The influences mentioned under (1) may be seen in tracings taken from cases of cardiac insufficiency, and have merely pathological interest. All the other influences, however, can be observed in the curves which are traced for psychological purposes. The changes in the general rise or fall of the curves are not so very hard to observe,[81] and for the observation of the rapidity of the heart-beats it is only necessary to trace a time-curve and count the number of beats or measure the length of every single beat. Also the changes of the height of the waves can easily be measured. This has been done conscientiously by several observers. It is by far harder to see the changes in the form of the catacrotic branch, and only a few keen observers have seen them. These changes of the pulse curve under the influence of feelings were proved as facts by experiments, but their interpretation was doubtful. With the exception of the rapidity of the heart-beats, which could easily be observed in some other way, all the symptoms of the influence of feelings on circulation are ambiguous. A difference in height of the single waves may be due to a change in the amount of blood which is pumped into the artery, but it also may be due to a change in the amplitude of the vibrations of the artery. The form of the catacrotic part of the sphygmographic curve may be changed by a different state of innervation of the arterial wall, but it also may be due to an increase or decrease of the friction of the surrounding tissues. The general rise or fall of the curve may indicate a change in the amount of blood which leaves the left ventricle, but it also may indicate a change in the amount of the capillary outflow. The problem, nevertheless, is fully determined, and a solution is suggested by the constructions in Fig. 5. The form of the resulting movement depends, first, on the length of the line _AB_, secondly, on the length of the line _AE_, and thirdly, on the nature of the elastic movement. An elastic movement is determined if three constants are known, one of which is the amplitude, the second the friction, and the third the elasticity. Only _AB_ can be measured directly, and there remain four unknown quantities to be determined. Four measurements must be sufficient for this purpose. It is obvious, however, that not any four measurements will do, but a method can be devised by which it is possible to determine each one of these four quantities. The problem can be solved in every case provided that the sphygmogram is trustworthy enough to justify the work. The length _AB_ is proportional to the time of one heart-beat, and the length of the line _AE_ is proportional to the amount of blood pumped into the arteries. The successful analysis of the pulse curves, therefore, shows changes of the action of the heart and makes it possible to distinguish them from the changes at the periphery.