大西洋奴隶贸易中奴隶和船员死亡率的决定因素（3）

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Crowding

Although contemporary critics of the slave trade widely regarded crowding

or "tight packing" of slaves as unhealthy, early regulations limited crowding,

and connections between density and mortality are inherently plausible within

a framework of the spread of infectious disease, recent quantitative studies

fail to establish a connection between slaves per ton and mortality.34 This

paper demonstrates that variations in crowding were crucial to variations in

death rates during loading. The contrasting results are reconcilable by

Figure 1, which shows that the chances of deaths changed little with increasing density above 1.5 slaves per ton. Admittedly Figure 1 does not extend to

densities in the area of 2 to 3 slaves per ton that prevailed outside the era

of regulation, but findings by others that overall mortality varied little

across voyages within the higher ranges are consistent with the hypothesis

that the relationship changed little across high densities. It appears that

Dolben's Act may have had little effect on mortality because the limits on

crowding were not sufficiently restrictive.

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拥挤

尽管对奴隶贸易的当代批评家普遍认为拥挤或"紧密装载"奴隶是不健康的，早期法规限制了拥挤，并且密度与死亡率之间的联系在传染病传播的框架内是合理的，但最近的量化研究未能证明单位吨奴隶与死亡率之间存在联系。这篇论文证明了在装载过程中，拥挤变化对死亡率变化至关重要。这些对立的结果可以通过图1得到调和，该图显示，随着密度超过每吨1.5名奴隶的增加，死亡几率几乎没有变化。值得承认的是，图1没有延伸到每吨2到3名奴隶的密度范围，而这种密度在法规管控之外普遍存在，但其他人的研究结果表明，在较高范围内航程的整体死亡率变化不大，这与假设相一致，即在高密度下，这种关系几乎没有改变。看起来，多尔本法案可能对死亡率影响不大，因为对拥挤的限制不够严格。

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Voyage Length

It has been widely, though not universally, noted that the share of the

cargo dying increased with time at sea.35 Whether there should have been a

positive relationship has not been debated. Instead controversy centers on

the profile of mortality within the voyage, and specifically on the relative

importance of high mortality rates at the beginning as opposed to the end of

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the journey. It has been argued that the former would have been associated

with poor conditions in Africa and the latter with poor conditions on the voy age, especially near the end of unusually long voyages. Neither of these pat terns is supported by this study, at least not for the major causes of death

studied in detail. This research suggests that high density possibly aggre—

vated by poor health before loading and poor nutrition during the voyage led

to high death rates from gastrointestinal diseases near the middle of the voy age.

These results suggest directions for further research. Data on voyage

length and share of slaves who died may be inadequate for measuring the im portance of provisioning because the diseases involved are crucial to the ar gument; specifically, if there was screening before loading one would expect

deaths from epidemic diseases having relatively long incubation periods (such

as smallpox and measles, in which it is about two weeks) to accumulate near

the end of the voyage. Furthermore, deaths resulting from reduced provisions

need not have been concentrated at the end of the voyage. Delays in voyages

crossing the equator occurred frequently in the doldrums off the coast of

Africa. Ship captains probably adjusted provisions as a function of where the

ship was in relation to where it was expected to be.36 Thus, rations could

have been cut early in the voyage and restored near the end of an unusually

long journey Even with "normal provisions the journey was probably debili tating, and thus the rise in death rates from respiratory diseases and scurvy

reported in Table 3 is consistent with the argument that conditions on the

ship were important to health.37 Third, high death rates early in the voyage

may be consistent with poor conditions in Africa, but low death rates early in

the voyage do not necessarily irrply that conditions in Africa were goodu;

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captains and surgeons may have avoided areas with epidemics and may have been

successful in screening slaves in poor health. Finally, greater attention

shoud be given to the interaction of conditions in Africa with those on the

ship. One of the contributions of the study of heights has been to alert

researchers to the nature and extent of interaction among nutrition, disease,

and growth.3A Thus, for example, the effects of famines in Africa on mortality during the voyage may have been a function of crowding, provisioning, and

voyage length

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航行时间长度

已广泛注意到，尽管不是普遍的，但货物死亡率随着航行时间增加而增加。是否应该存在正向关系并未受到争议。相反，争议集中在航行过程中的死亡情况，尤其是在旅程开始和结束时死亡率的相对重要性。有人认为前者可能与非洲的恶劣条件有关，而后者可能与航行中恶劣条件有关，特别是在异常长的航程接近尾声时。这项研究并未支持这两种模式，至少对于详细研究的主要死因而言。该研究表明，高密度可能加剧了装载前的糟糕健康状况和航行期间的营养不良，导致了航行中段发生胃肠疾病的高死亡率。

