NOTE ON GULDIN’S PROPERTIES. 33 
pointed, the second or third pair often longer than the others ; 
caudal-shield, very small. This genus is also characteristic of the 
lowest zones of fossiliferous strata. Some more or less obscura 
species, first found in Vermont, have lately been discovered in the 
Quebec Group of Anse au Loup, on the north shore of the Straits 
of Belle Isle. 
Vertebrated Animals.—Remains of vertebrated forms are of rare 
occurrence in Canadian rocks. Our Silurian strata are entirely desti- 
tute of any signs of these remains, and traces only have as yet been 
discovered in our Devonian beds. These consist of fish scales and 
impressions (North Cayuga; St. Marys; Malden; Kettle Point; 
Bear Creek). *In the higher Drift accumulations, the bones and teeth 
of the Mastodon and Mammoth, the latter an extinct species of 
elephant (Hlephas primigenius), are occasionally found ; and in these 
and more recent deposits, the remains of existing forms, such as those 
of the capelin (Mallotus villosus), the lump-sucker (Cyclostomus 
lumpus), the northern seal (Phoca Grenlandica), the Canadian beaver, 
Wapiti, &c., have also been discovered. No marine forms, however, 
have been found in these deposits west of Kingston, as explained 
more fully, in our remarks on the Drift and succeeding period, in the 
next division of our subject. 
NOTE ON GULDIN’S PROPERTIES. 
BY J. B. CHERRIMAN, M.A. 
PROFESSOR OF NATURAL PHILOSOPHY, UNIVERSITY COLLEGE, TORONTO. 
It is well known that Pappus, the Greek geometer who flourished 
toward the end of the fourth century of our era, is the author of the 
remarkable propositions which are generally called “ Guldin’s Proper= 
ties of the Centre of Gravity.” They occur, without demonstration, 
at the end of the preface to the seventh book of hig Collections, and 
were first printed in the Latin translation by Commandine in 1588, : 
Guldin, in his work published 1635-42, gave the statement of then 
in the same form with numerous applications, but still without 
demonstration ; and having in this work attacked Cavalleri’s method 
of indivisibles, Cavalleri in reply not only refuted Guldin’s attack but’ 
Vou, VIII. As 
