XI] OF SHELLS GENERALLY 797 



determinations of the breadth of the whorls in Ammonites (Arcestes) 

 intuslabiatus; these measurements Grabau gives for every 45° of 

 arc, but I have only set forth successive whorls measured along 

 one diameter on both sides of the pole. The ratio between alternate 

 measurements is therefore the same ratio as Moseley adopted, 

 namely the ratio of breadth between contiguous whorls along a 

 radius vector. I have then added to these observed values the 

 corresponding calculated values of the angle a, as obtained from 

 our usual formula. 



There is considerable irregularity in the ratios derived from these 

 measurements, but it will be seen that this irregularity only implies 

 a variation of the angle of the spiral between about 85° and 87°; 

 and the values fluctuate pretty regularly about the mean, which 

 is 86° 15'. Considering the difficulty of measuring the whorls, 

 especially towards the centre, and in particular the difficulty of 

 determining with precise accuracy the position of the pole, it is 

 clear that in such a case as this we are not justified in asserting that 

 the law of the equiangular spiral is departed from. 



Ammonites tornatus 



In some cases, however, it is undoubtedly departed from. Here 

 for instance is another table from Grabau, shewing the corre- 

 sponding ratios in an Ammonite of the group of Arcestes tornatus. 

 In this case we see a distinct tendency of the ratios to increase as 

 we pass from the centre of the coil outwards, and consequently for 

 the values of the angle a to diminish. The case is comparable to 



