This recipe is odd because it reads one-third scotch and one-half sloe gin.
It seems possible the first fraction is a typo, and the recipe should read 1/2 scotch and 1/2 sloe gin. If so, this error is reprinted across the editions and through the years without correction.
It is possible the mix of 1/2 and 1/3 is intentional. I haven’t checked every recipe in every edition, but if so, this is a rare or unique choice. When McElhone employs fractions, they usually add up to one (e.g., 1/3 + 2/3) OR they do not add up to one (e.g., 1/3 + 1/6) but contain various additions, some measured in teaspoons that are implied to make up the difference. (It’s not even clear to me whether McElhone’s fractions are meant to be fractions of the finished drink or fractions of an unnamed measuring vessel. He does have a few recipes explicitly measured in glasses, as in 1/3 glass.)
In any case, mixing fractional denominators that aren’t multiples of each other is not something he generally does, so pairing 1/2 and 1/3 is as weird as it reads. If there is some intent to go ever so slightly heavier on the sloe gin than the scotch, that would be an outlier of a nuance.
The 1/3 scotch, 1/2 sloe gin is repeated in Harry’s ABC 1923 and 1930 editions, as well as 1927 Barflies. I say take it as it stands, using 2/3 and 1 oz respectively, or 1 and 1.5. I would not assume that 1/3 is a consistent typo for 1/2. However, note the lemon juice from the Hoffman House recipe is not included in McElhone’s. I will permit an experimental reading where the missing 1/6 is lemon juice that was a casualty of math anxiety.
So far, if I’m convinced, it’s mainly because changing the proportions and omitting lemon juice keeps the McElhone recipe distinct as opposed to redundant. I’m fresh out of both sloe and blended scotch, so testing will have to wait until my restock.
The oldest crediting of this drink (at least to my knowledge) is from June 6th, 1903 when the Police Gazette acknowledged it had been submitted to their (back then) famous cocktail competition.
They printed the recipe a year later on December 17th, 1904 which is, as you have correctly deduced, equal measures.
As a side note, there’s a second branch of this drink made famous by Hugo Ensslin (and later Craddock) that removes the Sloe Gin and instead adds a few dashes of Jamaica Rum to go against the Scotch.
