Civil Engineering - Surveying - Discussion

Main plate of transit =360°,divided into 1080 equal div.

So Angular value of one div= (360/1080)*60 (for min) *60 (for sec) =1200"=S.

60div of vernier coincide exacty with 59div of the main scale so, n=60.
Least count = s/n = 1200/60= 20"

First of all, See the question this is telling us the main scale division 59 is equal's to 60 division of vernier it means we can understand from it is direct vernier condition((direct vernier condition (n-1)=n where as( n-1) is main scale division and (n) is division of vernier)).

So from direct vernier condition lest count will be (s/n) where (s) is the least count of the main scale and (n) is the division of the vernier.

So first we will find (s) so think that question does not have directly given but one hint is there which is 1080 division of transit means the main scale has 1080 division and we know transit is nothing but it is transit theodolite so total angle will be 360 degrees and now if we will 360/1080 then least count of the main scale can easily get but the question is ask in second not in degree.

So we will convert 360 degree into second 360*60*60 (1degree=60minutes, 1 minute=60sec)
now (360*60*60/1080)=1200 so (s)=1200.
and (n) is already given (n)=60.

Now:-
Least count = (s/n) =(1200/60) = 20.

L.C of the main scale:
1080/360 = 20.

Now, L.C of vernier is;
S/V=(20*60)/60=20".

An angle-measuring instrument reading up to one-sixth of a degree on the main scale is equipped with a vernier having 19 main scale divisions divided into 20 parts.
The correct least count for the instrument is 30 seconds.

The Least Count=(1/6 *)/20
=>1/6*60*60 sec/20 =30" ans.

All the explanations are correct assuming:

1 degree = 1hour equivalent.
So, we write 1° 00' 00"= 3600 secs.

360 deg =1080*M.
M=360/1080 =0.333 deg,
M*59 =60*V,
0.333*59/60 = v,
v=0.327777.

Least count = 0.3333-0.3277 = 0.005552 deg = 19.98 sec.

A transit in Theodolite is such that here,

1080 divisions =360 degree.
1 div =360/1080 degrees which is S the smallest div on the main scale.
n=60.

So, LC=S/n in second gives 20".

Thanks everyone for explaining the answer.

L scale = 360/1080.
= 0.3333333*3600sec.
= 1200sec.
No. Of divisions = 59.
= 1200/59 = 20.33.
Therefore, their least count is 20".

Here, it's 60/1080) *360.