这些结果为进一步研究提供了方向。由于所涉及的疾病对于论证至关重要，可能无法准确衡量供给的重要性，航行时间长度和死亡奴隶的份额的数据可能不足；具体而言，如果装载前进行了筛查，那么预期较长潜伏期（例如天花和麻疹，其潜伏期约为两周）的流行病性疾病的死亡人数可能会在航行结束时累积。此外，由于航行穿越赤道时常常在非洲沿岸的无风区遇到延误，造船长官可能会根据船位于预期位置的相对位置来调整供给。因此，在异常漫长的航程末端可能会削减口粮，并在航程接近尾声时恢复。即使有了“正常供给”，旅程可能仍然会削弱身体健康，因此表3中报告的呼吸系统疾病和坏血病的死亡率上升与船上的环境条件与健康状况的论点是一致的。第三，在旅程开始阶段的高死亡率可能与非洲的恶劣条件一致，但旅程开始阶段的低死亡率并不一定意味着非洲的条件良好；船长和外科医生可能会避开流行病区域，并且可能成功地筛选出健康状况差的奴隶。最后，应更加关注非洲条件与船上条件的相互作用。研究身高的一个贡献在于提醒研究人员营养、疾病和生长之间的相互作用的性质和程度。因此，例如，非洲的饥荒对航行期间的死亡率可能受到拥挤、供给和航行时间长度的影响。

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Age and Sex

Studies examining differential mortality by age have usually found that

rates were higher for children.39 No systematic pattern has emerged involving

males versus females. Findings in this study that chances of deaths from gas trointestinal diseases during loading were higher for children and females are

generally consistent with previous work.

Epidemics

Although the role of epidemics are difficult to appraise from aggregate

measures such as the share of slaves embarked who died, it is clear from qual itative evidence for the entire slave trade that the spread of infectious

diseases such as dysentery, smallpox, and measles were important in overall

mortality. As many as 20 to 30 percent or more of the ships in some trades,

especially those of the seventeenth and early eighteenth centuries, had deaths

as a share of slaves embarked in excess of 15 percent.40 In these data the

average share of slaves who died was 2.4 percent, the share exceeded 4 percent

for only 10 out of 92 vessels (the distribution is given in Table 11 of the

appendix) and the highest share in the sample was 13.8 percent. The favorable

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record stems in part from the lack of deaths from smallpox and measles. It also appears that the spread of dysentery may have been contained in these

data relative to vessels that had high mortality rates; only 60 percent of the

ships in the sample reported one or more and only 33 percent reported two or

more deaths from gastrointestinal diseases.

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年龄和性别

研究发现，在考察按年龄划分的死亡率时，儿童的死亡率通常较高。关于男性与女性之间的差异，尚未出现明确的模式。本研究发现，在装载过程中，儿童和女性患上胃肠疾病导致死亡的机会较高，这与之前的研究结果一致。

流行病

虽然很难根据总体统计的指标来评估流行病的作用，例如登船死亡率，但从整个奴隶贸易的质性证据来看，传染性疾病如痢疾、天花和麻疹的传播在整体死亡率中是重要的。在某些贸易中，特别是在17世纪和18世纪早期的贸易中，多达20%至30%或更多的船只中，登船奴隶死亡率超过了15%。在这些数据中，死亡比例的平均值是2.4%，只有10艘船的死亡比例超过了4%（详见附录的表11），样本中的最高死亡比例为13.8%。这记录部分归因于没有天花和麻疹导致的死亡。此外，据推测，在这些数据中，痢疾的传播可能相对于死亡率较高的船只得到了控制；样本中只有60%的船只报告了一次或更多次胃肠疾病导致的死亡，只有33%的船只报告了两次或更多次。

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Slaves and Crew

The issues of slave and crew mortality involve comparative levels and the

extent of interrelation. The few data available on these questions indicate

that crew mortality exceed that for slaves and that the two were positively,

though, weakly, correlated.41 The fact that slaves and crew tended to die

from different causes would lead one to expect at most a weak positive corre

lation between overall slave and crew death rates. This study suggests that

passage of gastrointestinal diseases from slaves to crews during the voyage

was a source of that correlation. Though minor in these data, respiratory

diseases and scurvy may have been important causes of death common to slaves

and crew in earlier eras of the trade.

