then, } \phi\left(\mathrm{K}_{\mathrm{Sj}} ; \text { def }\right)=\phi\left(\mathrm{K}_{\mathrm{Sj}} ; \text { def }\right)^{\infty}+\mathrm{S}_{\mathrm{KS}} \,\left(\mathrm{m}_{\mathrm{j}} / \mathrm{m}^{0}\right)^{1 / 2} \nonumber \]
The form of the equation (b) has all the hallmarks of a pattern required by the \(\mathrm{DHLL}\). In practice \(\mathrm{S}_{\mathrm{KS}}\) cannot be calculated because the required isentropic dependence of the relative permittivity of the solvent on pressure is generally not known. However a plot is obtained using equation (b) yielding an estimate of \(\phi\left(\mathrm{K}_{\mathrm{Sj}} ; \operatorname{def}\right)^{\infty}\).
For a large range of 1:1 salts \(\phi\left(K_{S_{j}} ; \operatorname{def}\right)^{\infty}\) is negative, a pattern attributed to electrostriction of neighbouring solvent molecules by electric charges on the ions [3-10]. \(\phi\left(\mathrm{K}_{\mathrm{S}_{j}} ; \text { def }\right)^{\infty}\) is more negative for solutions in \(\mathrm{D}_{2}\mathrm{O}\) than in \(\mathrm{H}_{2}\mathrm{O}\) as a consequence of more intense electrostriction in \(\mathrm{D}_{2}\mathrm{O}\) [5]. Further on the basis of the Desnoyers-Philip Equation, the difference \(\phi\left(\mathrm{K}_{\mathrm{Sj}} ; \mathrm{def}\right)^{\infty}-\phi\left(\mathrm{K}_{\mathrm{T}_{\mathrm{j}}}\right)^{\infty}\) is small but not negligible, amounting to approx. 10%. For alkylammonium ions in aqueous solutions \(\phi\left(\mathrm{K}_{\mathrm{Sj}} ; \operatorname{def}\right)^{\infty}\) decreases with increase in the hydrophobic character, matching a general increase in \(\phi\left(V_{j}\right)^{\infty}\) [11]. Group and ionic contributions to \(\phi\left(\mathrm{K}_{\mathrm{Sj}} ; \operatorname{def}\right)^{\infty}\) have been estimated [10,11]. Indeed \(\phi\left(\mathrm{K}_{\mathrm{Sj}} ; \text { def }\right)\) is approximately a linear function of \(\left(m_{j} / m^{0}\right)^{1 / 2}\) for a wide range of aqueous and non-aqueous salt solutions [11-13]; e.g. salts in \(\mathrm{DMSO}\) [14] and in propylene carbonate [15]. \(\phi\left(\mathrm{K}_{\mathrm{Sj}} ; \text { def }\right)\) for copper(I) and sodium perchlorates in cyanobenzene, pyridine and cyanomethane show almost no dependence on salt molality [16].
