89 
The confirmation of one deduction of such a nature causes us 
to construe others from the observations we have made. 
Now that the series of formulas from Jf to 11/5 shows no longer 
an hiatus, it is possible, proceeding from the extremities of the series, 
to follow to a certain degree the process of transformation forward 
and backward, and to indicate the stages by hypothetical formulas. 
The formula ///d is analogical to the formula //, and in analogy 
to the formula //c we can add to the formula ///) a formula J/Je, 
indicating that the last dorsal vertebra of ///4, the 19" of the 
series, has become a dorsolumbal vertebra. 
When, by reduction of the rib still existing on one side of the 
19" vertebra, this becomes a first lumbal vertebra, then we have 
the form ///d, in which, as in ///b and ///c, a sacrum consisting 
of 6 vertebrae must be extant. 
Now we can imagine, that the 29 vertebra becomes a sacrocaudal 
vertebra and thus the formula ///c is given. 
And when now this 29 vertebra has passed into the series of 
the caudal vertebrae, the result is a vertebral column having the 
formula ///7, which, as the formulas //f and /f, is characterized by 
the existence of 5 caudal vertebrae, the last, however, is now the 
33° of the series. 
The reduction of this 38°¢ vertebra gives a formula ZV, an anologon 
to formula ///, and now once more the dorsolumbal boundary, the 
lumbosacral boundary and the sacrocaudal boundary have been 
displaced one vertebra in a proximal direction, and at the distal 
extremity one vertebra has disappeared. Consequently for the fourth 
time successive groups of 5 lumbal, 5 sacral, and 4 caudal vertebrae 
would be extant. | 
I have not hesitated to mention these conciusions. because formula 
IV may indeed not be considered to be a hypothetical one. A verte- 
bral column of this composition has been described more particularly 
by Tencuinr') in Parma, who however adheres to the then already 
refuted doctrine of excalation, and supposes, that the 12" dorsal 
vertebra with its ribs is entirely missing. A similar vertebral column 
has also been observed and briefly described by Brancni’) in Siena. 
Whether this process whill continue further, cannot be said with 
certainty ; it might be possible. 
1) L Tencutnt, Mancanza della dodicesima vertebra dorsale e delle due ultime 
coste ete. L’Ateneo Medico Parmense, Anno 1. Fase. 2 p. 97—132. Parma 1887. 
2) S. Brancut, Sulla frequenza delle anomalie numeriche vertebrali nello scheletro 
dei normali e degli -alienati. Atti della R. Accad. dei Fisiocritici in Siena. Ser. IV, 
vol VII Fasc. 1—2. p. 29, osservazione V. Siena 1895. 