Although the literature on the slave trade seldom includes estimates of

crew mortality, West Africa acquired a reputation among Europeans as the

uwhite man's grave." Crew death rates probably remained high until progress

was made against malaria and yellow fever beginning in the mid—nineteenth

century. Thus the finding in this paper that the annual death rate during

loading and the voyage combined was 229.5 per thousand for the crew is not

surprising in light of other studies. The comparable figure among slaves of

82.8 per thousand is surprising for the extent to which it was below that for

the crew. The next section discusses the low death rate for slaves.

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## 来自ChatAI的消息:

奴隶和船员

奴隶和船员死亡率的问题涉及相对水平和相互关系的程度。有关这些问题的少量数据表明，船员的死亡率超过了奴隶的死亡率，而且两者呈微弱的正相关。奴隶和船员往往因不同的原因而死亡，这使人们预期奴隶和船员整体死亡率之间最多只存在微弱的正相关。此研究表明，在航行期间，奴隶传染胃肠疾病给船员是这种相关性的一个原因。尽管这些数据中的呼吸道疾病和坏血病是次要原因，但它们可能是早期贸易时期奴隶和船员共同死亡的重要原因之一。

尽管奴隶贸易文献中很少包含船员死亡率的估计数据，但西非在欧洲人中获得了"白人的坟墓"的声誉。直到19世纪中叶针对疟疾和黄热病的进展取得了进展之前，船员死亡率可能一直很高。因此，本文发现在装载和航行期间的年死亡率为每千人229.5，对于其他研究来说并不令人意外。而奴隶的相应数字则是每千人82.8，令人惊讶的是它比船员的死亡率低得多。下一部分将讨论奴隶的低死亡率。

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CONCLUDING REMARKS

Using data giving date and cause of death this study has found that

fevers and gastrointestinal diseases were the major cause of death for slaves

and crew in the English slave trade to the West Indies during the late 1700s.

The crew died primarily from fevers (mostly malaria) contracted in Africa, and

gastrointestinal diseases such as dysentery that spread during the voyage were

the major cause of slave deaths. The chances of slave and crew deaths varied

systematically by region of origin in Africa, season of the year, and day of

the voyage; for slaves alone by density on board ship, age, and sex; and for

the crew alone by recent occurrence of slave deaths from gastrointestinal

diseases during the voyage.

The incidence of mortality as measured by the number of deaths as a share

of slaves embarked was low in these data compared to the slave trade in other

times, which raises the question of the generality of these results. In light

of this study, why might death rates have been higher elsewhere? There are

several possible explanations. First, diseases such as smallpox and measles

that were prevalent in other times were virtually absent from these data.

Inoculation may have been effective in reducing the incidence of smallpox on

the ships of the surgeons' logs. Second, knowledge and experience involving

health and mortality in the slave trade had accumulated by the late 1700s.

Practices at this time were not guided by a germ theory of disease, but pre sumably trial, error, and observation had eliminated some practices that con tributed to deaths. One would expect that the rise in slave prices that

occurred from the late 1600s provided an incentive for innovation in health

care.42 Third, Dolben's Act may have lowered mortality. To the extent that

limits on capacity allowed room for more provisions, health may have

improved.43 The fact that deaths from respiratiory diseases and scurvy were

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low in these data is consistent with this explanation. In addition, the

incentives of the act may have encouraged surgeons to screen carefully slaves

in poor health. Fourth, conditions on slave ships were unhealthy, and the

less time spent in this environment, the lower the share of slaves who died.

Loading times and voyage length declined from the seventeenth through the end

of the eighteenth century.44 Finally, nutritional and demographic conditions

in Africa could have changed in ways that led to slaves who were in better

health before loading. Additional studies of slave mortality that make use of

data on date and cause of death and conditions in Africa may shed light on

these issues.

