640 



SCIENCE. 



[K S. Vol. XXII. No. 568. 



chelonians. Ponds, creeks, marsJies and rivers 

 are swarming with them, and surely a place 

 could be found which only requires fencing to 

 be turned into a scientific, experimental 

 * crawl,' where some hundreds of turtles of a 

 suitable kind could be turned loose, labeled, of 

 course, and examined from time to time 

 whether any of them are amending their ab- 

 normal shells. For physical reasons such an 

 experiment of possibly far-reaching, funda- 

 mental importance, can not be made in 

 Europe. H. Gadow. 



Cambeidge, Eng., 

 September 4, 1905. 



NOTE ON VECTOR SYMBOLS. 



The question of notation was always of 

 importance, and the introduction of new 

 methods depends a good deal on it. It is, of 

 course, highly desirable to have one system of 

 notation used by all the scientific world, but 

 at the same time it is also desirable that the 

 system in use shall be a simple and easy one. 



The vector-analysis becomes more impor- 

 tant every day in the study of physics. It is, 

 therefore, necessary to have a vector notation 

 as simple as possible. The notation used to- 

 day is far from being uniform, and still the 

 tendency is towards the introduction of Ger- 

 man letters for the symbolization of vectors. 

 May be that when printed, the German letters 

 look well, and are well distinguished from the 

 Latin alphabet. The student, no matter of 

 what nationality, can learn to recognize them 

 just as he learns to recognize the Greek alpha- 

 bet. But the question is the writing of the 

 German characters. Those that try to picture 

 a German print-letter on the board when 

 necessary to use the vector symbols in a lec- 

 ture before a class will know how difficult this 

 is. And to use different signs when written 

 and different signs when printed does not seem 

 reasonable. Why not use as symbols for vector 

 quantities the Latin alphabet? The Latin 

 alphabet is almost universal, and there is no 

 difficulty whatever to write this alphabet. 

 I, therefore, propose — with Professor Karl 

 Heun in Germany — to use the following nota- 

 tion for vectors, a notation as simple as it 

 can be. 



All vector quantities are written as fol- 

 lows : a, 1), d, •■ ■, A, B, G, •• \ and their 

 tensors respectively : a, h, d, • • •, A, B, G, • • '. 

 The scalar-product of two vectors a and 

 h is written : a h, which, by definition, is 

 '--^ah cos (a^ &). The vector-product of two 

 vectors a, h is written thus : ab, and because 

 it is itself a vector it can be written : c = ah. 

 The tensor of this vector: c:=^db sin {a, h). 

 Thejunit vector can be written, for instance, 

 d^, h^, "•, so that d = ad^, g=^ e e^, •••. 



The advantage and simplicity of this system 

 of notation speak for themselves. 



h. sohappee. 

 University of Arkansas, 

 Fayetteville, Ark., 

 August 8, 1905. 



THE OCCURRENCE OF ICHTHYOSAUR-LIKE REMAINS 

 IN THE UPPER CRETACEOUS OP WYOMING. 



Through the kindness of Professor S. W. 

 Williston, I have recently received two frag- 

 mentary vertebrse found by Mr. W. H. Reed 

 in the Benton Cretaceous near the north end 

 of Medicine Bow Mountains. Although very 

 fragmentary, these vertebrse appear to repre- 

 sent a genus allied to Ichthyosaurus. As this 

 reptilian group has not been. known in North 

 America in beds as late as the Benton, the 

 discovery is of considerable interest. 



The larger fragment consists of the upper 

 three fourths of a deeply biconcave vertebral 

 centrura apparently from the cervical or an- 

 terior dorsal region. The centrum is very 

 thin antero-posteriorly, and in this respect 

 somewhat resembles the corresponding centra 

 in Baptanodon discus. The sides are consid- 

 erably damaged, so that it is not possible to 

 make a definite statement concerning the rib 

 articulation, but it seems to have been double, 

 as in Baptanodon. A foramen close to the 

 upper end of the diapophyses is larger than 

 any I have seen in this position in the typical 

 Ichthyosaurs, and adds somewhat to the diffi- 

 culty of making a definite determination of 

 the relationships of this form. 



When more material is available it will be 

 interesting to learn whether this form really 

 represents a true Ichthyosaurus or possibly a 

 more highly specialized form of Baptanodon 



