Wet nursing was the most common solution when mothers could not feed their own infants through the early nineteenth century, as I discussed in this earlier answer.

As the nineteenth century went on and maternal nursing became more and more normal, fewer women acted as professional wet nurses and they became harder to find when needed. Upper- and middle-class families were more and more suspicious of these working-class women from unknown backgrounds - what diseases or personality traits were they passing along to the children in their care? Were they drunks who might accidentally drop the baby into the fire? European chemists and doctors first began to experiment with adding cream and starches to cow's milk in order to fortify it enough to act as a substitute for breast milk, and by the 1870s American manufacturers had entered the market. At this point, advertising no longer had to position formula against the dangers of wet nurses - they were gone, and the "this brand is the best" type of advertising became the norm. In some cases, this formula would be premade by a manufacturer, as today, but in others, what was marketed was a literal formula. Dr. L. Emmett Holt, the Dr. Spock of his day, published a set of formulas for "the early months" in a table in The Care and Feeding of Children in 1894 (link here goes to the 1917 edition):

Formula	I.	II.	III.	IV.	V.	VI.	VII.	VIII.	IX.
Milk ... oz.	6	6 1/2	7	7 1/2	8	8 1/2	9	9 1/2	10
Sugar ... "	1	1	1	1	1	1	1	1	1
Water ... "	14	13 1/2	13	12 1/2	12	11 1/2	11	10 1/2	10
Flour ... tablesp's	0	0	0	0	0	0	0	0	1

How should such formulas as those in the table be used?

Beginning at birth, Formula I might first be given, and the strength of the food increased about once a week, up to No. V, after that every two weeks until No. IX is reached.

Such a formula as No. IX will be reached by an average healthy infant at about three months of age. After this, the next group of formulas may be used, but the increase should be made more slowly, about once a month, up to No. XII, then about every two months, reaching No. XIV at about ten months. This may be continued up to twelve months.

Formula	IX.	X.	XI.	XII.	XIII.	XIV.
Milk ... oz.	10	11	12	13	14	15
Sugar ... "	1	1/2	1/2	1/2	1/2	1/2
Water ... "	10	9	8	7	6	5
Flour ... tablesp's	1	1 1/2	1 1/2	1 1/2	2	3

Scientific infant feeding really goes hand-in-hand with the domestic science movement as a whole, although this segment seems to have been presided over by men, where theories about the caloric intake of adults and how women should cook with scientifically-created recipes tended to come from female proponents. Despite the commercial success of prepared formulas and mashed infant foods, however, they didn't agree with all infants - and in cases where it seemed that a baby was suffering from malnutrition due to a commercial food, doctors did prescribe hiring a wet nurse.