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结论

根据提供死亡日期和死因的数据，本研究发现在18世纪晚期的英国奴隶贸易中，发烧和胃肠疾病是奴隶和船员死亡的主要原因。船员主要因在非洲感染的发烧病（主要是疟疾）而死亡，而旅途中传播的痢疾等胃肠疾病是奴隶死亡的主要原因。奴隶和船员的死亡几率因非洲的起源地、年份的季节和航程的日子而有系统地变化；仅针对奴隶，还有船上的密度、年龄和性别；仅对船员来说，还有奴隶在航行中死于胃肠疾病的最近发生情况。

根据奴隶登船人数中死亡人数的比例作为死亡率的衡量标准来看，相对于其他时期的奴隶贸易数据而言，这些数据中的死亡率较低，这引发了关于这些结果适用性的问题。考虑到这项研究，为什么其他地方的死亡率可能更高呢？有几种可能的解释。首先，在其他时期流行的天花和麻疹等疾病在这些数据中几乎不存在。接种疫苗可能在减少船上天花发生率方面起了作用，而船医日志记录可能证明了这一点。第二，到18世纪晚期，奴隶贸易中围绕健康和死亡的知识和经验已经积累。这个时期的做法并不是以病原体理论为指导的，但可以推测试验、错误和观察已经消除了一些导致死亡的做法。可以预期，从17世纪末开始奴隶价格的上涨为创新医疗提供了激励。第三，Dolben法案可能降低了死亡率。从容量限制的角度来看，提供更多的物资可能有助于改善健康。这些数据中呼吸道疾病和坏血病的死亡率较低与这一解释一致。此外，该法案的激励可能鼓励船医仔细筛选健康状况不佳的奴隶。第四，奴隶船上的条件不健康，越少时间待在这种环境中，死亡比例就越低。从17世纪到18世纪末，装货时间和航程长度都有所减少。最后，非洲的营养和人口状况可能会发生改变，导致在装船前处于较好健康状态的奴隶。进一步利用有关死亡日期和死因以及非洲情况的奴隶死亡的研究可能会对这些问题有所启示。

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Studies of modern labor markets show that workers receive higher wages

for jobs that, other things being equal, are unpleasant or dangerous.45 The

acquisition of crew members for slave ships constitutes an economic laboratory

fr t"j of employment under very hazardou conditions. Interest'ng ques

tions about this labor market include the size of compensating wage differen tials, whether higher wages were received for destinations to the higher mor tality regions of Africa, the extent to which prospective crew members were

informed about the risks, and the nature of compensation. With regard to the

last point one might expect that crew members who were knowledgeable about the

risks would have insisted on some compensation in the form of a signing bonus

that was spendable before the hazardous journey began.

Comparative studies of mortality rates on ocean voyages would help to

place the slave trade in perspective and to elucidate causes of mortality on

slave and non—slave voyages.46 Data on non-slave voyages to the U.S. are

available, for example, from passenger lists and from forms required by the Pas senger Act of 1819. The agenda for research on these questions should include

the relationship of health before departure to health and mortality during the

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voyage, the influence of provisioning on mortality, crowding and mortality,

seasonal patters of mortality, age and sex distributions and mortality, the

course of death rates during the voyage, and the time trend in mortality.

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现代劳动市场研究显示，工人在其他条件相等的情况下，从事令人不愉快或危险的工作会获得更高的工资。45 外国奴隶船的船员选拔构成了一个经济实验室，处于极其危险的工作条件下。关于这个劳动市场的有趣问题包括补偿工资差异的大小、是否因为前往非洲较高死亡率地区而获得更高工资、潜在船员对风险了解的程度以及补偿的形式。关于最后一点，可以预期那些了解风险的船员在危险旅程开始之前会坚持要求一笔可支配的签约奖金作为补偿。

比较海上旅行的死亡率研究有助于正确看待奴隶贸易，并阐明奴隶和非奴隶航行中死亡率的原因。46 例如，可以从乘客名单和1819年《旅客法》要求的表格中获取关于前往美国的非奴隶航行的数据。关于这些问题的研究议程应包括出发前健康状况与航行期间的健康和死亡率之间的关系、供应对死亡率的影响、拥挤与死亡率、季节性死亡模式、年龄和性别分布与死亡率、航行期间死亡率的变化以及死亡率的时间趋势。

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30

Appendix: Discussion of the Data

Origins

"An act to regulate, for a limited time, the shipping and carrying of

slaves in British vessels from the coast of Africa," also known as flolben's

Act, emerged from the parliamentary debates over the slave trade in 1788.

The act limited vessels to five slaves for every three tons of burden up to

201 tons, and one slave per ton for every ton above 201.48 Ship captains ex ceeding this limit were subject to a fine of £ 30 per slave above the limit.

