PREFACE. vii 



learnt to advocate the use of hypotheses. I take the 

 extreme view of holding that Francis Bacon, although he 

 correctly insisted upon constant reference to experience, 

 had no correct notions as to the logical method by which, 

 from particular facts, we educe laws of nature. I en- 

 deavour to show that hypothetical anticipation of nature 

 is an essential part of inductive inquiry, and that it is the 

 Newtonian method of deductive reasoning combined with 

 elaborate experimental verification, which has led to all 

 the great triumphs of scientific research. 



In attempting to give an explanation of this view of 

 Scientific Method, I have first to show that the sciences of 

 number and quantity repose upon and spring from the 

 simpler and more general science of Logic. The Theory of 

 Probability, which enables us to estimate and calculate 

 quantities of knowledge, is then described, and especial 

 attention is drawn to the Inverse Method of Proba- 

 bilities, which involves, as I conceive, the true principle 

 of inductive procedure. No inductive conclusions are more 

 than probable, and I adopt the opinion that the theory of 

 probability is an essential part of logical method, so that 

 the logical value of every inductive result must be deter- 

 mined consciously or unconsciously, according to the 

 principles of the inverse method of probability. 



The phenomena of nature are commonly manifested in, 

 quantities of time, space, force, energy, &c., and the ob- 

 servation, measurement, and analysis of the various quan- 

 titative conditions or results involved, even in a simple 

 experiment, demand much employment of systematic pro- 

 cedure. I devote a book, therefore, to a simple and 

 general description of the devices by which exact measure- 

 ment is effected, errors eliminated, a probable mean result 

 attained, and the probable error of that mean ascertained. 

 I then proceed to the principal, and probably the most 

 interesting, subject of the book, illustrating successively 



