The "Sandow's exercises" that Bloom thinks about in Calypso and Circe come from a book that sits on his bookshelves, "Eugen Sandow's Physical Strength and How to Obtain It." Sandow was internationally famous as a "body-builder" (he coined the term), and he became a kind of guru of physical fitness in the 1890s and early 1900s. Ireland went gaga over him after an 1898 series of performances.
Friedrich Wilhelm Müller, born in Prussia in 1867, gave himself the stage name Eugen Sandow when he began performing in European circuses in the 1880s. In addition to performing staggering feats of strength, he adopted poses that would highlight particular aspects of his musculature, as professional bodybuilders do today. In the 1890s Sandow opened schools that taught exercise routines, healthy diets, and weight training. He published a monthly magazine called Physical Culture starting in 1898, wrote several books (which included charts prescribing amounts of weight and numbers of repetitions), invented new kinds of exercise equipment, and championed isometric exercises (merely tightening and releasing muscle groups) as a complement to weight-lifting.
In addition to performing internationally, Sandow organized bodybuilding competitions, trained soldiers, and served for a while as a personal trainer to King George V. In May 1898 he delivered a run of spectacular performances in Dublin's Empire Palace Theatre. More than 1,300 people came on the first night to see him effortlessly lift enormous dumbbells, throw human beings around like beanbags, rip three decks of playing cards stacked on top of one another, and lift up a platform containing a piano while the pianist continued playing on it. Sandow enjoyed a sky-high reputation in Ireland for many years after the 1898 tour, and sold many copies of his books as well as the Sandow Developer, a pulley system for dumbbells that anticipated modern weight-lifting machines. A good account of the Irish Sandow craze can be found at www.theirishstory.com.
Sandow's most famous book, Strength and How to Obtain It (1897)—Joyce got the title slightly wrong—supplied a chart for recording measurements of particular muscle groups, so that the practitioner could track their growing size. Ithaca observes that these "indoor exercises . . . designed particularly for commercial men engaged in sedentary occupations, were to be made with mental concentration in front of a mirror so as to bring into play the various families of muscles and produce successively a pleasant rigidity, a more pleasant relaxation and the most pleasant repristination of juvenile agility." Later, when it details the contents of Bloom's desk drawer, the chapter mentions "a chart of the measurements of Leopold Bloom compiled before, during and after 2 months' consecutive use of Sandow-Whiteley's pulley exerciser (men's 15/-, athlete's 20/-) viz. chest 28 in and 29 1/2 in, biceps 9 in and 10 in, forearm 8 1/2 in and 9 in, thigh 10 in and 12 in, calf 11 in and 12 in."
Alas, like many later 20th and 21st century individuals who have purchased exercise advice and exercise equipment, Bloom suffered a lapse of enthusiasm after his two months of faithful adherence. Ithaca notes that his Sandow's routines were "formerly intermittently practised, subsequently abandoned." In Calypso, his brief plunge into black gloom on Dorset Street makes him resolve to improve his physical conditioning: "Morning mouth bad images. Got up wrong side of the bed. Must begin again those Sandow's exercises." In Circe, a near encounter with a tram causes him to renew the resolution: "Close shave that but cured the stitch. Must take up Sandow's exercises again."
Sandow advocated what he called the "Grecian ideal" of male
beauty, shaping his own body to measurements of muscles that
he took from statues in museums. Bloom's interest in the
Sandow ideal is clearly of a piece with his admiration for the
standards of beauty embodied in Greek
statues, both male and female. His mimetic desire for
the one and sublimated sexual desire for the other merge with
any purer aesthetic appreciations he may have, making his
response to this great art form as much "kinetic" as "static,"
in the terms that Stephen propounds in Part 5 of A
Portrait of the Artist.
 Bloom's conscious thoughts about Sandow are limited to
desiring physical strength, but his mimetic attraction to this
brilliant self-promoter may express professional envy as well.
As Vike Martina Plock observes in Joyce, Medicine, and
Modernity (UP of Florida, 2010), "Both physically and
commercially Sandow has achieved what Leopold Bloom can only
dream of: physical superiority and professional success in
advertising" (119). Sandow's books and magazine, his
theatrical triumphs, his classes, his exercise products, his
marketing of his services as a consultant, his modeling for
photographs: Bloom would count himself fortunate to achieve
any one of these commercial successes.
In a personal communication, fitness trainer and writer Andrew Heffernan adds several other interesting pieces of information. Sandow completely changed the look of weight-lifters: "Prior to him, strongmen were thick-waisted beer-guzzling bears." In order to accentuate the resemblance to ancient statues, he would cover himself in white powder that gave his body the appearance of having been carved from marble. And Sandow "was—and remains—the model for the trophy given annually to the winner of the Mr. Olympia contest—bodybuilding's top prize." Heffernan's photograph of one of these trophies appears here.