A problem is further complicated by the fact that the \(\mathrm{DHLL}\) for \(\phi\left(K_{\mathrm{S} j} ; \text { def }\right)\) is itself a complicated function of salt molality [17], \(\mathrm{S}_{\mathrm{KS}} \,\left(\mathrm{m}_{\mathrm{j}} / \mathrm{m}^{0}\right)^{1 / 2}\) being however the leading term. A problem is encountered with the differential dependence of the molar volume of the solvent \(\mathrm{V}_{1}^{*}(\ell)\) on pressure at constant \(\mathrm{S}(\mathrm{s} \ln )\) describing how the volume of the solution would depend on pressure if it were held at the same entropy of the solution. Thus [18]
\[\begin{aligned}
-\left[\frac{\partial \phi\left(\mathrm{V}_{\mathrm{j}}\right)}{\partial \mathrm{p}}\right]_{\mathrm{s}(\mathrm{aq})} &=\left[\kappa_{\mathrm{s}}(\mathrm{aq})-\kappa_{\mathrm{s} 1}^{*}(\ell)\right] \,\left[\mathrm{m}_{\mathrm{j}} \, \rho_{1}^{*}(\ell)\right]^{-1}+\kappa_{\mathrm{s}}(\mathrm{aq}) \, \phi\left(\mathrm{V}_{\mathrm{j}}\right) \\
&+\left[\mathrm{m}_{\mathrm{j}} \, \rho_{1}^{*}(\ell)\right]^{-1} \, \mathrm{T} \, \alpha_{1}^{*}(\ell) \,\left\{\left[\alpha_{\mathrm{p}}(\mathrm{aq}) / \sigma(\mathrm{aq})\right]-\left[\alpha_{\mathrm{p} 1}^{*}(\ell) / \sigma_{1}^{*}(\ell)\right]\right\}
\end{aligned} \nonumber \]
By definition,
\[\phi\left(\mathrm{K}_{\mathrm{Sj}} ; \operatorname{def}\right)=\left[\kappa_{\mathrm{s}}(\mathrm{aq})-\kappa_{\mathrm{S} 1}^{*}(\ell)\right] \,\left[\mathrm{m}_{\mathrm{j}} \, \rho_{1}^{*}(\ell)\right]^{-1}+\kappa_{\mathrm{s}}(\mathrm{aq}) \, \phi\left(\mathrm{V}_{\mathrm{j}}\right) \nonumber \]
Then,
\[\begin{aligned}
&-\left[\frac{\partial \phi\left(\mathrm{V}_{\mathrm{j}}\right)}{\partial \mathrm{p}}\right]_{\mathrm{S}(\mathrm{aq})}=\phi\left(\mathrm{K}_{\mathrm{sj}} ; \mathrm{def}\right) \\
&\quad+\left[\mathrm{m}_{\mathrm{j}} \, \rho_{1}^{*}(\ell)\right]^{-1} \, \mathrm{T} \, \alpha_{1}^{*}(\ell) \,\left\{\left[\alpha_{\mathrm{p}}(\mathrm{aq}) / \sigma(\mathrm{aq})\right]-\left[\alpha_{\mathrm{p} 1}^{*}(\ell) / \sigma_{1}^{*}(\ell)\right]\right\}
\end{aligned} \nonumber \]
Consequently the difference between \(-\left[\frac{\partial \phi\left(\mathrm{V}_{\mathrm{j}}\right)}{\partial \mathrm{p}}\right]_{\mathrm{s}(\mathrm{aq})}\) and \(\phi\left(\mathrm{K}_{\mathrm{sj}} ; \mathrm{def}\right)\) is determined by the property \(\Delta \phi\), defined in equation (f).
\[\Delta \phi=\left\{\left[\alpha_{\mathrm{p}}(\mathrm{aq}) / \sigma(\mathrm{aq})\right]-\left[\alpha_{\mathrm{p} 1}^{*}(\ell) / \sigma_{1}^{*}(\ell)\right]\right\} \nonumber \]
However \(\Delta \phi / \mathrm{m}_{\mathrm{j}}\) is indeterminate at infinite dilution . But using L’Hospital‘s rule,
\[\operatorname{Limit}\left(\mathrm{m}_{\mathrm{j}} \rightarrow 0\right) \Delta \phi / \mathrm{m}_{\mathrm{j}}= \left[\left[\rho_{1}^{*}(\ell) \, \alpha_{p 1}^{*}(\ell) / \sigma_{1}^{*}(\ell)\right] \,\left\{\frac{\phi\left(E_{p j}\right)^{\infty}}{\alpha_{p 1}^{*}(\ell)}\right]-\left[\frac{\phi\left(C_{p j}\right)^{\infty}}{\sigma_{1}^{*}(\ell)}\right]\right\} \nonumber \]
Despite the thermodynamic polish given to the analysis of isentropic compressions, the problem of contrasting conditions ‘at constant \(\mathrm{S}(\mathrm{aq})\)’ and ‘at constant \(\mathrm{S}_{1}^{*}(\ell)\)’ underlies the analysis.
Footnotes
[1] A. Passynski, Acta Physicochim. URSS, 1938, 8 ,385.
[2] B. B. Owen and P. L. Kronick, J. Am. Chem.Soc.,1961, 65 ,84.
