The 'mysteries of mesmerism' promised in this advertisement suggest that Annie De Montford was a stage hypnotist, someone who, by careful suggestion to audience members, could guess what they were thinking or provoke them to behave out of character. Annie De Montford was a famous and prolific mesmerist in the 1870s, but appears to have retired professionally in 1882 due to unexplained illness.
This advert, with its striking double acrostic pattern (the vertical rows of text, read down the page, spell words on both right and left margins), demonstrates the peculiar interrelationship of science and the supernatural in the mid-Victorian period. ‘Mesmerism’ was a popular theory in physics that all animate and inanimate objects are in communication through invisible fields of energy. This theory 'explained', among other things, why some people began to behave strangely during a full moon: the moon was effectively broadcasting its energy to them and suppressing their own good sense. People who could control their own invisible electrical field, and thereby induce others to behave in certain ways, were known as ‘mesmerists’.
Mesmerism (the name derives from Austrian scientist Franz Anton Mesmer, who proposed the theory) had been discredited as science by the time of this advertisement, but the poetic and supernatural aspects of the theory were irresistible to stage illusionists and audiences.