The Palmer Method is the plain, unshaded American business hand of the early twentieth century, written with the whole arm rather than the fingers and taught in most US schools until the 1950s.
Letterforms
Palmer letters are Spencerian letters with the ornament removed: the same ovals and slant, but no shading, no flourished capitals and a lighter, faster line made with a coarse pen or a pencil. The slant is moderate rather than steep. Loops are plain and the same size throughout a word. Capitals are simple and quick, and several are recognisably the capitals US children still learn.
Joins and lifts
The lowercase is fully joined and the capitals mostly join too, because the method prized speed and continuity: a clerk was expected to write a page without lifting the pen except between words. The dots and crossbars go on afterward. The distinctive feature is the movement itself, made from the shoulder and forearm with the fingers still, which the method drilled with pages of ovals and push-pulls before any letter was taught.
Where it comes from
Austin Norman Palmer published his guide to business writing in 1894 and sold the method to schools across the United States over the following decades as a faster, less fussy alternative to Spencerian. It dominated American handwriting instruction for the first half of the twentieth century and is the immediate ancestor of the traditional slant model taught today, which kept its letterforms and dropped the arm-movement drills.
Practising it
The method's own drills still work: rows of ovals and straight push-pull strokes written from the arm, then the lowercase in groups, then joined words. The site renders the hand in its traditional slant face, since the letterforms are nearly the same. The traditional slant page covers the modern model, and the Spencerian page the hand Palmer simplified.