TRANSACTIONS OF SECTION F. 679 



first view. Another fixes attention on the powers of the soil, and allows for other 

 elements, as for friction. .So, in the theory of Money, the state of credit or the 

 quantity of metal have each been regarded as the prime variable.' It need not be 

 pointed out how unfavourable to exact science is such a state of the subject-matter. 

 Imagine an astronomer hesitating whether in the determination of Jupiter's move- 

 ments the sun or the planet Saturn played the most important part. That is the 

 condition of many of our speculations. 



It will not be expected that from such materials any very elaborate piece of 

 rea.soning can be constructed. Accordingly another point of contrast with mathe- 

 matical physics is the brevity of our calculations. The whole difhculty is in the 

 statement of our problems. The purely computative part of the work is incon- 

 siderable. Scarcely has the powerful engine of symbolic language been applied 

 when the train of reasoning comes to a stop. The case is like that of the swell in 

 ' Punch," who, about to enter a hansom, enquires solicitously of the driver whether ha 

 has got a good horse. ' Yes, sir; very good 'oss.' ' Aw — then dwive to next door. 

 However, our road, though short, is so slippery as to require every precaution. 



It follows that in Economics, unlike Physics, the use of symbols may perhaps 

 be dispensed with by native intelligence. It must be admitted that the correct 

 theory of value has been rediscovered by Menger, and restated by his follower, 

 Bohm-Bawerk, without the explicit use of mathematics. Without the law, they 

 have done by nature the things contained under the law. Still, under a higher 

 dispensation, they might have attained greater perfection. Nor can equal accuracy 

 be ascribed to all the followers of Menger. Nor is the terseness which comes of 

 mathematical study a characteristic of this Austrian school (?«). 



Another point of contrast between the mathematical science of the physicist 

 and the economist is that the former appeals to a larger public. Mathematics is 

 as it were the universal language of the physical sciences. It is for physicists what 

 Latin used to be for .scholars ; but it is unfortunately Greek to many economists. 

 Hence the writer who wishes to be widely read — who does not say, with the 

 French author, J'vnprhne pour moi — will do well not to multiply mathematical 

 technicalities beyond the indispensable minimum, which we have seen reason to 

 suppose is not very large. The parsimony of symbols, which is often an elegance 

 in the physicist, is a necessity for the economist. Indeed, it is tenable that our 

 mathematical constructions shoidd be treated as a sort of scaffolding, to be removed 

 when the edifice of science is completed. As Professor Marshall, one of the 

 highest authorities on this subject, says : ' When a man has cleared up his mind 

 about a difficult economic question by mathematical reasoning, he generally finds 

 it best to throw aside his mathematics and express what he has to say in language 

 that is understanded of the people.' - Upon this view mathematical discipline might 

 be compared to grammar or to the study of classical literature, which it is profitable 

 to have learnt thoroughly, while it is pedantic to obtrude one's learning. 



From these considerations it may appear that our little branch of learning is of 

 quite a rudimentary form. The solid structure and regular ramifications of the 

 more developed mathematical sciences are wanting. A le.<s unfavourable contrast 

 would be presented if we compared our method, not with applied mathematics 

 generally, but with that particular branch of it which comes nearest to ours in its 

 proximity to human interests — the use of the Calculus of Probabilities m social 

 statistics. 



There is really only one theorem in the higher part of the calculus, but it is a 

 very difficult one, the theory of errors, or deviation from averages. The direct 

 applications of this theory to human affairs are not very considerable. Perhaps 

 the most conspicuous example is afforded by an investigation to which, if I had 

 undertaken to review the work done in our subject.s during the past year, I ought 

 to have directed particular attention — Mr. Galton's rigid proof of the fact and 



' Compare Cournot : ' Ce que I'un ndglige dans une premiere approximation comme 

 un fait secondaire et accessoire, un autre le regardera comme le fait principal et 

 dominant.' — Principcs, Book iv., chap. 7. 



^ Academy, June 18, 1881. 



