January 10, 1896.] 



SCIENCE. 



67 



suspicion that I have committed fraud, while 

 in the other case no one thinks of such a thing, 

 unless — and here lies the gist of the whole mat- 

 ter — unless I or somebody else predicted ex- 

 actly the succession of heads and tails that oc- 

 curred. The remarkableness lies in the coin- 

 cidence, not in the mere numerical probability ' 

 of the configuration. Now the distribution of 

 cards mentioned by Prof. Mendenhall and the 

 succession of throws of a coin in which all are 

 heads are both natural arrangements that 

 readily occur to the mind, and hence are as 

 striking subjects for coincidence as actually pre- 

 dicted arrangements. The fact is that an un- 

 predicted arrangement is not judged ' remark- 

 able, ' because its probability is compared with 

 that of each and every (individual) other possible 

 arrangement, while with a predicted or other 

 coinciding arrangement the comparison is be- 

 tween its probability and that of any other pos- 

 sible arrangement (no matter what). We may 

 call the ratio of such comparison the ' ratio of 

 surprise,' if you will. When heads turn up 

 twice in succession the numerical probability 

 ( i ) is precisely that of every other possible 

 succession of heads and tails, but its ratio of 

 surprise is J-^f:= J, whereas that of an arrange- 

 ment not subject to comparison with some pre- 

 dicted or conspicuous arrangement is Jh-J=1. 

 The distribution of cards already mentioned 

 belongs to the former class of configurations, 

 and its ' ratio of surprise ' is almost infinitesi- 

 mal. It is therefore very remarkable, while an 

 ordinary deal would not be so. 



Professor Mendenhall of course does not need 

 to be told of any of these things, but it seems 

 worth while to call attention to what will seem, 

 to the non-mathematical reader, a lack of cor- 

 respondence between scientific and ordinary 

 language— a thing to be avoided when possible. 

 Arthur E. Bostwick. 



montclaie, n. j. 



the development of the embryo of pteris. 

 To THE Editor of Science — Sir: For two 

 years I have been in correspondence with 

 various biologists concerning a very evident 

 error in Sedgwick and Wilson's Biology, and 

 had I supposed it possible that the new edition 

 would repeat such an error, I would have at 



least tried to prevent it. I refer to the oosphere 

 quadrant developments as mentioned in the 

 texts, old edition, bottom page 98 and top of 

 page 99 ; New edition, top of page 140. He 

 says in both places : ' The lower anterior quad- 

 rant as it undergoes further division grows out 

 into the first root ; the upper anterior quadrant 

 in like manner gives rise to the rhizome and the 

 first leaf. ' 



In a note below Fig. 80, in both editions he 

 gives the truth in the matter but says : ' In 

 Pteris serrulata the development is slightly ( ! ) 

 different. ' 



Where and how does the author obtain his 

 authority for the statement as it stands in the 

 text, making the root spring from the anterior 

 quadrant ? 



Please call attention of botanists to this state- 

 ment, and if any of them have obtained such a 

 result with Pteris aquilina, let us hear from them 

 and see their drawings. 



F. D. Kelsey'. 



Oberlin, Ohio, December 12, 1895. 



To THE Editor of Science — Sir .• Prof. Kel- 

 sey has our thanks for pointing out an obvious 

 error in our description of the development of 

 the embryo of Pteris from the oospore. We can 

 only regret that while corresponding ' for two 

 years,' concerning the matter, 'with various 

 biologists,' he did not include us among the 

 number, as he might then, possibly, have saved 

 himself some trouble and would have enabled 

 us more promptly to correct the error. 



The Authors op the General Biology. 



LINE DRAWINGS OF BLUE PRINT. 



The method of making line drawings upon a 

 blue print, mentioned by Mr. Slosson on page 

 893 of the last volume, is capable of being made 

 very useful. I have used it for a number of 

 years, and some of the results have appeared in 

 the horticultural bulletins of the Cornell Ex- 

 periment Station. I have no artistic ability, 

 and yet one of these blue-print drawings was 

 highly commended by an artist, who, fortu- 

 nately, knew neither who the draughtsman was 

 nor what was the method of its making ! 



L. H. Bailey. 



Cornell University. 