[3] F. J. Millero, in Activity Coefficients of Electrolyte Solutions, ed. R. M. Pytkowicz, CRC Press, Boca Raton, Fl,1979 , chapter 13.
[4] F. J. Millero, F. Vinokurova, M. Fernandez and J. P. Hershey, J. Solution Chem.,1987, 16 ,269.
[5] J. G. Mathieson and B. E. Conway, J. Chem. Soc Faraday Trans.1, 1974, 70 ,752.
[6] B. B. Owen and H. L. Simons, J. Am. Chem. Soc.,1957, 61 ,479
[7] Transition metal chlorides(aq); A. Lo Surdo and F. J. Millero, J. Phys. Chem.,1980, 84 ,710.
[8] Nitroammino cobalt(III) complexes(aq); F. Kawaizumi, K. Matsumoto and H. Nomura, J. Phys. Chem., 1983, 87 ,3161.
[9] Sodium nitrate(aq) and sodium thiosulfate(aq); N. Rohman, and S. Mahiuddin, J. Chem. Soc. Faraday Trans.,1997, 93 ,2053.
[10] Bipyridine and phenanthroline complexes of Fe(II), Cu(II), Ni(II) and Cu(II) chlorides(aq); F. Kawaizumi, H. Nomura and F. Nakao, J. Solution Chem.,1987, 16 ,133
[11] R. Buwalda, J. B. F. N. Engberts, H. Høiland and M. J. Blandamer, J. Phys. Org. Chem., 1998, 11 , 59.
[12] E. Ayranci and B. E. Conway, J. Chem. Soc. Faraday Trans.1, 1983, 79 ,1357.
[13] G. Peron, G. Trudeau and J.E.Desnoyers, Can J.Chem.,1987, 65 ,1402.
[14] J. I. Lankford, W. T. Holladay and C. M. Criss, J. Solution Chem.,1984, 13 ,699.
[15] J. I. Lankford and C. M. Criss, J. Solution Chem.,1987, 16 ,753.
[16] D. S. Gill, P. Singh, J. Singh, P. Singh, G. Senanayake and G. T. Hefter, J. Chem. Soc., Faraday Trans., 1995, 91 , 2789.
[17] J. C. R. Reis and M. A. P. Segurado, Phys.Chem.Chem.Phys.,1999, 1 ,1501.
[18] M. J. Blandamer, J. Chem. Soc. Faraday Trans.,1998, 94 ,1057.


7.2: Force
Pressure is the force applied over a specific area. It is the weight of water expressed as pounds divided by the area expressed as inches squared (in\(^2\)). Therefore, the resulting unit is pounds per square inch (psi). However, in the previous section we looked at pressure based on the height or elevation of a column of water and compared it against a conversion factor.
Recall the following conversion factors:
0.433 psi = 1 foot and 1 psi = 2.31 feet
Let’s take a look at what 1 psi is actually saying. One (1) pound of force per square inch of surface area. Therefore, if you have one (1) pound of water and place it on one (1) square inch of area, the resulting pressure would be 1 psi.
The definition of force can be explained as the push or pull which an object can change the velocity of the object on which it is applied. If the pressure is known and the area of which the pressure is being applied, the force can be calculated. See the example below:
A pressure of 100 psi exerts how much force against an area of 1 in\(^2\)?
In this example, there is
\[\dfrac{100 \text {lbs}}{\text{in}^{2}} \times \text{in}^{2} \nonumber \]
This would equate to 100 lbs of force because the in\(^2\) would cancel.
This says that 100 pounds of force is being exerted. Another example of calculating the force in pounds would be by calculating the entire volume of water and then converting to the water of the volume of water. Look at the example below.
If a tank with a 100 ft diameter and is 20 ft tall, what is the force at the bottom? In this example, the dimensions of the tank can be used to calculate the volume of water.
\[V=0.785 \times(100 \mathrm{ft}) 2 \times 20 \mathrm{ft} \times 7.48=1,174,360 \mathrm{gal} \nonumber \]
This volume can now be converted to pounds.
\[1,174,360 \text { gal } \times 8.34 \text { lbs/gal }=9,794,162 \text { lbs } \nonumber \]
This is the force exerted.
