xx.] METHOD OF VARIATIONS. 443 



useful, again, to measure the height of a snow-covered 

 mountain within a foot, when the thickness of the snow 

 alone may cause it to vary 25 feet or more, when in short 

 the height itself is indefinite to that extent. 1 



Maintenance of Similar Conditions. 



Our ultimate object in induction must be to obtain the 

 complete relation between the conditions and the effect, 

 but this relation will generally be so complex that we can 

 only attack it in detail. "We must, as far as possible, 

 confine the variation to one condition at a time, and estab- 

 lish a separate relation between each condition and the 

 effect. This is at any rate the first step in approximating 

 to the complete law, and it will be a subsequent question 

 how far the simultaneous variation of several conditions 

 modifies their separate actions. In many experiments, 

 indeed, it is only one condition which we wish to study, 

 and the others are interfering forces which we would avoid 

 if possible. One of the conditions of the motion of a pen- 

 dulum is the resistance of the air, or other medium in 

 which it swings ; but when Newton was desirous of prov- 

 ing the equal gravitation of all substances, he had no 

 interest in the air. His object was to observe a single 

 force only, and so it is in a great many other experiments. 

 Accordingly, one of the most important precautions in 

 investigation consists in maintaining all conditions con- 

 stant except that which is to be studied. As that admir- 

 able experimental philosopher, Gilbert, expressed it, 2 

 "-There is always need of similar preparation, of similar 

 figure, and of equal magnitude, for in dissimilar and un- 

 equal circumstances the experiment is doubtful." 



In Newton's decisive experiment similar conditions were 

 provided for, with the simplicity which characterises the 

 highest art. The pendulums of which the oscillations were 

 compared consisted of equal boxes of wood, hanging by 

 equal threads, and filled with different substances, so that 

 the total weights should be equal and the centres of oscil- 

 lation at the same distance from the points of suspension. 



1 Humboldt's Cosmos (Bohn), vol. i. p. 7. 

 1 Gilbert, De Magnete, p. 109. 