Surgeons on board slave ships were required to maintain a journal encompassing

slave loading, slave and crew deaths, and causes of death. The law specified

that the collector at the port of destination was to administer on oath to the

surgeon attesting the truth of the journal. Captains received £ 100 and sur geons received £ 50 if deaths as a fraction of the largest number of slaves on

board did not exceed 2 percent. The awards were £ 50 and £ 25, respectively,

if the rate did not exceed 3 percent.

Characteristics

An extensive search of the House of Lords Record Office and the Public

Record Office produced 92 surgeons logs that are substantially complete.49

The typical journal begins with a brief description of the vessel (name, names

of master and surgeon, home port and tonnage) followed by sections on loading

and unloading by day in categories of men, women, boys, and girls: chronologi cal lists of slave and crew deaths; and the oath signed by the surgeon.

The dates of departure from Africa of the ships in the sample span the

period from 1792 to 1796. Roughly one-third of the departures occurred in

1793 and only 9 voyages took place in 1794. The typical vessel loaded for 119

days, (s.d. = 92 days) but the range of experience encompassed 1 to 529 days.

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Approximately 28,770 slaves departed from Africa, of whom 63.7 percent were

males and 9.6 percent were children. The average ship carried 313 slaves and

had a capacity of 222 tons. All the major regions of supply along the west

coast of Africa are represented in the sample; 3 originated from Senegambia,

11 from Sierra Leone, 2 from the Windward Coast, 13 from the Gold Coast, 7

from the Bight of Benin, 8 from the Bight of Biafra, 18 from Congo—Angola, and

the area of origin for 30 vessels is unknown. The typical voyage took 56 days

(s.d. = 15.3 days) and the range was from 23 to 105 days. All the slaves were

destined for the British West Indies and three—quarters of the ships went to

Jamai ca.

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附录：数据讨论

来源

《一项调控有限期限内英国船只从非洲海岸运送奴隶的法案》，俗称弗洛本法案，起源于1788年关于奴隶贸易的议会辩论。该法案规定，船只负载量在201吨以下，每3吨负载可以搭载5名奴隶；超过201吨的每1吨负载可以搭载1名奴隶。超过限制的船长将被罚款30英镑每名超过限制的奴隶。奴隶船上的医生需要记录奴隶装载情况、奴隶和船员的死亡以及死因的日志。法律规定，目的港口的收税员要对医生进行宣誓并证明日志的真实性。如果船上的死亡比例不超过最大奴隶数量的2%，船长将获得100英镑的奖励，医生将获得50英镑的奖励。如果比例不超过3%，奖励分别为50英镑和25英镑。

特点

在上议院记录办公室和公共记录办公室进行了广泛搜索，找到了92份基本完整的医生日志。典型的日志以对船只的简要描述（名称、船长和医生的姓名、母港和吨位）开始，然后是按日进行的装载和卸载的部分，分为男性、女性、男孩和女孩的类别；接下来是奴隶和船员死亡的按时间顺序的列表；最后是医生签署的宣誓。样本中船只从非洲起航的日期跨越了1792年至1796年。大约三分之一的航程发生在1793年，只有9次航行在1794年进行。典型的船只装载工作持续了119天（标准差=92天），但经验范围从1天到529天不等。大约有28,770名奴隶从非洲出发，其中63.7%为男性，9.6%为儿童。平均每艘船载有313名奴隶，载重量为222吨。样本中涵盖了非洲西海岸沿线所有主要供应地区：塞内加尔-冈比亚地区有3艘船，塞拉利昂有11艘船，广岛海岸有2艘船，黄金海岸有13艘船，贝宁湾有7艘船，比亚弗拉湾有8艘船，刚果-安哥拉有18艘船，而有30艘船的起源地不详。典型航程耗时为56天（标准差=15.3天），范围从23到105天不等。所有奴隶都被运往英属西印度群岛，四分之三的船只前往牙买加。

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Bi ases

The logs of 16 vessels specify the day of arrival at the port of destina tion. Arrival times for 71 vessel were inferred from the day the surgeon's

oath was signed. Arrival information is incomplete or lacking for 5 logs.

Presumably the surgeon ceased to record deaths when the vessel reached port.50

If the oath was administered after the day the vessel reached port, then death

rates calculated for the end of the voyage would be biased downwards because

the number of days at risk for recording deaths would be overstated.

