definite amount of water. Cardinal Cusanus suggested then that the water-clock should be employed for estimating the pulse frequency. His idea was that the amount of water which flowed while a hundred beats of the pulse were counted, should be weighed, and this weight compared with that of the average weight of water which flowed while a hundred beats of the normal pulse of a number of individuals of the same age and constitution were being counted.

This was a very simple and a very ingenious suggestion. We have no means of knowing now whether it was adopted to any extent or not. It may seem rather surprising that a cardinal should have been the one to make such a suggestion. Cusanus, however, was very much interested in mathematics and in the natural sciences, and we have many wonderful suggestions from his pen. He was the first, for instance, to suggest, more than a century before Copernicus, that the earth was not the centre of the universe, and that it would not be absolutely at rest or, as he said, devoid of all motion. His words are: "Terra igitur, quæ centrum esse nequit, motu omni carere non potest." He described very clearly how the earth moved round its own axis, and then he added, what cannot fail to be a surprising declaration for those in the modern times who think such an idea of much later origin, that he considered that the earth itself cannot be fixed, but moves as do the other stars in the heavens. The expression is so astonishing at that time in the world's history that it seems worth the while to give it in its original form, so that it may be seen

clearly that it is not any subsequent far-fetched interpretation of his opinion, but the actual words themselves, that convey this idea. He said: "Consideravi quod terra ista non potest esse fixa, sed movetur ut aliæ stella."

How clearly Cusanus anticipated another phase of our modern views may be judged from what he has to say in" De Docta Ignorantia " with regard to the constitution of the sun. It is all the more surprising that he should by some form of intuition reach such a conclusion, for the ordinary sources of information with regard to the sun would not suggest such an expression except to a genius, whose intuition outran by far the knowledge of his time. The Cardinal said: "To a spectator on the surface of the sun the splendor which appears to us would be invisible, since it contains, as it were, an earth for its central mass, with a circumferential envelope of light and heat, and between the two an atmosphere of water and clouds and of ambient air." After reading that bit of precious astronomical science announced nearly five centuries ago, it is easy to understand how Copernicus could have anticipated other phases of our knowledge, as he did in his declarations that the figure of the earth is not a sphere, but is somewhat irregular, and that the orbit of the earth is not circular.

Cusanus was an extremely practical man, and was constantly looking for and devising methods of applying practical principles of science to ordinary life. As we shall see in discussing his suggestion for the estimation of the pulse rate later on, he made many other similar suggestions for diagnostic

purposes in medicine, and set forth other applications of mathematics and mechanics to his generation.

Many of Cusanus' books have curiously modern names. He wrote, for instance, a series of mathematical treatises, in Latin of course, on "Geometric Transmutations," on "Arithmetical Complements," on "Mathematical Complements," on "Mathematical Perfection," and on "The Correction of the Calendar." In his time the calendar was in error by more than nine days, and Cusanus was one of those who aroused sufficient interest in the subject, so that in the next century the correction was actually made by the great Jesuit mathematician, Father Clavius. Perhaps the work of Cusanus that is best known is that " On Learned IgnoranceDe Docta Ignorantia," in which the Cardinal points out how many things that educated people think they know are entirely wrong. It reminds one very much of Josh Billings's remark that it is not so much the ignorance of mankind that makes them ridiculous, as the knowing so many things that ain't so. It is from this work that the astronomical quotations which we have made are taken. The book that is of special interest to physicians is his dialogue "On Static Experiments," which he wrote in 1450, and which contains the following passages:

"Since the weight of the blood and the urine of a healthy and of a diseased man, of a young man and an old man, of a German and an African, is different for each individual, why would it not be a great benefit to the physician to have all of these various differences classified? For I think that a

physician would make a truer judgment from the weight of the urine viewed in connection with its color than he could make from its color alone, which might be fallacious. So, also, weight might be used as a means of identifying the roots, the stems, the leaves, the fruits, the seeds, and the juice of plants if the various weights of all the plants were properly noted, together with their variety, according to locality. In this way the physician would appreciate their nature better by means of their weight than if he judged them by their taste alone. He might know, then, from a comparison of the weights of the plants and their various parts when compared with the weight of the blood and the urine, how to make an application and a dosage of drugs from the concordances and differences of the medicaments, and even might be able to make an excellent prognosis in the same way. Thus, from static experiments, he would approach by a more precise knowledge to every kind of information.

"Do you not think if you would permit the water from the narrow opening of a clepsydra [waterclock] to flow into a basin for as long as was necessary to count the pulse a hundred times in a healthy young man, and then do the same thing for an ailing young man, that there would be a noticeable difference between the weights of the water that would flow during the period? From the weight of the water, therefore, one would arrive at a better knowledge of the differences in the pulse of the young and the old, the healthy and the unhealthy, and so, also, as to information with regard to various diseases, since there would be one weight and, therefore, one pulse in one disease, and another weight and another pulse in another disease. In this way a better judgment of the differences in the pulse could be obtained than from the touch of the vein, just as more can be known from the urine about its weight than from its color alone.

"Just in the same way would it not be possible to make a more accurate judgment with regard to the breathing, if the inspirations and expirations were studied according to the weight of the water that passed during a certain interval? If, while water was flowing from a clepsydra, one were to count a hundred expirations in a boy, and then in an old man, of course, there would not be the same amount of water at the end of the enumeration. Then this same thing might be done for other ages and states of the body. As a consequence, when the physician once knew what the weight of water that represented the number of expirations of a healthy boy or youth, and then of an individual of the same age ill of some infirmity or other, there is no doubt that, by this observation, he will come to a knowledge of the health or illness and something about the case, and, perhaps, also with more certainty would be able to choose the remedy and the dose required. If he found in a healthy young man apparently the same weight as in an old and decrepit individual, he might readily be brought to the conclusion that the young man would surely die, and in this way have some evidence for his prognosis in the case. Besides, if in fevers, in the same way, careful studies were made of the differences in the weight of water for pulse and respiration in the warm and the cold paroxysms, would it not be possible thus to know the disease better and, perhaps, also get a more efficacious remedy?"

As will be seen from this passage, Cusanus had many more ideas than merely the accurate estimation of the pulse frequency when he suggested the use of the water-clock. Evidently the thought had come to him that the specific gravity of the substances, that is, their weight in comparison to the weight of water, might be valuable information.