Exercise 7.2
- Calculate the force exerted on a 6” diameter valve with a pressure of 90 psi.
- What is the force at the base of a 100 ft tall tower filled with water and a diameter of 10 ft?
- A water tank is 50 feet tall and half full. If the diameter is 75 feet, what is the force exerted at the bottom?
- A fire hydrant with a 2 ½” opening has a pressure of 130 psi. What is the corresponding force?


9.3: Local Moving Orders for Mass
moving orders front the local commander, spacetime!
Navigation satellites near Earth drift away from "perfect" orbits because thin air and solar radiation pressure affect their motion. Figure \(\PageIndex{1}\) shows an experimental satellite that carries a "conscience" designed to assure that the same motion will be maintained when it encounters these disturbances as when it moves through perfect emptiness. The "conscience" - called a proof mass - is a separate sphere that floats inside the larger ship. The proof mass undergoes no acceleration relative to the ship as long as the ship moves freely. When relative motion does occur, the error in the tracking must be due to the satellite. By small rockets the satellite gives itself a brief spurt of acceleration and comes back into step with the inner proof mass - the satellite’s conscience. Though resistance is present, the rocket thrust overcomes it. The satellite takes the same course it would have taken had both resistance and thrust been absent.
FIGURE 9-2.
"The marble index of a mind forever
Voyaging through strange seas of thought, alone."-Wordsworth
ot know what I may appear to the world; but to myself I seem to have been only like a boy, playing on the sea-shore, and diverting myself, in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me."  Because he looked on the whole universe and all that is in it as a riddle, as a secret which could be read by applying thought to certain evidence, certain mystic clues which God had laid about the world to allow a sort of philosopher’s treasure hunt to the esoteric brotherhood. He believed that these clues were to be found partly in the evidence of the heavens and in the constitution of elements (and that is what gives the false suggestion of his being an experimental natural philosopher), but also partly in certain papers and traditions handed down by the brethren in an unbroken chain back to the original cryptic revelation in Babylonia. He regarded the universe as a cryptogram set by the Almighty-just as he himself wrapt the discovery of the calculus in a cryptogram when he communicated with Leibnitz. By pure thought, by concentration of mind, the riddle, he believed, would be revealed to the initiate."-Keynes
"Conscience-guided" satellite. What guides the conscience?
As satellite and proof mass come to empty space, they fly through it in perfect step, without use of rockets or sensing devices. What a remarkable harmony they present! The inner proof mass does not see outer space. It does not touch, feel, or see the ship that surrounds it on every side. Yet it faithfully tracks the ship’s route through spacetime. Moreover, this tracking is as perfect when the proof mass is made of aluminum as when it is made of gold. How do proof masses - of whatever atomic constitution and whatever construction - know enough to follow a standard worldline? Where does mass get its moving orders?
Locally, answers Einstein. From a distance, answers Newton.
Einstein says that the proof mass gets its information in the simplest way possible. It responds to the structure of spacetime in its immediate vicinity. It moves on a straight line in the local free-float frame. No simpler motion and no straighter motion can be imagined.
Newton says that the inner proof mass gets its information about how to move from a distance, via a "force of gravity." Motion relative to what? Motion relative to an ideal, God-given, never-changing Euclidean reference frame that spans all of space and endures for all time. He tells us that the proof mass would have moved along an ideal straight line in this global frame had not Earth deflected it. How can this ideal line be seen? How sad! There is nothing, absolutely nothing, that ever moves along this ideal line. It is an entirely imaginary line. But it nevertheless has a simple status, Newton tells us, in this respect: Every satellite and every proof mass, going at whatever speed, is deflected away from this ideal line at the same acceleration (Figure \(\PageIndex{3}\)).
Physics is simple only when analyzed locally.