Fortunately 12 vessels reported the actual day of arrival and have the

oath. In this sample the average lag between the day of the oath and the

reported day of arrival is 2.1 days, and the range is from 0 to 5 days. The

distortion to calculated death rates is relatively minor if the experience of

these vessels applied to those for which we lack information.

Throughout the period of the slave trade entrepreneurs commonly rewarded

masters, surgeons, and certain members of the crew for efforts to maintain the

health of the cargo. Bonuses took the form of shares of the sales receipts,

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head money, and privilege slaves.51 The extent to which Dolben's Act may

have contributed to total incentives is not clear; entrepreneurs could have

allowed legislated incentives to substitute for their own.

Table 11 shows the frequency distribution of recorded deaths as a share

of slaves exported from Africa. The clusters of observations at or below 2

percent and 3 percent combined with the cut-off point for bonuses under Dol—

ben's Act raise the suspicion that some deaths may not have been recorded.

The observation that death rates in the Atlantic slave trade were rela tively low during the 1790s appears to support the underreporting thesis.52

In defense of the data, however, it should be recognized that good reasons

exist for the low death rate (see the concluding section of the paper). While

substantial underreporting cannot be entirely ruled out, the favorable situa tion with respect to epidemic diseases of smallpox and measles, for example,

makes the calculated aeath rates plausible.

Even if there was substantial underreporting, the implications for our

understanding of determinants of mortality heavily depends upon selectivity of

underreporting. If deaths were not reported at random, for example, then many

conclusions about regional influences, seasonal patterns, and the course of

events during the voyage remain largely intact.

A selective form of underreporting perhaps worth discussion involves the

end of the voyage. The decline in calculated death rates after the middle of

the voyage combined with the chronological organization of the journals sug gests that a simple strategy for collecting bonuses under Dolben's Act for

ships that were near the margin for collection was to neglect to report deaths

near the end of the voyage. Since all slaves loaded had to he accounted for,

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this required falsification of loading records. While this form of underreporting may have existed, it is relevant to note that the time profile of

deaths (available for gastrointestinal diseases only) on vessels that exceeded

the 3 percent minimum reached a peak on day 35 of the voyage and then declined

at a rate similar to that for the entire sample shown in Figure 2.

## 来自ChatAI的消息:

在16艘船的日志中，指定了抵达目的港的日期。从医生宣誓签署的日期可以推断出其他71艘船的抵达时间。其中5艘船的抵达信息不完整或缺失。推测医生在船到港后停止记录死亡情况。如果医生宣誓的日期在船到港之后，那么根据航行末期计算的死亡率会有向下的偏差，因为记录死亡情况的风险天数会被夸大。幸运的是，有12艘船报告了实际的抵达日期和医生宣誓的日期。在这个样本中，医生宣誓日期与报告的抵达日期之间的平均差距为2.1天，范围为0至5天。如果这些船只的经验适用于我们缺乏信息的船只，那么对计算的死亡率的扭曲相对较小。在奴隶贸易时期，企业家常常奖励船长、医生和某些船员为维持货物健康所做的工作。奖金以销售收据的份额、头钱和特权奴隶的形式存在。德尔本法可能对总奖励做出了贡献，但目前还不清楚；企业家可能已经允许法定的激励取代了他们自己的激励。表11显示了记录的死亡人数占从非洲出口的奴隶的比例的频数分布。观察到在2%和3%的水平以及德尔本法规定的奖金截止点以下的聚集现象使人怀疑可能有一些死亡未被记录。大西洋奴隶贸易在1790年代的死亡率相对较低似乎支持了低报告率的观点。然而，在捍卫数据的同时，应该认识到低死亡率存在充分的理由（参见本文的结论部分）。即使存在相当大的低报告率，对我们理解死亡率决定因素的影响还严重依赖于随机性的低报告率选择性。例如，如果死亡率不是随机报告的，那么关于地区影响、季节模式和航行过程的许多结论基本上仍然成立。一个值得讨论的选择性低报告形式涉及航程的结束。航程中期后计算的死亡率下降与日志的时间顺序组织结合起来，暗示了在接近收集边际的船只中，一种简单的获得德尔本法奖金的策略是忽视航程末期的死亡情况报告。由于所有上船的奴隶都必须核对，这就需要虚假记录装载信息。虽然可能存在这种类型的低报告，但值得注意的是，那些超过3%最低要求的船只上的死亡情况（仅有胃肠疾病可得数据）在航程第35天达到顶峰，然后以与整个样本相似的速率下降（见图2）。