Civil Engineering - Surveying - Discussion

1080/60 = 18.

According to the answer sheet answer is 20.

Least count is equal to ratio of (length of one division on main scale to no. of divisions of vernier) i.e least count= s/n.

S = 360/1080.

N = 60.

Lc = 1/180 degrees = 20 seconds.

Please explain clearly from where 360 came.

@Ansha.

The total degree of rotation =360°.

Thank you all for explaining it.

Least count = length of one division on the main scale/ no. of divisions of vernier.

Legth of one division on main scale= 360/1080.
= 0.3333333 degrees,
= 0.3333333 x 3600 sec,
= 1200 sec.

No of divisions of vernier = 60.

Therefore, Least count= 1200/60 = 20.

(1080/60) - (1080/59)= .3°=20".

Least Count = S/n.

S = Least count of main scale = 360/1080
n = no of divion on vernier scale = 60

In transit main plate their is circle scale with 360 degree
So S=360/1080 = 1/3

Now least count = 1/3 ÷ 60 = 1/180 degree
Convert in seconds
L.C = 1/180 *60*60 =20 seconds.

Total angle 360.
Dividing in 1080 part.
So 1 part in main scale = 1/3 degree or 20'.
1 part of main scale dividing in vernier 60 part
So 1 part in vernier = 20'/60 = 1/3' = 20"

Least count = S - V.

Where S is the length of one division of main scale which is nothing but least count of main scale and V is the length of one division of vernier scale.

From the above problem we can conclude that (n-1) division of main scale is divided into n division of vernier scale because 60 divisions of vernier coincide exactly with 59 divisions of the main scale.

Therefore, n*V=(n-1)*S ------- (A)

Now, S= L.C of main scale = 360/1080 = 1/3 degrees because in transit main plate there is a circle with 360 degrees.

S= (1/3) degrees = (1/3)* 3600 sec= 1200 seconds.

Now from (A) 60*V=59*1200
V=1080 seconds.
Therefore Least Count = S - V = 1200 - 1080 = 20 seconds.