In 1916, she became the first female magistrate in Canada and the fifth in the British Empire after Elizabeth Webb Nicholls, Jane Price, E. Cullen and Cecilia Dixon of Australia (all appointed to office in 1915).

Murphy is known as one of "The Famous Five" (also called "The Valiant Five")[2]—a group of Canadian women's rights activists that also included Henrietta Muir Edwards, Nellie McClung, Louise McKinney and Irene Parlby.

However, upon appeal to the Judicial Committee of the British Privy Council, the court of last resort for Canada at that time, the women won their case.

[3] However, there has been some criticism of her later work, mainly for her role in the Sexual Sterilization Act of Alberta and her allegations that a ring of immigrants from other countries, particularly China, would corrupt the white race by getting Canadians hooked on drugs.

[4] In her book The Black Candle, she wrote: "It is hardly credible that the average Chinese peddler has any definite idea in his mind of bringing about the downfall of the white race, his swaying motive being probably that of greed, but in the hands of his superiors, he may become a powerful instrument to that end.

[6] As a child, Murphy frequently joined her two older brothers Thomas and Gowan in their adventures; their father encouraged this behaviour and often had his sons and daughters share responsibilities equally.

Murphy grew up under the influence of her maternal grandfather, Ogle R. Gowan, a politician who founded a local branch of the Orange Order in 1830, and two uncles, one a Supreme Court justice and the other a senator.

In addition to these organizations, Murphy began to speak openly and frankly about the disadvantaged and the poor living conditions that surrounded their society.

In 1916, Murphy successfully persuaded the Alberta legislature to pass the Dower Act that would allow a woman legal rights to one-third of her husband's property.

Edmonton lawyer, Eardley Jackson, challenged her position as judge because women were not considered "persons" under the British North America Act 1867.

This understanding was based on a British common law ruling of 1876, which stated, "women were eligible for pains and penalties, but not rights and privileges.

In 1919, Murphy presided over the inaugural conference of the Federated Women's Institutes of Canada, which passed a resolution calling for a female senator to be appointed.

She enlisted the help of four other Albertan women and on 27 August 1927 she and human rights activist and ex-MLA Nellie McClung, ex-MLA Louise McKinney, women's rights campaigner and author Henrietta Edwards, and sitting Alberta cabinet minister and MLA Irene Parlby signed the petition to the federal Cabinet, asking that the federal government refer the issue to the Supreme Court of Canada.

On 18 October 1929, in a decision called Edwards v. Canada (Attorney General), the Privy Council declared that 'persons' in Section 24 of the BNA Act of 1867 should be interpreted to include both males and females; therefore, women were eligible to serve in the Senate.

[13] Although Murphy's views on race changed over the course of her life,[14] the perspective contained in her book The Black Candle is considered the most consequential because it played a role in creating a widespread "war on drugs mentality" leading to legislation that "defined addiction as a law enforcement problem".

Using extensive anecdotes and "expert" opinion, The Black Candle depicts an alarming picture of drug abuse in Canada, detailing Murphy's understanding of the use and effects of opium, cocaine, and pharmaceuticals, as well as a "new menace", "marijuana".

[16] Murphy's concern with drugs began when she started coming into "disproportionate contact with Chinese people" in her courtroom because they were over-represented in the criminal justice system.

[17] In addition to professional expertise and her own observations, Murphy was also given a tour of opium dens in Vancouver's Chinatown by local police detectives.

Although Murphy's anti-drug screeds were widely read and helped spread the drug panic across Canada, she was not respected by the Division of Narcotic Control because of the creative liberties she took in presenting research they had assisted her with.

[20] Drug addiction, however, not the Chinese immigrant, is "a scourge so dreadful in its effects that it threatens the very foundations of civilization", and which laws, therefore, need to target for eradication.

[21] Murphy's distaste for non-whites is reflected in scholarly debates, but what is not controversial is that The Black Candle was written "for the express purpose of arousing public demands for stricter drug legislation" and that in this she was to some degree successful.

On the other hand, she may have deliberately tried to distance herself from those prejudices, especially the ones propagated by the more vulgar and excitable Asian exclusionists in British Columbia to maximize her credibility and sway her more moderate readers.

She wrote to the UFA government's Minister of Agriculture and Health, George Hoadley that two female "feeble-minded" mental patients had already bred several offspring.