OF ARTS AND SCIENCES. 433 



tions around the cavities of the other side, and as it builds by continual 

 trimming and saving, we may infer that the form of the honey-cell does 

 not require, in the bee's instinct, any reference to supersensible prop- 

 erties of form, but only a reference to sensible economy and facility of 

 construction ; especially as no one would contend that the utility, to 

 innumerable nest-building animals, of spherical and cylindrical surfaces, 

 depends upon their economy (which is still greater than that of the 

 honey-cell), rather than upon their far more obvious symmetries and 

 facilities for construction. It appears, therefore, that the instinct of the 

 bee does not differ in kind from instincts in general. 



Mr. Newcomb discussed the objections raised by Mr. Mill, 

 and others, against Laplace's presentation of the doctrine of 

 probabilities. 



Many objections have within late years been brought against the fun- 

 damental basis of the theory of probabilities as laid down by Laplace. 

 Some of these proceed from an entire misapprehension of the mathe- 

 matical and logical signification to be attached to the term prohahility ; 

 others from a defect in Laplace's theory considered as a philosophical 

 structure, which, although not necessarily leading to any error in the 

 treatment of any special problem, has nevertheless been adduced as a 

 reason why Laplace fell into the assumed mistakes. However, as it 

 is conducive to sound reasoning to have the fundamental principles of 

 every deductive science laid down with as much logical clearness and 

 accuracy as possible, let us first consider the question, What is proba- 

 bility? 



The pi-obability of a proposition has sometimes been defined as the 

 amoimt of our belief in the truth of that proposition. Here, however, 

 a difficulty arises from the fact, that neither belief, nor any other affec- 

 tion of the mind, admits of being measured as a quantity. We may 

 apply the terms greater or less to belief, but we cannot say how much 

 greater or less. Nor does this inability proceed from the imperfection 

 of the faculties, as when we experience a difficulty in determining by 

 the feeling whether one weight is twice as heavy as another. It is in- 

 herent in the nature of things. In order that we may say of one thing 

 that it is twice as large as another, we must be able to conceive of it 

 as susceptible of division into two independent parts, or as formed by 

 the superposition of two such parts, each of which can be considered 



VOL. IV. 55 