Einstein says: Face it; there is no ideal background Euclidean reference frame that extends over all space. And why say there is, when even according to Newton no particle, not even a light ray, ever moves along a straight line in that ideal reference frame. Why say spacetime is Euclidean on a large scale when no evidence directly supports that hypothesis? To try to set up an all-encompassing Euclidean reference frame and attempt to refer motion to it is the wrong way to do physics. Don’t try to describe motion relative to faraway objects. And locally the worldline that a satellite follows is already as straight as any worldline can be. Forget all this talk about "deflection" and "force of gravitation." I’m inside a spaceship. Or I’m floating outside and near it. Do I feel any "force of gravitation?" Not at all. Does the spaceship "feel" such a force? No. Then why talk about it? Recognize that the spaceship and I are traversing a region of spacetime free of all force. Acknowledge that the motion through that region is already ideally straight.
How can one display the straightness of the motion? Set up a local lattice of meter sticks and clocks, a local free-float (inertial) reference frame-also called a Lorentz reference frame (Chapter 2). How does one know the frame is free-float? Watch every particle, check every light ray, test that they all move in straight lines at uniform speed relative to this frame. And having thus verified that the frame is free-float, note that the proof mass too moves at a constant speed in a straight line-or remains at rest - relative to this local free-float frame. What could be simpler than the moving orders for mass: "Follow a straight line in the local free-float reference frame." Does a proof mass have to know the location of Earth and Moon and Sun before it knows how to move? Not at all! Surrounded on all sides by the black walls of a satellite, it has only to sense the local structure of spacetime-right where it is - in order to follow the correct track.
Physics is simple only when analyzed locally
Figure \(\PageIndex{1}\): Figure and data from Journal of Spacecraft, Volume 11 (September 1974), pages 637-6 4 4 , published by the American Institure of Aeronautics and Astronautics. Data also from D. B. De Bra, APL Technical Digest, Volume 12: pages 14-26.
Figure \(\PageIndex{2}\) from Philosophiae Naturalis Principia Mathematica (Joseph Streater, London, July 5, 1686); Morre translation into English revised and edited by Florian Cajori and published in two paperback volumes (University of California Press, Berkeley, 1962). This is also the source of rhe quote in Section 9.6: “Absolute space, in its own namre, without relation to anything external, remains always similar and immobile.”


5.4: Creating Different Document Types in Google Docs
By the end of this section, you will be able to:
- Create and share a template
- Create a business memo
- Create a letter and associated letter for mailing
- Create a business card
- Create a brochure and a flyer
- Create an invoice
Like Microsoft, Google has ready-made templates for many types of documents. This section will walk through how to make different types of documents using these templates, as well as how to upload other templates and create documents from scratch. In contrast to Word, Google gives users the power to share their documents with the public or internally, simply by uploading them to Google Drive and granting permissions to download them. Using a simple URL, anyone can find and use publicly available, user-generated templates.
Google also has its own default Template Gallery , which contains a few different types of templates for workplace documents such as project proposals, meeting notes, newsletters, and contracts. However, the document types we will cover in this section—that is, many of the same ones we covered in Creating Different Document Types in Microsoft Word—do not have existing templates in the Google default Template Gallery. We will walk through how to approach creating these documents using a few different methods.
Templates
All the documents covered in this section can be saved as your own template. If you want to publish a template so that everyone can use it (i.e., to all Google users worldwide), you may do so. When you are finished formatting your document, you can go to Google’s template gallery and select Submit a template at the top. Note that not all Google accounts can submit templates. This feature is available only with the paid Business and Education programs in Google.
After you submit a template, Google will ask you to browse for the file in your Google Drive, then you can enter a description so that people who search for a certain kind of document (for example, an invoice, memo, business card, or cover letter) will be able to find it. Next, select the category the document fits in, and the language of the written text. Finally, click on Submit template to finish the process.
Another way to publish a template is to share it with others in a shared location so that your collaborators or coworkers can access it. (The chapter Creating and Working in Documents covered how to share documents with others.) Then, you can send the template to your coworkers by email, by sharing the link. The only caveat with sharing templates is that shared templates should not be directly edited because this would alter the template itself. You can set this shared template to “View only” if you are concerned about this happening. Otherwise, explain to the collaborators that when accessing the document, they should not edit it. Instead, they should use the Make a copy command.
