Measurement of changes in the dimensions of Solid Bodies. 451 
3. The distance passed over independently by the pendulum dur- 
ing each observation increases by an increasing quantity.—This 
case may perhaps be most quickly illustrated by a numerical 
example arranged algebraically, the changes introduced being 
far larger than ever would be met with in practice. 
Let the true number, «, equal 30; the first reading equal 25; 
we then have: Resatigs 
a 25 
ras 30 param A 
2 + (i1+2)= 29 
25+30+ 4+ (343)= 65 
5 10+ (6+4)= 45 
25-+ 304+ 20+ (10+5) = 90 
2 + 35+ (154+ 6)= 81 
25 + 30-+4 56+ (21 +7) = 139 
Differences. M’. M”. M. 
al 
. . . 5 
27 29 31°5 30°2 
36 j . ede . 
| 20 28 32°5 80°25 
; es o7- 33°5 80°25 
58 f 
It is evident in this case, that even the final mean will be 
affected with a small constant error; still for practical purposes 
this difference from the correct quantity will. be far below the 
unavoidable errors of observation. : 
As the method with three columns applies to an increasing 
rate, it is evident that it will apply equally well to one which 
diminishes, and it hence follows that if the motion decreases 
till it is zero, and then begins to increase, being affected with 
the opposite sign, its effects will still be eliminated by the pro- 
ceeding above HE 
I proceed now to give some examples to show the character 
of the results that can be expected from the horizontal pendu- 
lum under very unfavorable conditions, i. e., when exposed 
vibration and changes of temperature. All the observations 
given below were made in the day-time, the quietest portions 
being selected when comparatively few locomotives and trains 
of cars were passing; no extraordinary precautions with regard 
to temperature were employed, the pendulum not being en- 
closed except in its glass case. All the observations are in the 
form of determinations of the value of a scale-division, a pro- 
ceeding well calculated to illustrate the capabilities of the in- 
strument. The first four constitute a coherent series, the same 
adjustment of apparatus being used in them all; the others are 
independent sets made with different adjustments, and intended 
to illustrate the effects of change of temperature, ete. 
