EPSG:24378 Kalianpur 1975 / India I should be the local CRS in the region you mentioned. The extent seems to fit to that:
To get this picture using QGIS, create these text files:
E N
73.4775 34.3629
and
Easting Northing
3250193.00 1115573.00
3249214.00 1111220.00
Load each into QGIS as Delimited Text File, with blank as delimiter and setting CRS to EPSG:4326 for the first and EPSG:24378 for the second. Project CRS is EPSG:3857 to add Openstreetmap background with the openlayers plugin.
If the data is older than 1975, you might as well look for Kalianpur 1962 or Kalianpur 1880.
You can use GDAL cs2cs or ogr2ogr to reproject the data to any other CRS. For Google Maps, EPSG.4326 would be best.
You can find details on the transformation from Cassini-Soldner to ARC1960 UTM in this article:
http://cae.uonbi.ac.ke/sites/default/files/cae/cae/Gordon%20Okumu%20Wayumba%20F80-81401-2009.pdf
In Table 4.8, a set of four reference points is given, with an equation to transform from Cassini to UTM:
E= b * n + a * e + ∆E
N= a * n - b * e + ∆N
Where a= Scos (θ), b= S sin(θ)
N and E are the local UTM coordinates
(n,e) are local Cassini coordinates
Computed values are given in Table 5.8:
Parameter Value Accuracy Units
S 1.0000169 ±0.000002 -
θ -0.000886 ±0.000002 rad
∆N 10000167.51 ±0.35 m
∆E 277419.49 ±0.35 m
I get a standard deviation of the four points of 10 meters with those values.
Alternatively, you may use:
E = d * n + f * e + ∆E
N = a * n - b * e + ∆N
with:
a 1.00023
b -0.00077
∆N 10000201.67
d -0.00086
f 1.00033
∆E 277420.75
Quality of the reference points is now within 2 meters.
These transformations are valid for the Cassini Soldner projection centered on the 37° meridian, against UTM 37S based on ARC1960 datum (not WGS84!).
For the 39° meridian, transformation parameters are given in table 5.3:
PARAMETER VALUE
a 1.002248791
b 0.0007371372
∆N 10001507.607
∆E 500339.6901
Again, only valid for transformation to UTM zone 37S. Appendix 11 and 12 of the document have coordinates for both systems, and here the standard deviation is under 1 meter.
Best Answer
Assuming your coordinates are offshore to Cyprus, UTM 36N EPSG:32636 is a good destination coordinate system. Otherwise, you might have swapped longitude and latitude, or missed negative signs for South and West coordinates.
Transform coordinates from NOAA and Transforming coordinates from WGS84 to Gauss-Krüger 5 describe how to transform coordinates in R using proj4::ptransform or rgdal::spTransform.
See also https://stackoverflow.com/questions/30429384/how-to-transform-longitude-latitude-degree-to-utm-r-rgdal-sp