If you would like to access a Google template (not the user-generated templates) in Docs, go to File, New, and choose From template gallery. This will give you the listing of the templates available. Notice they are categorized by usage (business, education, and so on).
Business Memos
We reviewed the business memo’s goals and overall form in Creating Different Document Types in Microsoft Word. These basic understandings remain true when you are creating a memo in Docs. The only difference between Docs and Word is how you access the template to create one.
There is no default business memo template in Docs. Google’s Template Gallery has plenty of templates, including ones for cover letters and project proposals. This means that you have to search the internet for one, upload one from Microsoft, or create it from scratch.
One way to find a user-generated business memo template is to go to Google’s search engine and type “memo template site https://docs.google.com ” into the search bar (see Figure 5.41). This will search for all public templates with the description “memo template.” However, this will get you a wide range of templates, so you should evaluate them carefully to find a memo format that you like and that looks professional.
You could also use a template from Microsoft and convert it to a Google Doc. We chose to use a template from Microsoft’s productivity template page here. Use the same template we used in Creating Different Document Types in Microsoft Word Figure 5.42. Save it as a .docx file, then upload it to Google Drive. While you have the uploaded template open in the Docs window, choose Make a copy, to keep the original file as a template. Then, you can fill in the required memo fields with your own information.
Letterhead, Letters, and Envelopes
The process and requirements for making a letterhead are the same in Docs as they are in Word. You fill it out with the same components—name, address, other contact information—which are placed in the same location on your documents (at the top). You can use a letterhead for any kind of business or personal correspondence, but this example will use a cover letter. Although Docs does not have a specific template called Cover Letter in its default Template Gallery , it does have a few that are simply called Letter.
First, start at the welcome screen, which is the first screen you see when you navigate to docs.google.com. Select Template Gallery at the top right. If you are using a business account, you will see a tab with your business name at the top left, and a tab that says General. If your company has its own templates, you will see them in the first tab. But look at Google’s default templates first and choose General. Scroll down until you see templates for Letters. Some of the templates would work as a letterhead template (Figure 5.43). Select the template you like, and Google will automatically open a new document for you. Simply replace the template text with your information on the letterhead (name, address, phone, email address), then add today’s date, the recipient’s name and address, and the body text, as Figure 5.44 shows.
To print and mail the letter, take the professional step of having a custom-printed envelope. To create and modify an envelope in Docs, you have two options: get a user-generated template or template from Microsoft, or install an add-on. Unfortunately, there are no default envelope templates in the Template Gallery, so you have to get creative.
To use the first option, you must do a manual search in your browser’s search bar. (This is the same process we used to find a business memo template.) Type in “envelope template site docs.google.com,” and you will see a number of user-generated envelope templates. You can select one of these and add the information of the addressor and the addressee. These templates could be modified.
The other option involves installing an add-on. There are several recommended add-ons from Docs’ users in forums. An add-on is an addition to the base software program. Add-ons can be very specialized, such as specific add-ons for graphic design, or they can be more general, such as the one we can use to make printed envelopes. To search for an add-on, go to the search bar at the top right side of the screen, as shown in Figure 5.45. Here, you can search for a mail merge add-on, which will give you the tools to print envelopes. A tip is to find an add-on that many users have downloaded and installed, so you know that it is effective. You can also filter the results to show which will work with specific programs and by price. There are many free add-ons for general usage. The more specialized add-ons might require you to pay a fee. You can see the add-on’s name, rating, and number of users at the bottom of each result listed. To access the add-on, click on it in the Extensions menu (see Figure 5.46).
There are many add-ons that increase the capabilities of Docs. As you have read throughout this book, Word typically offers more features than Docs. Yet, if you install many specialized add-ons, this gap becomes smaller. Read this article on popular add-ons for Docs to learn more.
Business Cards
As with other document types discussed so far, Google does not have a default template for business cards. You have a few choices on how to move forward: upload a Microsoft template to your Drive, find a user-generated template, or install an add-on.
