ILLUSTRATIONS OF THE LOGIC OF SCIENCE. 295 



that one side denies important facts, and that the other does not. But 

 what I do say is, that the above single question was the origin of the 

 whole doubt ; that, had it not been for this question, the controversy 

 would never have arisen ; and that this question is perfectly solved in 

 the manner which I have indicated. 



Let us next seek a clear idea of Weight. This is another very easy 

 case. To say that a body is heavy means simply that, in the absence 

 of opposing force, it will fall. This (neglecting certain specifications 

 of how it will fall, etc., which exist in the mind of the physicist who 

 uses the word) is evidently the whole conception of weight. It is a 

 fair question whether some particular facts may not account for grav- 

 ity ; but what we mean by the force itself is completely involved in 

 its effects. 



This leads us to undertake an account of the idea of Force in gen- 

 eral. This is the great conception which, developed in the early part 

 of the seventeenth century from the rude idea of a cause, and con- 

 stantly improved upon since, has shown us how to explain all the 

 changes of motion which bodies experience, and how to think about 

 all physical phenomena; which has given birth to modern science, 

 and changed the face of the globe ; and which, aside from its more 

 special uses, has played a principal part in directing the course of mod- 

 ern thought, and in furthering modern social development. It is, 

 therefore, w T orth some pains to comprehend it. According to our rule, 

 we must begin by asking what is the immediate use of thinking about 

 force; and the answer is, that we thus account for changes of motion. 

 If bodies were left to themselves, without the intervention of forces, 

 every motion would continue unchanged both in velocity and in 

 direction. Furthermore, change of motion never takes place abrupt- 

 ly ; if its direction is changed, it is always through a curve without 

 angles ; if its velocity alters, it is by degrees. The gradual changes 

 wdiich are constantly taking place are conceived by geometers to be 

 compounded together according to the rules of the parallelogram of 

 forces. If the reader does not already know what this is, he will find 

 it, I hope, to his advantage to endeavor to follow the following ex- 

 planation ; but if mathematics are insupportable to him, pray let him 

 skip three paragraphs rather than that we should part company here. 



A path is a line whose beginning and end are distinguished. Two 

 paths are considered to be equivalent, which, beginning at the same 

 point, lead to the same point. Thus the two paths, A B C D E and 

 A F G II E, are equivalent. Paths which do not begin at the same 

 point are considered to be equivalent, provided that, on moving either 

 of them without turning it, but keeping it always parallel to its origi- 

 nal position, when its beginning coincides with that of the other path, 

 the ends aho coincide. Paths are considered as geometrically added 

 together, when one begins where the other ends ; thus the path A E 

 is conceived to be a sum of A B, B C, C Z>, and D E. In the paral- 



