Duncan MacDougall managed (apparently overcoming any ethical qualms over human experimentation) to put six dying people on a bed equipped with sensitive springs, and claimed to have observed a sudden loss of weight – about ¾ of an ounce – at the exact moment of their death. Having reasoned that such loss could not be explained by bowel movements or evaporation, he concluded he must have measured the weight of the soul. A follow-up experiment also showed that dogs (which were healthy, so they were probably poisoned on purpose by the good doctor) don't seem to suffer the same sort of loss, therefore they don't have souls (sorry, you canine lovers).
This is an excellent example of where pseudoscience and belief go wrong, on a variety of levels. Let us start with MacDougall's claim itself: it turns out that his data were decidedly unreliable by any decent scientific standard. Not only was the experiment never repeated (by either MaDougall or anyone else), but his own notes (published in American Medicine in March 1907) show that of the six data points, two had to be discarded as “of no value”; two recorded a weight drop, followed by additional losses later on (was the soul leaving bit by bit?); one showed a reversal of the loss, then another loss (the soul couldn't make up its mind, leaving, re-entering, then leaving for good); and only one case actually constitutes the basis of the legendary estimate of ¾ of an ounce. With data like these, it's a miracle the paper got published in the first place.
Second, as was pointed out immediately by Dr. Augustus P. Clarke in a rebuttal also published in American Medicine, MacDougall failed to consider another obvious hypothesis: that the weight loss (assuming it was real) was due to evaporation caused by the sudden rise in body temperature that occurs when the blood circulation stops and the blood can no longer be air-cooled by the lungs. This also elegantly explains why the dogs showed no weight loss: as is well known, they cool themselves by panting, not sweating like humans do.