To use a Microsoft template, go to Microsoft's template page and choose the same business card template you used in Creating Different Document Types in Microsoft Word. You will be making some changes to it in Docs. You can use a letter-size paper to print the cards, but remember that business cards should be on cardstock, and may need to be professionally printed.
You can also look for a user-generated template on docs.google.com. As with the other template types, type “ business card template site https://docs.google.com ” into your browser’s search bar or search engine to look. Once you find a template, you can add your information and company logo as usual. You may also change the design of the template by adding shapes and lines from Google Drawings (see the chapter on Document Preparation.)
Brochures and Flyers
Docs has some default templates for brochures and flyers. But the brochures are not formatted in the traditional trifold way. In fact, the brochure templates are very similar to the flyer templates in Google.
Figure 5.47 shows a two-page brochure template. Note that it is a trifold format, like we saw in Creating Different Document Types in Microsoft Word. To create a trifold brochure, you can use a Word template and open it in Docs. You might have to adjust some of the spacing when using a Word template in Docs, but it gives you a good framework to start designing your brochure.
Image Usage and Restrictions
The internet has put any number of resources at our fingertips. As we create documents, we may want to include images or graphics to augment the visual appeal of the document or to highlight certain information. Of course, many of us do not have the skill to create these on our own. Here, the internet can be very useful—you can conduct an image search on just about any topic and find relevant images, and then copy and paste, or save and insert, these images. But, first, you need to determine whether the creator has given permission to do so; otherwise, you are taking a work that isn’t yours and using it in a way that the creator didn’t intend.
Most images you find will have an associated license or require attribution, as they are created by someone else, usually for someone else. Normally, a large company like WorldCorp would have a paid subscription to a site such as AP Newsroom for a repository of licensed stock images.
However, you can also find many open-source images that are available freely and without cost. Wikimedia Commons is one popular open-source image repository. But, even here, you must carefully read the different licenses associated with the image in question. While some images on Wikimedia Commons may be public domain—that is, without any copyright restrictions at all—others may have varying types of Creative Commons licenses, which may come with restrictions on usage and attribution.
The most permissive type of Creative Commons license is a CC BY license. According to Creative Commons “This license allows reusers to distribute, remix, adapt, and build upon the material in any medium or format, so long as attribution is given to the creator. The license allows for commercial use.”
The least permissive type of license is a CC BY-NC-ND. First, the creator must be given attribution. Second, it allows for use and distribution in any format but can’t be altered and can’t be used for commercial purposes.
There are varying degrees of Creative Commons licenses between these two types.
Invoices
As with the other document types, there is no default template in the Template Gallery for invoices. Luckily, we can still search through the huge number of user-generated templates by searching for “invoice template site https://docs.google.com .” This internet search will return all public templates that people have added to their own Google Drives. After you find the invoice template of your choice, you can save it by going to the File menu, and selecting the Make a copy command, as Figure 5.48 shows.
Again, you can always import a Microsoft template and modify it in Google. For example, try using the same template you chose in Creating Different Document Types in Microsoft Word. As you start to work on the invoice, you can update it with company-specific information and logos. To save it as your own template, go to the File menu, and select Make a copy. Then, go to your Drive and rename it to “invoice template” or something similar.
As with any other template, you may want to restrict editing permissions so the template itself cannot be changed, as the chapter on Creating Different Document Types in Microsoft Word explains. By setting the permissions to “View only,” every time you open the template for a new invoice, you would have to use the Make a copy command in order to create an editable version. Then, from your new editable version, you may proceed to change the data and save it under a different name.


5.5: Managing Stress
How can I help handle my stress?
Everyone has to deal with stress. There are steps you can take to help you handle stress in a positive way and keep it from making you sick. Try these tips to keep stress in check:
Develop a new attitude
- Become a problem solver. Make a list of the things that cause you stress. From your list, figure out which problems you can solve now and which are beyond your control for the moment. From your list of problems that you can solve now, start with the little ones. Learn how to calmly look at a problem, think of possible solutions, and take action to solve the problem. Being able to solve small problems will give you confidence to tackle the big ones. And feeling confident that you can solve problems will go a long way to helping you feel less stressed.
