Hence optical depth is dimensionless, and in particular is not a length ; however, the optical depth to an object will typically approach zero as the distance to the object decreases.

Hence a submarine at shallow depth can use these frequencies.

Hence, this leaky bucket determines whether adding some amount of water would exceed or conform to a limit on the rate at which water can be added, set by the leak rate, and a limit on how much water can be added in a burst, set by the depth of the bucket.

Hence " it is evident that wisdom, knowledge and understanding are eternal and self-subsistent things, superior to matter and all sensible beings, and independent upon them "; and so also are moral good and evil.

Hence his injunctions to the analyst to eschew memory and understanding, to " bring to bear a diminution of the ' light ' - a penetrating beam of darkness ; a reciprocal of the searchlight.

Hence, an understanding of Oneness is critical in any analysis of UPCI doctrine.

Hence, it damages the prospects for peace based on mutual respect and understanding.

Hence, determining a person's system of constructs would go a long way towards understanding him, especially the person's essential constructs that represent very strong and unchangeable beliefs ; and also the constructs a person applies to him / herself.

Hence, these semantical methods were pathetically inadequate for understanding the semantics of any but a few small artificial languages or mutilated fragments of natural languages.

Hence the study of joseki is regarded as a double-edged sword and useful only if learned ( not by rote ) by understanding the principles behind each move.

Hence understanding the algebraic structure of the mapping class group often reduces to questions about the Torelli group.

Hence, in practice, both sides in a conflict attack civilians, with the understanding that these are legitimate and lawful targets in war.

Hence the production and study of protonium would be of interest also for the understanding of internucleon forces.

Hence organizational ecology has spent considerable effort on understanding the founding and mortality rates of organizations.

Hence our understanding of Peirce's graphical logic is likely to change as the remaining 23 volumes of the chronological edition appear.

Hence, for Lenin, those who would bring about the revolution must devote all their energies and resources to understanding the range of Marx's thought.

Hence SNA aimed to reduce the main non-computer costs and other difficulties in operating large networks using earlier communications protocols.

Hence RTÉ Two was aimed at those that did not have the UK channels.

Hence this power launched a series of friendship treaties aimed at forging the relations between France, Czechoslovakia, Kingdom of Serbs, Croats and Slovenes, and Romania.

Hence, anyone who feels offended by any content published on a blog, an online newspaper and, most likely, even on Wikipedia would have the right for a statement (" correction ") to be shown, unaltered, on the page, aimed to contradict and disprove the allegedly harmful contents, regardless of the truthfulness of the information deemed as offensive, and its sources.

Hence they aimed firstly to lay the foundation of administration in a restricted manner with the following basic objectives –

Hence, the flow conditions at the anode of free burning arcs resemble those near a stagnation point.

Hence, karma cannot bestow the fruits of actions at a future date according to one's merit.

Hence it took a prominent part in the Peloponnesian War until the crushing defeat at Idomene ( 426 ) which crippled its resources.

Hence it would follow that the war lasted from shortly after 507 BC down to the congress at the Isthmus of Corinth in 481 BC

Hence, by metonymy, it would be employed to denote at times the shield which it supported, and at other times a cuirass, or chlamys, the purpose of which it in part served.

Hence, as some scholars of China suggest, the Xia and the Shang can possibly refer to political entities that existed concurrently, just as the early Zhou is known to have existed at the same time as the Shang.

Hence the slope of the graph of the squaring function at the point ( 3, 9 ) is 6, and so its derivative at x

Hence, the bridging is then done in hardware, allowing packets to be forwarded at full wire speed.

Hence, fossils range in age from the youngest at the start of the Holocene Epoch to the oldest from the Archaean Eon, up to 3. 4 billion years old.

Hence feminism influences the film industry by creating new ways of exploring and looking at masculinity / femininity and male / female roles.

Hence, Weird Tales may only have owned the rights to at most six of Lovecraft's tales.

Hence, those with less pigmented skin survived and had children at higher rates because their skin allowed more UV light for the production of vitamin D. Thus, the skin of those in the group that left the African continent and went far north gradually developed adaptations for relatively greater translucence compared to equatorial hues.

Hence, with respect to an inertial frame, an object or body accelerates only when a physical force is applied, and ( following Newton's first law of motion ), in the absence of a net force, a body at rest will remain at rest and a body in motion will continue to move uniformly — that is, in a straight line and at constant speed.

Hence they occur at low densities even in healthy populations.

Hence the Krebs Cycle can start at acetyl-CoA when fat is being broken down for energy if there is little or no glucose available.

Hence it is that what names theirs carried, ours do the like, and the Fathers make no scruple at it — no more need we.

Hence, at any given level in the inheritance chain, there can be at most one implementation of any method.

Hence, the passing of time was more discernible in the very early years, such as the graduation of Spider-Man ; and what started as children or teenaged characters, such as Kitty Pryde, Franklin Richards, Valeria Richards, Power Pack, or the New Mutants are all allowed to age at wildly shifting rates ( in the second case even backwards at times ), whereas surrounding characters somewhat dependent on a certain age limit do not change at all.

Hence, the description of each text occurrence can be retrieved by reading the list of text-ordered information-cell addresses and outputting the description indicated by the information cell for each occurrence.

Hence, a successor corporation in a C reorganization appears entitled to sue for a refund of taxes paid by the merged corporation despite section 203.

Hence S breaks up into uncountably many orbits under G. Using the axiom of choice, we could pick a single point from each orbit, obtaining an uncountable subset X of S with the property that all of its translates by G are disjoint from X.

Hence the Rococo style was highly dominated by the feminine taste and influence.

Hence he commissioned a book entitled The Quintessence of Histories to be worked upon by calligraphers, but forbade its illustration by the by-now largely dissolved Society of Miniaturists.

Hence, by reducing angiotensin II levels, ACE inhibitors may reduce GFR, a marker of renal function.

Hence ahimsa as a binding code of conduct implies a ban on hunting, butchery, meat eating, and the use of animal products provided by violent means.

Hence, catalysts can enable reactions that would otherwise be blocked or slowed by a kinetic barrier.

Hence, by descent and destiny, each Jew stands under the divine command to obey God's will.

Hence, for the lead this would be two counts with the weight on the left leg while the right leg moves, two counts with weight on the right leg while the left leg moves, followed by a quick step onto the left and then a quick step onto the right.

Hence, democracy allows for political minorities to be oppressed by the " tyranny of the majority " in the absence of legal protections of individual or group rights.

Hence the three defining properties of equivalence relations can be proved mutually independent by the following three examples:

Hence, readers are recommended to consult instead the alphabetical index or the Propædia, which organises the Britannicas contents by topic.

Hence, ecologists classify ecosystems hierarchically by analyzing data collected from finer scale units, such as vegetation associations, climate, and soil types, and integrate this information to identify emergent patterns of uniform organization and processes that operate on local to regional, landscape, and chronological scales.

Hence, and so we may divide by and rearrange the equation into the standard form

" Hence, the form was used initially for funeral songs, typically accompanied by an aulos, a double-reed instrument.

Hence, nation-states with strong traditions of ethnic nationalism tend to define nationality or citizenship by jus sanguinis ( the law of blood, descent from a person of that nationality ) while countries with strong traditions of civic nationalism tend to define nationality or citizenship by jus soli ( the law of soil, birth within the nation-state ).

Hence England and, by extension its modern successor state, the United Kingdom of Great Britain and Northern Ireland, is in fact an Empire ruled by a King endowed with the imperial dignity.

Hence, much has been preserved, quoted by Eusebius, which otherwise would have been destroyed.