Hot Orange Shake

This is a raw-egg drink in which the egg is never cooked, only warmed. That single fact rules it out as written, and it is worth being clear about why.

• The egg is never brought to a safe temperatureWater from a kettle drops sharply the moment it hits a cold egg-and-cream mixture in a glass, and the whole is drunk immediately. Nothing here holds the egg anywhere near the range at which Salmonella is destroyed, and the shell is broken straight into the shaker with no heat step at all.
• Hot water is not a substitute for cookingEgg proteins begin to set at roughly 145F and above, and safety depends on holding a temperature for a period, not merely touching it. A mug topped up from the tap or kettle gives a brief, uneven, and unmeasurable warming. If you want a hot egg drink, use a current recipe built around a custard base or pasteurized shell eggs.
• Why the period saw no problemRaw egg was standard in the soda-fountain repertoire and in invalid cookery, given freely to children and convalescents. Egg-borne Salmonella was not recognized as a significant hazard until much later in the twentieth century, so books of this era shake raw eggs into malteds, flips, and nogs without comment.
• Orange syrupFor reference, the syrup called for is almost certainly a sweetened fountain syrup rather than orange juice: a heavy sugar syrup flavoured with orange in some form. Substituting juice would change both the sweetness and the body the recipe assumes.
• The shakerA fountain shaker was a plain metal tumbler, shaken by hand. Here the shaking appears to serve to combine the egg and cream rather than to chill: nothing in the instruction adds ice.