- Be flexible. Sometimes, it’s not worth the stress to argue. Give in once in awhile or meet people halfway.
- Get organized. Think ahead about how you’re going to spend your time. Write a to-do list. Figure out what’s most important to do and do those things first.
- Set limits. When it comes to things like work and family, figure out what you can really do. There are only so many hours in the day. Set limits for yourself and others. Don’t be afraid to say NO to requests for your time and energy.
Relax
- Take deep breaths. If you’re feeling stressed, taking a few deep breaths makes you breathe slower and helps your muscles relax.
- Stretch . Stretching can also help relax your muscles and make you feel less tense.
- Massage tense muscles . Having someone massage the muscles in the back of your neck and upper back can help you feel less tense.
- Take time to do something you want to do. We all have lots of things that we have to do. But often we don’t take the time to do the things that we really want to do. It could be listening to music, reading a good book, or going to a movie. Think of this as an order from your doctor, so you won’t feel guilty!
 Getting enough sleep helps you recover from the stresses of the day. Also, being well-rested helps you think better so that you are prepared to handle problems as they come up. Most adults need 7 to 9 hours of sleep a night to feel rested.
- Eat right. Try to fuel up with fruits, vegetables, beans, and whole grains. Don’t be fooled by the jolt you get from caffeine or high-sugar snack foods. Your energy will wear off, and you could wind up feeling more tired than you did before.
- Get moving. Getting physical activity can not only help relax your tense muscles but improve your mood. Research shows that physical activity can help relieve symptoms of depression and anxiety.
- Don’t deal with stress in unhealthy ways. This includes drinking too much alcohol, using drugs, smoking, or overeating.
Connect with others
- Share your stress. Talking about your problems with friends or family members can sometimes help you feel better. They might also help you see your problems in a new way and suggest solutions that you hadn’t thought of.
- Get help from a professional if you need it. If you feel that you can no longer cope, talk to your doctor. She or he may suggest counseling to help you learn better ways to deal with stress. Your doctor may also prescribe medicines, such as antidepressants or sleep aids.
- Help others. Volunteering in your community can help you make new friends and feel better about yourself.
What Are Relaxation Techniques?
Relaxation techniques include a number of practices such as progressive relaxation, guided imagery, biofeedback, self-hypnosis, and deep breathing exercises. The goal is similar in all: to produce the body’s natural relaxation response, characterized by slower breathing, lower blood pressure, and a feeling of increased well-being.
Meditation and practices that include meditation with movement, such as yoga and tai chi , can also promote relaxation. You can find additional information about these practices on the NCCIH web site.
What Is Meditation?
Meditation is a mind and body practice that has a long history of use for increasing calmness and physical relaxation, improving psychological balance, coping with illness, and enhancing overall health and well-being. Mind and body practices focus on the interactions among the brain, mind, body, and behavior.
There are many types of meditation, but most have four elements in common: a quiet location with as few distractions as possible; a specific, comfortable posture (sitting, lying down, walking, or in other positions); a focus of attention (a specially chosen word or set of words, an object, or the sensations of the breath); and an open attitude (letting distractions come and go naturally without judging them).
What the Science Says About the Effectiveness of Meditation
Many studies have investigated meditation for different conditions, and there’s evidence that it may reduce blood pressure as well as symptoms of irritable bowel syndrome and flare-ups in people who have had ulcerative colitis. It may ease symptoms of anxiety and depression, and may help people with insomnia.
No matter which techniques or strategies you select to help cope with stress more effectively, keep in mind that it takes time and effort to reap the benefits from them.
Contributors and Attributions
Public domain content
- How to Handle Stress. Authored by: womenshealth.gov. Provided by: Office on Women's Health, U.S. Department of Health and Human Services. Located at: https://www.womenshealth.gov/publications/our-publications/fact-sheet/stress-your-health.html . License: Public Domain: No Known Copyright
- Relaxation Techniques for Health. Authored by: National Center for Complementary and Integrative Health. Provided by: National Institutes of Health. Located at: https://nccih.nih.gov/health/stress/relaxation.htm . License: Public Domain: No Known Copyright