I believe that Haldane defined the cost of natural selection as the number of selective deaths (normalized to the population size) required for a substitution. As an example, if the population size of a haploid organism were 10,000, Haldane calculated the substitution cost of going from one individual carrying a favorable trait to the entire population carrying the trait as follows. Cost = - ln(p₀), where p₀ is the initial frequency of the favorable trait. For this example, p₀ is 1/10,000. The natural log (ln) of 1/10,000 is -9.21, which leads to a cost of 9.21. A cost of 9.21 indicates that 9.21 times the population size must die in order for the substitution to occur. Since the population size is 10,000 for our example, this means that approximately 92,100 individuals must die for the favorable trait to become fixed. The conclusion that the cost represents the number of deaths required for the substitution to occur is from very careful reading and rereading of his paper. Here are some excerpts from "The Cost of Natural Selection" that led me to this conclusion.

"The principal unit process in evolution is the substitution of one gene  for another at the same locus. ... I shall show that the number of deaths needed to carry out this unit process by selective survival is independent of the intensity of selection over a wide range."  page 511

"It is convenient to think of natural selection provisionally in terms of juvenile deaths. If it acts in this way, by killing off the less fit genotypes, we shall calculate how many must be killed while a new gene is spreading through a population."  page 512

"[Haldane is speaking about the process of natural selection in a deteriorating environment]... But meanwhile, a number of deaths, or their equivalents in lowered fertility, have occurred. If selection at the i^th selected locus is responsible for d_i  of these deaths in any generation the reproductive capacity of the species will be P(1 - d_i) of that of the optimal genotype , or exp(-Sd_i) nearly, if every d_i is small. Thus the intensity of selection approximates to Sd_i."  page 514

[D is what Haldane called the substitution cost or the cost of natural selection.]
"Let D_i be the sum of the values of d_i over all generations of selection, ..."  page 514

Haldane then goes on to discuss the calculation of D for many different cases - haploid, diploid, etc. On page 516, summing up the haploid case, he says:

"We may, therefor, take  it that when selection is fairly slow, the total number of selective deaths over all generations is usually 5-15 times the total number in the population in each generation, 10 times this being a representative value."

Finally, Haldane's 1960 paper "More Precise Expressions for the Cost of Natural Selection" (Journal of Genetics 57:351-360) begins with a very clear definition of the cost of natural selection:

"Haldane (1957) gave expressions for the "cost" of natural selection, that is to say for the total number of deaths, or their equivalent in reduced fertility, sometimes called "genetical deaths", which must occur in a population of constant size before a gene is replaced by one of its allelomorphs. Smith (1958) and Kimura (1960) have accepted the theory; the latter uses the term "substitutional load", for the component of the deathrate at any time which is due to this evolutionary process.

There are lots of other quotes in the "The Cost of Natural Selection" along this line. Haldane clearly defined the cost of natural selection to be the cumulative total of all selective deaths in the course of a gene substitution (normalized to the population size). Obviously, for the population size to remain constant, there must be an equivalent number of surplus births somewhere. Therefor, the cost can also be said to represent the amount of reproductive excess required to keep the population from declining due to the deaths required for the substitution to occur.