A physician and toxicologist who experimentally investigated the action of water on lead. Comparisons involving dissolved salts and surface deposits showed why metal exposure depends on water chemistry as well as the presence of lead.^[ref]

Physician and toxicologist. National Portrait Gallery: identified portraits, including the circa-1860 photograph catalogued as NPG x45706.

A physician who documented severe gastric damage in a case of oxalic-acid poisoning. The report connected clinical circumstances with postmortem findings, while a single case could not establish an invariant appearance in every poisoning.^[ref]

Physician and forensic scientist. Wellcome Collection: identified portrait M0003164, an archival reproduction of a photograph.

A physician who connected diseased pork, microscopic parasites and trichinellosis in an 1864 account. Identifying organisms in tissue supplied a different kind of explanation from treating the condition as nonspecific food spoilage.^[ref]

Physician and author of On Poisoning by Diseased Pork by Julius Althaus. Wikimedia Commons image index, including the identified portrait file Julius Althaus.jpg.

A medical author who organized urinalysis around physical, chemical and microscopic observations. Relating measurements to clinical interpretation illustrates why one urine finding should be assessed alongside the sampled material and other evidence.^[ref]

Author of Urinalysis in Clinical Methods by David M. Roxe, identified by the chapter and PubMed record. No birth dates or expanded name are inferred.

A bounded exact-name and institutional portrait search did not establish a securely identified portrait. The commercial physician profile returned an image label, but this was not sufficient to establish an authenticated portrait of the chapter author; no likeness is supplied.

A physician who investigated diagnosis, prognosis and treatment in delirium tremens. His clinical discussion documents disagreement over interventions such as opium and stimulation, making it useful evidence of how treatment claims were evaluated at the time.^[ref]

Physician and author of Practical Notes on Diagnosis, Prognosis, and Treatment in Cases of Delirium Tremens by Thomas Laycock. Verified Wellcome portrait record, M0003163.

A physician who analyzed the first British Pharmacopoeia. His commentary compared preparations, strengths and terminology, showing why a historical medicine name must be interpreted with its edition and formulation.^[ref]

Wellcome authority record.

A physician who compiled practical observations about drugs and their use in nineteenth-century medicine. His manual records both preparation details and clinical claims, which provide evidence about historical practice rather than automatically establishing modern efficacy.^[ref]

Royal College of Physicians biography and authenticated portrait.

Additional portrait catalogue: Wellcome photograph of a drawing of Waring.

Naturalist who defended spontaneous generation, using the term heterogenesis for the origin of living forms from nonliving organic material. His experiments and interpretations belonged to the nineteenth-century controversy over whether growth in preparations required pre-existing organisms.^[ref]

Verified external portrait record: wellcomecollection.org/works/ctma9gk7

Microbiologist and chemist whose experiments connected fermentation with living microorganisms and challenged spontaneous generation. Experiments separating access to air from access to dust-bearing contamination made the origin of growth in an infusion a question of controlled exposure rather than appearance alone.^[ref]

Coauthor of Maintenance and Validation of Liquid-in-Glass Thermometers by Christina D. Cross and others.

An author credited on Mercury Barometers and Manometers by W. G. Brombacher and others.

An author credited on Mercury Barometers and Manometers by W. G. Brombacher and others.

An author credited on Mercury Barometers and Manometers by W. G. Brombacher and others.

An ecologist whose work connected the logistic map and other simple mathematical models to population dynamics.^[ref]

Stephen Hales (1677–1761) made plant physiology quantitative by measuring water loss, sap movement and pressure. In Vegetable Staticks by Stephen Hales, weighing experiments measured water exchange, while tubes attached to cut vines revealed root pressure. Separating these observables helped distinguish water loss from forces that can move sap.^[ref]

External portrait: www.npg.org.uk/collections/search/portrait/mw02821/Stephen-Hales

An anatomist whose 1863 lecture discussed the origins of cells in pathological lesions. Portrait catalogue: Wellcome Collection M0016782, identified portrait, after an 1881 photograph.

For finite lists, if $x\oplus (y\otimes z)=(x\oplus y)\otimes z$ and $x\oplus a=a\otimes x$, then the right fold with step $\oplus$ and seed $a$ equals the left fold with step $\otimes$ and seed $a$. The two steps need not be identical. Equality of the resulting values does not imply equal time complexity; list concatenation is an important example.

A large lipoprotein particle assembled by enterocytes to transport dietary long-chain lipids through intestinal lymph.

Remove the integrality requirements from an integer program while retaining its linear inequalities and variable bounds. Every original feasible point remains feasible. Thus the relaxed optimum is an upper bound for a maximization problem and a lower bound for a minimization problem. An optimal relaxed feasible point need not have integer coordinates. Variable bounds that were implied only by an informal declaration such as binary must be made explicit before removing integrality.

An equality representation of a linear program in which each basic variable and the objective function are expressed using nonbasic variables, and all variables are nonnegative. Introducing slack variables into $Ax\le b$ gives $s=b-Ax$. Setting the nonbasic variables to zero yields its basic solution; nonnegative resulting basic values make this a basic feasible solution. A simplex algorithm pivot exchanges a basic and nonbasic index and rewrites these expressions.